Monitoring the upper atmospheric temperature and interplanetary magnetic field with the GRAPES-3 muon telescope

This paper utilizes the GRAPES-3 muon telescope to monitor how variations in the interplanetary magnetic field and upper atmospheric temperature modulate the flux, spectrum, and angular distribution of Galactic Cosmic Rays, particularly those below 30 GeV/nuc affected by solar phenomena.

The Gist

Imagine the Earth is wrapped in a giant, invisible blanket called the atmosphere. High above us, invisible particles from deep space (Cosmic Rays) are constantly raining down, crashing into this blanket and creating a shower of secondary particles, including muons. Think of muons as the "raindrops" of this cosmic shower that actually make it all the way to the ground.

The GRAPES-3 experiment in India is like a giant, super-sensitive umbrella (a muon telescope) that catches these raindrops. For 22 years, this umbrella has been counting how many muons hit the ground every hour, day and night.

The scientists behind this study wanted to answer a simple question: Why does the number of muons hitting the ground change over time?

They discovered that two main "weather patterns" in space and the sky are pulling the strings:

1. The "Hot Air Balloon" Effect (Atmospheric Temperature)

Imagine the atmosphere as a giant hot air balloon.

• When the upper atmosphere gets hot: The air expands, like a balloon inflating. This makes the "journey" for the muons longer. Since muons are unstable and decay (disappear) over time, a longer trip means more of them vanish before they reach the ground.
  • Result: Hotter upper air = Fewer muons.
• When the upper atmosphere gets cold: The air shrinks (deflates). The muons have a shorter trip, so more of them survive the journey.
  • Result: Colder upper air = More muons.

The scientists found that for every degree the upper atmosphere heats up, the muon count drops by about 0.22%. It's a negative relationship: heat up the sky, and the muon rain slows down.

2. The "Solar Shield" Effect (Interplanetary Magnetic Field)

Now, imagine the Sun is a giant magnet that throws out a magnetic wind (the Interplanetary Magnetic Field or IMF).

• When the Sun is active: The magnetic shield gets stronger and thicker. It acts like a force field, deflecting the incoming cosmic rays away from Earth. Fewer cosmic rays mean fewer muons are created in the first place.
  • Result: Stronger magnetic field = Fewer muons.
• When the Sun is quiet: The shield weakens, allowing more cosmic rays to sneak through and create muons.
  • Result: Weaker magnetic field = More muons.

The scientists found that for every tiny increase in the magnetic field strength, the muon count drops by about 0.57%.

The Detective Work: Untangling the Knot

Here is the tricky part: Both the temperature and the magnetic field change over time, and they often change at the same time. It's like trying to figure out if a car is slowing down because of the brakes (temperature) or the engine trouble (magnetic field) when both are happening simultaneously.

To solve this, the scientists used a clever digital tool called a Fast Fourier Transform (FFT). Think of this as a high-tech music equalizer.

• They took the 22 years of data and broke it down into different "frequencies" (like separating bass from treble).
• They isolated the 1-year cycle (the seasonal temperature changes) and the 11-year cycle (the solar magnetic cycle).
• By filtering out the "noise" of one to listen clearly to the other, they could calculate exactly how much each factor was responsible for the changes in muon counts.

They did this in a loop (iteratively), refining their numbers until they got the most precise answer possible.

Why Does This Matter?

This paper is a big deal because it proves that the GRAPES-3 telescope can act as a real-time weather station for the upper atmosphere and space.

• Monitoring the Sky: If we know how the magnetic field behaves (from satellites), we can use the muon counts to tell us exactly how hot the upper atmosphere is, even without a thermometer up there.
• Monitoring Space Weather: Conversely, if we know the upper atmosphere's temperature, we can use the muon counts to measure the strength of the Sun's magnetic shield.

In a nutshell: The scientists turned a giant muon detector into a dual-purpose tool. By counting cosmic "raindrops," they can now measure the temperature of the sky and the strength of the Sun's magnetic field with incredible precision, helping us understand our planet's connection to the rest of the solar system.

Technical Summary

1. Problem Statement

Galactic Cosmic Rays (GCRs) interacting with Earth's atmosphere produce secondary muons. The flux of these atmospheric muons is modulated by two primary factors:

1. Upper Atmospheric Temperature: Temperature variations cause the atmosphere to expand or contract, altering the path length mesons (pions/kaons) travel before decaying into muons. This affects the muon flux reaching the ground.
2. Interplanetary Magnetic Field (IMF): The solar wind and heliospheric magnetic field modulate the primary GCR flux entering the heliosphere (solar modulation).

The Challenge: These two effects occur simultaneously and often on overlapping timescales (seasonal vs. 11-year solar cycles). Previous studies using the GRAPES-3 experiment were limited to a 6-year dataset (2005–2010), which was insufficient to fully disentangle the long-term solar cycle trends from seasonal atmospheric effects. Furthermore, isolating the specific contribution of the IMF from temperature-driven variations requires a robust deconvolution method to avoid cross-contamination of coefficients.

2. Methodology

The study utilizes 22 years of continuous data (2001–2022) from the GRAPES-3 muon telescope in Ooty, India, spanning three solar cycles (declining Cycle 23, full Cycle 24, and rising Cycle 25).

Data Sources & Processing:

• Muon Data: Collected by a large-area (560 m²) telescope detecting ~4 billion muons/day (>1 GeV). An automated correction algorithm (Bayesian Blocks + Savitzky-Golay filter) was applied to mitigate instrumental drifts and efficiency variations.
• Temperature Data: Derived from NASA's MERRA-2 dataset to calculate the Effective Temperature ($T_{eff}$), a weighted average of atmospheric temperatures down to the observation level.
• Magnetic Field Data: Hourly IMF magnitude ($B_{scalar}$) from ACE and WIND spacecraft at Lagrange Point L1.
• Preprocessing: A 60-day running average (low-pass filter) was applied to all datasets to suppress short-term noise while preserving seasonal and solar cycle trends.

Analytical Approach:
The authors employed a simultaneous iterative fitting method utilizing Fast Fourier Transforms (FFT) and narrow band-pass filters:

1. Frequency Isolation: FFT analysis identified a distinct peak at 0.002738 cycles per day (1-year periodicity) in both muon flux and temperature data. A narrow band-pass filter isolated this annual component to separate it from the 11-year solar cycle.
2. Initial Coefficient Estimation:
   • Temperature Coefficient ($\alpha_T$): Calculated by fitting the filtered muon flux variation against $\Delta T_{eff}$.
   • Magnetic Coefficient ($\gamma_M$): Calculated by correcting the muon flux for temperature effects and then fitting the residual against $\Delta B_{scalar}$.
3. Iterative Deconvolution: Since the 11-year solar modulation can contaminate the seasonal signal (and vice versa), the authors iteratively corrected the data:
   • Step A: Correct muon data for IMF effects using the current $\gamma_M$.
   • Step B: Re-calculate $\alpha_T$ from the IMF-corrected data.
   • Step C: Correct muon data for temperature effects using the new $\alpha_T$.
   • Step D: Re-calculate $\gamma_M$.
   • This loop was repeated until $\alpha_T$ and $\gamma_M$ converged (stabilized after 3 iterations).
4. Systematic Uncertainty: The analysis was repeated for hadronic attenuation lengths ($\lambda$) ranging from 80 to 180 g cm⁻² to quantify systematic errors associated with the assumed interaction depth.

3. Key Contributions

• Extended Dataset: The first analysis of GRAPES-3 muon data spanning 22 years, covering three solar cycles, significantly improving statistical precision over previous 6-year studies.
• Iterative Deconvolution: Development and application of a novel iterative fitting technique that successfully separates the anti-correlated effects of atmospheric temperature and the interplanetary magnetic field, which were previously difficult to disentangle.
• High-Precision Coefficients: Determination of the temperature and magnetic field coefficients with unprecedented statistical precision (<0.01% uncertainty) and quantified systematic uncertainties.
• Validation of Detector Stability: Demonstration that the GRAPES-3 telescope, despite being a ground-based instrument, can serve as a stable, long-term monitor for space weather and atmospheric conditions.

4. Key Results

For an assumed hadronic attenuation length of $\lambda = 120$ g cm⁻², the final converged coefficients are:

• Temperature Coefficient ($\alpha_T$):
  $$\alpha_T = -0.2241 \pm 0.0003 \text{ (stat.)} \pm 0.0220 \text{ (syst.)} \% \text{ K}^{-1}$$

  • Interpretation: A negative coefficient indicates that as upper atmospheric temperature increases, the muon flux decreases (due to increased path length and muon decay). The iterative process increased the magnitude of this coefficient by ~23% compared to initial non-iterative estimates.

• Magnetic Field Coefficient ($\gamma_M$):
  $$\gamma_M = -0.574 \pm 0.027 \text{ (stat.)} \pm 0.011 \text{ (syst.)} \% \text{ nT}^{-1}$$

  • Interpretation: A negative coefficient indicates that stronger interplanetary magnetic fields suppress the primary cosmic ray flux, reducing the muon rate.

• Convergence: The coefficients stabilized quickly after three iterations, confirming the robustness of the method. The systematic uncertainty is primarily driven by the uncertainty in the hadronic attenuation length ($\lambda$).

5. Significance

• Real-Time Monitoring: The study validates the GRAPES-3 muon telescope as a viable, real-time monitor for upper atmospheric temperature (with ~10% accuracy) and the interplanetary magnetic field (with ~6% accuracy).
• Climate and Space Weather: These measurements offer a ground-based proxy for atmospheric conditions, potentially aiding in the validation of climate models and the understanding of solar-terrestrial interactions.
• Future Applications: With the advent of the Aditya-L1 mission (India's solar observatory), which provides near real-time IMF data, this methodology can be applied to the 169 independent directional bins of the GRAPES-3 telescope. This could enable tomographic imaging of the upper atmosphere, mapping temperature variations across different atmospheric columns.
• Scientific Consistency: The results align with theoretical predictions and data from other high-energy experiments (like MINOS and IceCube), validating the phenomenological framework of muon production and decay in the atmosphere.