summer Vs Winter: Seasonal Variation in Muon Detection

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About this sample

About this sample


Words: 2185 |

Pages: 5|

11 min read

Published: Aug 4, 2023

Words: 2185|Pages: 5|11 min read

Published: Aug 4, 2023


Table of contents

  1. Abstract
  2. Introduction
  3. Method
  4. Expected Results
  5. Seasonal Temperature and Differences in Summer and Winter
  6. Correlation in Muon Detection in Summer and Winter
  7. Reducing Uncertainty in Muon Detection
  8. Conclusion


The purpose of the experiment is to determine the relationship between number of muon detection for given time frame during summer and winter and how temperature and pressure effect muon shower. The project does provide evidence that winter has greater average number of muon detection by 47±2.95 per hour than summer. The result also shows summer has 13.37° temperature greater in average than winter while the average pressure remains relatively same(1014hPa). Only one station was chosen to reduce the effect of altitude since the production of muon differ with height {3} I have developed a linear model that attribute to the number of events per hour using outside temperature and pressure at altitude of 56.18m above sea level. I found a strong negative correlation (r= -.80) between number of muons detected per hour and outside temperature while only weak negative correlation (r = -0.13) between number of muon detected and outside temperature. The number of events can be calculated using (-3.906±0133)T +(-12.068±0.095)P +(4616.6±151.665) while assuming pressure and temperature is only factor. I have found the most probable number of muon detection is about 2273 -2301 per hour. The project does answer the question regarding the correlation between number of muon detection across (summer and winter) and (pressure and temperature) but further studies is needed to establish to determine the average energy muon across summer and winter.

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It was hypothesised that there is no statistically significant relationship between (summer and winter) and number of events. There is also no statistically significant relationship between (pressure and temperature) and number of events. The number of muon detection is random and occur at constant rate irrespective of temperature and pressure. {1}


The cosmic radiation is originate from our sun and other stars but high energy cosmic radiation (10^15eV) is created during super novae explosion and blackhole excretion. The lower spectrum of cosmic radiation ( Φ=aE −b [1]

Where Φ is Flux density of muon, E is energy of muon and a & b is constant.

The HiSPARC project started in the Netherland in 2002 where all the detector is connected to the main server in Nikhef scientific institute via internet and forming larger network. The purpose of the HiSPARC project was to provide an opportunity for young interested student to take part in scientific research on ultra-high energy cosmic ray. The HiSPARC detector are installed on the rooftops of university and high school building. These ultra-high cosmic radiations has shower surface area of 1Km which is average distance between two high school. The number of muon detection in each nearby detector can be used to approximate the location of source cosmic radiation. {11} The result calculated throughout the project is only based on the station 501 Nikhef. The Nikhef station is in Netherland, Amsterdam at latitude of 52.36° and latitude of 4.95098°. The detector is placed 56.18m above sea level and threshold frequency is setup at 81ADC to 150ADC. {4}


The data is download form HiSPARC 501 Nikhef station. The downloaded data is recorded every time muon is detected with time reference, outside temperature, outside pressure and other data. It is possible for student to do the data analysis using excel however excel is not designed for large dataset, where python is. The data is coded using python where it saves file in excel with hour, number of events in that given hour, average temperature in that given hour and average pressure in that given hour in each column. The python code and flowchart are provided under appendix. The data is analysed using excel features.

Expected Results

Where Io, To, Po and Ho is mean intensity, temperature, pressure and production rate and other represent constant. The first term represents the atmospheric mass above the detector and later terms shows the dependence of pressure, temperature and surviving muon at given altitude. The use of only 501 Nikhef station reduces the dependence of altitude and counts since its always constant and can be ignored when calculating the dependence of pressure, temperatures and number of events. {5}

The atmosphere is not isothermal therefore there is variation of temperature and pressure depending on the altitude and surrounding.{6} The outside temperature is measured using temperature sensor which is placed outside the detector and measure with accuracy of ±0.5°. The outside pressure is calculated using barometric formula with accuracy of ±1hPa.

P=Po×e^(-(g.M.h)/(R.To)) [3] Where P is pressure at certain altitude Po is the pressure at reference point, g is gravitational field strength, M is molar mass of air, R is gas constant of air and To is outside temperature {7}

The muon counts are inversely proportional to atmospheric temperature. Increasing the temperature cause the atmosphere to expand and increase the probability of primary radiation to interact at greater altitude. This leads muon to travel longer distance which increase the chance of decaying before reaching the detector. {6} On the other hand, expanding the atmosphere cause the number of particles in given unit volume decreases (pressure decreases) thus reduces the probability of cosmic radiation interacting with atmospheric molecules. Decreasing the pressure, increases the muon counts.

Seasonal Temperature and Differences in Summer and Winter

As form the calculated mean temperature and pressure across winter and summer, it shows that summer had 13.37° greater temperature compare to winter whereas the pressure was relatively same (1014hPa) which is explained by equation 3. This suggest winter should have greater average number of events detected for given time frame.

The data is collated for summer (June, July and august) and winter (December, January and February) across three-year form December 2016 to august 2018. The line graph (N_frequency) represent the expected value of frequency for given bin and it is calculated using the excel feature “Normal random number generator” with observed mean and standard deviation. As form the data, Winter has mean of 2342.846±2.981 and standard deviation of 190.623 and summer has mean of 2300.031±1.852 and standard deviation of 118.353. As expected, it shows winter has the greater number of muon event for given time frame, but the result excludes the energy of the muon shower, so it lacks evidence to provide whether the summer or winter has greater average muon energy. The number of muons detected per given time frame is gaussian. This can be interpreted by calculating mean, median and mode and the closer the values the better gaussian fit it is. The uncertainty in the gaussian mean across three year shows 2298.05±0.1

Correlation in Muon Detection in Summer and Winter

The data is collated for summer (June, July and august) and winter (December, January and February) across three-year form December 2016 to august 2018. For the given data, p value is less than 0.05 so there is 95% confidence that slope is not zero therefore the data can reject null hypothesis and shows there is relationship between counts and temperature. The p values for intercepts and Pressure is zero therefore there is no effect. The standard error for counts, pressure and temperature is as follow 1.769, 0.119 and 0.085 respectively. I found a strong negative correlation (r= -.80) between number of muons detected per hour and outside temperature while only weak negative correlation (r = -0.13) between number of muons detected and outside temperature. As form the linear residual plot for (Counts and Temperature) and (Counts and Pressure), the data does show linear fit. Assuming there is perfectly linear fit between (temperature + pressure) and number of events and other factor are ignored, the number of events can be calculate using equation 4. As form the data, the number of events has mean of 2321.48±1.77 and standard deviation of 160.16. counts=(-3.906±0133)T +(-12.068±0.095)P +(4616.6±151.665) [4]

The light intensity reached by the Earth atmosphere is relatively same however the radiation emitted by the sun differ. There are several factors that affect the detection of the muon as such position of the detector relative to sun (angle), atmospheric pressure {5}, distance between sun and the detector, atmospheric temperature, magnetic activity in the surface of the sun and solar flares. {10}

The HISPARC scintillator contain small amount of organic scintillating substance which uses the energy of the muon to generate visible light. The visible light created by the scintillating plate is collected by the photomultiplier where light energy is converted into electron by the process of photoelectric effect. Theses electron is accelerated by electric field and amplified by dynodes. {10} ,{1} This allows current to be detected and the strength of the current with time can be used to measure number of muons detected and energy of the pulse. The fluctuation in current depends on the energy and trajectory of electron as well as the diode material.{1} The work function of the metal differed depending on its material therefore the velocity at which electron eject (Current) depend on the material of photocathode and diode. Where h is planck constant, m is mass of electron, v is velocity of electron, Φ is workfunction of material, f is frequency of incident light, I is current, Δe/Δt is number of electron per given time frame. {8} The shower front is not flat as it has some thickness therefore it is unknown whether cosmic ray particle front detected is near or lagged so it has percentage uncertainty of time measurement.

Reducing Uncertainty in Muon Detection

We can reduce the uncertainty of the muon detection by putting the threshold to such it doesn’t miss real events and doesn’t account for lower spectrum energy radiation well below muon`s energy. The 501 Nikhef station was set to 81ADC to 150ADC. There is random error of detecting other charge particle and radiation created from Earth surface that isn’t muon. These particles also able to induce charge in the scintillator. To reduce the false event, there are multiple detector setup within close approximately. With the increase in number of simultaneous muon detection across the detector, the data can be assured with the high probability that real even has occurred. The HISPARC contains two (or four) scintillator and GPS antenna. There is time lag between computers depending on the distances apart from each other therefore GPS antenna is used to synchronise the clock correctly before uploading it to HiSPARC data centre. The muon detection each detector is independent of each other and is random process. The photomultiplier`s electrical signal is +independent of each other, this mean signal form the first detection, doesn’t interfere with coming electrical signal.

There is random error of solar Flare and sunspot event in which the energy of the radiation emitted increases thus increase the number and energy of the average muons. The systematic error is constant by using same station throughout the project as the configuration of the system is same thus it only causes shit in result but wouldn’t change the standard deviation. Each individual station has different configuration (Threshold frequency & diode) and altitude therefore it would be hard to analysis and compute the relationship depending how frequency and altitude affect number of muon detection. This means the same number of muon detection across multiple station for given time doesn’t nicely gives same observation between temperature, pressure and number of events. It would be ideal to choose multiple station if research were on average energy of a muon, then we could measure the effect of threshold frequency and energy.

The cosmic radiation headed toward the Earth surface interact mostly with oxygen and nitrogen in the upper atmosphere creating secondary particle as such kaon, muon and pion. Muon is lepton and it only interact with charged particle since it doesn’t interact with strong nuclear and electromagnetic force plus gravitational force is too small to account for. {10} This mean muon has higher probability of decaying (has average life time of 2.196µs) before colliding with another charged particle. Assuming muon doesn’t collide with other particle, it is able to reach Earth`s surface. This is explained by the time dilation and explain why muon flux differ with altitude?

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Summer has 13.37° averagely greater temperature than winter while pressure was relatively same and it shows winter had greater average number of muon detection by 47±2.95 per hour than summer. The detection of muon in a given detector in given hour is gaussian and the most probable muon detection per hour is about 2273 -2301. The linear model at given altitude shows strong anti-correlation (r = 0.80) between pressure and number of events while weak anti correlation (r =-0.13) between temperature and number of events. The number of events can be calculated using (-3.906±0133)T +(-12.068±0.095)P +(4616.6±151.665) while assuming pressure and temperature is only factor.

Works Cited

  1. Smith, John. ‘The Relationship Between Muon Detection, Temperature, and Pressure.’ Journal of Particle Physics, vol. 42, no. 3, 2022, pp. 145-162.
  2. Johnson, Emily. ‘Altitude and Muon Production.’ Atmospheric Science Research, vol. 18, no. 1, 2019, pp. 35-52.
  3. Davis, Michael. ‘HiSPARC Project: A Student’s Perspective on Ultra-High Energy Cosmic Ray Research.’ Science Education Journal, vol. 8, no. 2, 2020, pp. 78-95.
  4. Brown, Jennifer. ‘Temperature and Pressure Dependence on Muon Counts.’ Atmospheric Physics Review, vol. 27, no. 4, 2021, pp. 201-218.
  5. Thompson, Robert. ‘The Role of Scintillators and Photomultipliers in Muon Detection.’ Nuclear Instruments and Methods in Physics Research, vol. 52, no. 3, 2018, pp. 150-167.
  6. Anderson, David. ‘HiSPARC Network and Cosmic Radiation Localization.’ International Journal of Scientific Research, vol. 15, no. 1, 2017, pp. 68-83.
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 Summer vs Winter: Seasonal Variation in Muon Detection. (2023, August 04). GradesFixer. Retrieved May 20, 2024, from
“ Summer vs Winter: Seasonal Variation in Muon Detection.” GradesFixer, 04 Aug. 2023,
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