The SMU Muon Observatory project utilizes a particle detector in the Fondren Science Building to detect the passage of short-lived subatomic particles known as “muons.” Muons are heavy cousins of the more familiar electron, which is found in every atom in the universe. Unlike the electron, which lives forever once it comes into existence, the life of a muon is fleeting. If you trap a muon, your victory will be brief: muons only live for an average of 2.2 millionths of a second, or 2.2 microseconds.
The data from this instrument is currently used here for two things:
- Creating a “weather-like” view of cosmic ray muon activity. Weather is here used as an analogy for the activity levels of muons at the location of the detector.
- Measuring the lifetime of the muon.
- 1 Live Data
- 2 Background Information
- 3 Cosmic Rays and Variation in Muon Rates
- 4 The Data Analysis
- 5 References
Muon Weather Conditions
Click the image to toggle between a 1-day “weather”, 1-day “seasonal”, and 365-day “seasonal” view.
How do I understand the current conditions?
Weather is here used as an analogy. In the same way that you are familiar with the concept of “weather” as summarizing the present conditions of temperature, pressure, humidity, density, and precipitation in your local area (basically, what air and water is doing where you live), we can think about what the activity level of muons is doing in the area of SMU and Dallas. Instead of temperature, etc. we have the rate at which muons stream through the particle detector. More muons per unit time means more activity, and vice versa.
The rate at which muons pass through Fondren Science varies in cycles over the year, in many ways akin to the way seasons change on Earth and weather changes in response. We define the following terms:
- “Weather”: the rate of muons through the detector (in a 15-minute time block) after subtracting the predicted rate on this day of the year.
- “Seasonal”: the rate of the muons through the detector after subtracting the previous 365-day average number of muons through the detector in any 15-minute time period.
The rate expected on any given day through the detector is based on a fit of a sine function to the previous 364 days of data. The historical average is determined by a simple average over the previous 365 days of data. We compare the current raw rate (typically about 1000 muons every 15 minutes) to either that sine-function prediction or that historical rate. For “weather,” we define the following scale to help you get a “quick feel” for how that compares to expectations. Our measure of the “deviation” from that average is based on the standard deviation of historical data from the prediction, including also uncertainties in the prediction.
Muon Weather Condition Icons
Muon Seasonal Condition Icons
Learn more about how the data are modeled from the Modeling Cosmic Ray Muon Data page.
Muon Lifetime Measurement
The rate at which muons stop in the detector, and subsequently decay, is quite low. Only the lowest-energy muons raining down on the Earth can be stopped by such a compact instrument. The rate at which we observe events in the instrument suitable for lifetime measurement is just a few per hour. The above image automatically refreshes every 30 seconds, but don’t hold your breath while waiting for it to noticeably change!
The detector and its electronics were constructed by Professors Tom Coan and Jingbo Ye. The detector consists of a volume of scintillator optically connected to a photomultiplier tube (PMT). This is all sealed in a light-tight container. When electrically charged particles move through the scintillator, interacting with atoms in the material, this causes light to be emitted. The PMT received the light, converts it to electrical signals, and amplifies the signals. The electronics that readout the PMT take in electrical pulses from the PMT and signal process them. A pulse of sufficient quality initiates (“triggers”) a counter in the electronics; if a second pulse of sufficient quality is received by the electronics within 20,000 nanoseconds, this is stored as a “muon decay event”. Otherwise, the counter times out, records the event, and resets the trigger for the next pulse. These timeout events are useful for recording the raw rate at which muons pass through the scintillator but don’t get captured and decay; this is useful for assessing the local rate of cosmic ray radiation from outer space.
Learn more about the detector and the details of muon physics from Professors Tom Coan and Jingbo Ye and their “Muon Physics” handbook.
The data are retrieved by a small computer (currently a Raspberry Pi linux machine) using a serial port interface. This computer interface was established with expertise from SMU OIT’s Internet-of-Things Developer, Guillermo Vasquez. The data are pipelined from the detector electronics to the USB port on the computer. Software polls the USB port, loads the data buffered there, formats it, and saves it to disk. One file per day is stored; each line in the file represents a muon candidate (either a timeout event or a decay event). Each file is about 2.5 Megabytes in size, uncompressed.
The Physics of Muon Passage, Stopping, Capture, and Decay
The muons raining down on Fondren Science are created when cosmic rays strike molecules in the air above the campus. The collisions produce particles called “charged pions,” which decay in about 0.1 billionth of a second to muons. Two kinds of muons can be produced: positively charged and negatively charged.
The most common muons have kinetic energies of about 1 billion electron-Volts, or 1 GeV (for muons that come straight down from the sky to the earth). Such a muon is traveling at immense speed – 99.6% the speed of light. The detector, depicted above, is only about 1 foot high. At this speed, such a muon would punch through the detector, depositing 2 MeV/cm of material (for a total of 60 MeV of energy loss in material), slowing to just 99.5% the speed of light, and doing all of this in about 1 nanosecond.
Less common are the lower-energy muons. These can have kinetic energies of about 50 MeV; such a muon would slow in the detector, losing 2 MeV/cm of material traversed, and would lose all kinetic energy before leaving the detector. The detector will have stopped it. If this is all that happens, on average 2.2 microseconds later the stopped muon will decay.
How long does it take to stop a muon? This can happen in about 10 nanoseconds (billionths of a second), even taking into account that the muon slows as it loses energy.
However, negatively charged muons have a good chance of being captured by an atom in the detector when they slow down. Just like their cousin electrons, they can fall into orbit around a central nucleus… say, of a Carbon atom in the detector. Their orbits will be tighter than those of electrons – about 200 times tighter. Under these conditions, muons can interact with the nucleus before they decay, and the subsequent emission of energy can look a lot like muon decay. This process – atomic capture of muons and subsequent interaction (via the weak nuclear force) with the nucleus – shortens the time between pulses of energy in the detector from 2.196 microseconds to 2.043 microseconds, the typical timescale of this interaction with a Carbon nucleus.
The “Bohr Radius” of the muon orbit around the nucleus is a measure of how close it gets to the nucleus. For a typical atom in organic material, this is just 10 times the radius of the nucleus.
Since approximately half the muons reaching Fondren Science Building are positively charged, and half negatively charged , the observed decay time of the muon will be skewed low by the following degree: 0.5*2196ns + 0.5*2043ns = 2120 nanoseconds.
In the fit of a decay model to the data above, it’s impossible to discern between the two kinds of muon; therefore, we expect the observed lifetime of the muon to be observed to be shorter than the 2196 nanoseconds of the purely stopped, uncaptured muon.
Cosmic Rays and Variation in Muon Rates
Cosmic ray rates, and subsequently muon rates through our detector, are not perfectly constant. While we typically observe an average of 1000 muons every 15 minutes passing through the detector, in any block of time (e.g. 15 minutes) that number has natural variation.
One source is total randomness. In any 15 minute window, you can predict the typical rate of muons but not the precise count of muons – this is because of inherent randomness in the processes that produce cosmic rays, their arrival at the Earth, their interactions with the atmosphere, the decay of the muon primogenitors, and the decays or interactions of the muons themselves. This leads to natural randomness in the variation.
Another source is known variations in the long-term trends of cosmic rays and muons. For example. it is known that the temperature of the stratosphere has a strong, almost seasonal, influence on the rates of muons reaching the surface of the Earth (c.f. ). In the summer months of the northern hemisphere, the stratosphere warms and its density correspondingly decreases. A less dense target for cosmic rays means more cosmic rays, and more importantly, cosmic ray progenitors, can travel on average farther in the upper atmosphere. This leads to more chance of decay, which leads to more muons. One therefore expects more muons in warmer months and fewer in colder months, with a seasonal variation that follows a long-period sinusoidal function.
The graphs above allow for visualization of all of these things. “Seasonal” views appear when one subtracts a single, long-time-period average of counts from the current rate through the detector. Rates below average are “winter-like,” and rates above average are “summer-like”. “Weather” views appear when one subtracts the daily expected rate for that seasonal period from the current rate through the detector. This allows us to spot very calm periods of muon activity (“clear skies”), compared to high-rates of unexpected muon activity (“thunderstorms”).
The Data Analysis
The data for the lifetime determination are “unbinned,” meaning we begin with each and every detector event with a time between triggers less than 20 microseconds. In addition, we remove data with a trigger time lower than 1 microsecond, as the electronics has a known problem with short-duration triggers. A model of the data is constructed using the ZFit python library; the data are modeled using an exponentially decaying component (the muon decay) and a flat rate of random coincidences (e.g. two muons pass through the detector within 20 microseconds). The model’s parameters – the lifetime of the muon and the fraction of the data represented by the real muon decays – are determined by using the MINUIT algorithm to maximize the probability that the model, plus its parameter values, describe the observed data (minimize the negative-log-likelihood). The model is then displayed overlaid on the data, binned into specific time windows. Goodness-of-fit measures (p-value and chi-square) are reported, and the model is found to describe the data very well.
Learn more about how the data are modeled from the Modeling Cosmic Ray Muon Data page.
 O.C. Allkofer, W.D. Dau. “The muon charge ratio at sea level in the low momentum region.” Physics Letters B, Volume 38, Issue 6, 1972, Pages 439-440, ISSN 0370-2693, https://doi.org/10.1016/0370-2693(72)90177-3.
 F. Ronga. “Seasonal variations of the rate of multiple-muons in the GranSasso underground laboratory.” arXiv 1609:08363. 2016. https://arxiv.org/pdf/1609.08363.pdf