Over the winter break, I have picked up my little muon detector data side project that started in the spring term of 2020. A few days ago, I remarked on how I wanted to take account of “weather” in the data – variations around a daily expectation given seasonal conditions – and “seasons” – long-term trends in the data.
Based on almost 290 days of data since I began this project, it was clear that the counts vary with time with short-period and long-period trends. Let us define a muon “timeblock” as a quarter-hour (15 minute) duration of data-taking. In a single timeblock, the detector typically reports the passage of about 1000 muons. What 290 days of data has taught me is what many previous experiments have also seen: there are overall fewer muons per timeblock in colder months and more in warmer months. So there is something of an annual overall trend, sinusoidal in shape, as well as shorter-term variations (hourly, daily, over multiple weeks, etc.).
I have now captured the seasonal effect using s sine function model. This is fitted to all previous days of data, excluding the current one, to find the best model parameters that describe the past. Today’s rate is then extrapolated from the function, including the effect of model parameter statistical uncertainty from the fitting process. This allows me to identify “weather” conditions – deviations from the daily expectations.
It is currently “winter-like” now. That means we expect, on average, the muon rate to be below the yearly average. Yesterday, we saw additionally “colder” muons weather, with quite a lull in muon counts given the expected rate in each timeblock. Today, things appear to be “heating” back to the expectation, and we will see where the day takes us.
I am spending some time playing around with the cosmic ray muon data from an instrument in the SMU Physics Department. That instrument is located in the basement hallway of Fondren Science Building. I already setup a “dashboard” of information derived from the instrument, available here: https://blog.smu.edu/saso/projects/muon-observatory/. If you want to learn more about the instrument, cosmic rays, and muons, you can check out that dashboard.
I’ve wanted to take account of the variation, over the seasons, of the muon rate through the instrument. Previous research on cosmic ray muons (there is a lot of this, since cosmic rays were discovered a century ago) suggests this variation is due to the change in temperature (and thus density) of the stratosphere over the year. More dense air = more cosmic ray interactions = fewer decays to muons.
The effect should be roughly sinusoidal, so I am trying to incorporate a sine function fit (done) into the muon rate subtraction (in progress) to better account for daily expectations. Right now, my subtraction is just of the entire running average of the count of muons, which reveals an annual variation … but fails to capture daily expectations. So, basically, I isolated muon climate (long time periods) but not muon weather (short time periods) in my current graphs … and I want to capture weather.
If you want to learn more about muons, check out my dedicated lecture on the subject from my Modern Physics course:
I’ve written extensive python and C++ code to analyze the raw data from the muon detector. That detector provides two pieces of data: the time between two pulses in the detector, and the time at which the pulses were received (e.g. wall-clock time). This is then turned into the information on the dashboard using code. This employs Panda dataframes, ZFit and ROOT to do data modeling and extrapolation/interpolation, and Matplotlib to do graphing (among other things). It’s been my fun pandemic side project since March, 2020.
On Saturday, we took a break from the pandemic to go outside and look for a comet. We live in a Dallas suburb, but one which has grown a lot in 10 years. The skies are not quite as dark as they used to be, but we thought it might be possible to spot and view Comet Neowise.
We set out just before 9pm to a local city park. Jodi had the binoculars I got from my grandfather when he passed away; I had the new DSLR camera Jodi got me for Christmas last year. The sky was still showing the last glow of sunset, and city lights coming on across North Texas was being gently scattered back down to Earth, creating a faint but irreducible haze in the sky. We found a good spot to try to see the comet. Jodi located it with an iOS skywatching app, and we waited for more darkness to settle.
While waiting, we took stock of the night sky. Planets and stars peeked out of the twilight Arcturus glowed orange overhead. Jupiter lit the sky closer to the southern horizon, with the four Galilean Moons clearly visible under even modest magnification. Our real prize was to be found just below the cup of the Big Dipper. As the sky conditions settled to just about the best possible, we started spotting the stars of the Big Dipper more closely and hunting for the comet.
We knew to start from Merak, the star that makes up the front lower edge of the dipper’s cup. Go straight down from Merak, and the comet would lie somewhere along that line. Indeed, once we employed the binoculars, the bright core of the comet and the fainter long arcing wisp of its tail were clear. This was incredibly thrilling; I’ve never had a chance to see a comet first-hand before.
I got the camera setup and aimed in the general area where the comet should appear. In particular, we noted that Neowise was framed by a triangular arrangement of background stars. Spotting those was hard on the camera, but after a few long exposures at high ISO (>1600), it was clear where to center the shot to best pickup the comet.
After a bunch of photos, we packed up and went home. It was 10pm, way past our bedtime. It had been worth it. With all madness raging down here on Earth, it’s nice to see a cosmic tourist taking a drive through the inner solar system. Neowise will not to return for several thousand years. When it comes back, I wonder if humanity will still be here to see it?
In 1970, Hall, Lind, and Ristenen (Univ. of Colorado at Boulder) published a paper in the American Journal of Physics (AJP, vol. 38, No. 10) on “A Simplified Muon Lifetime Experiment for the Instructional Laboratory.” Basically, it articulates precisely the experiment at the heart of a similar instrument at SMU. Muons are produced in cosmic rays raining down on the atmosphere. Some muons make it all the way to sea level. Some of those are moving slowly enough to be stopped when passing through material. If that material gives off light in response to the slowing, stopping, and then decay of the muon, it is possible to use the light to measurement the lifetime of the muon.
Hall et al. reported on a run of their experiment of 695 hours (about 29 days!). I’ve had nothing but time on my hands, and after discovering the Hall paper when I started playing around with the SMU instrument I was inspired to repeat their experiment.
As of today, I have 695 hours of data from the muon detector at SMU. Based on a model fitted to the data (an exponential decay function added to a flat background), I find the lifetime of the muon to be nanoseconds (ns). The accepted lifetime is ns. The Hall et. al result using a similar but earlier version of the experiment found . (note: they quote the half-life, but that is easily converted to the lifetime [average life of the muon] by dividing the half-life by ln(2)).
In 1970, as now, the lifetime of the muon has not changed within the resolution of two 695h data sets, taken independently and 50 years apart. There is a wonder in the power of scientific investigation to reveal those things that are steady and constant in the cosmos.