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Stony Brook course CEB558/PHY315: Hands-On Science with Cosmic Rays

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Contents 1 March 18, 2008 (no class) 1.1 Graphing Counts 1.2 Barometric Pressure 1.3 Comparing Number of Cosmic Rays and Barometric Pressure 1.4 Pressure Dependence of Cosmic Ray Data

March 18, 2008 (no class)

Stony Brook is not in session this week (spring break?), but since I will be missing a class or two later this spring I came to class anyway to make up the class. That turned out to be a good idea. Dr. Dima Vavilov was there, and since there were no other students demanding his attention, we had good discussions about what to do with the data. Unfortunately there were some network problems, so I couldn't go to some link that I wanted to. I guess that will be my homework. We came up with the following as a first idea of what to do with the data.

• First we successfully combined the date and time in Excel into one number that Excel could understand, so I graphed the same data as last week using an XY scatter graph. Now it will be possible to see breaks in the data, whereas before data points were graphed sequentially without breaks.
• I need to graph about 1 week of data together on one graph. Hopefully I will be able to append successive days of data. Dima says 200 is a good number of data points on a graph, so if I average my data over 30 minute time intervals then I will have more than that, but not a lot more. I may change my mind about the length of time to average, depending on what data I can find for pressure.
• Find a source of data for local barometric pressure. I have heard that this data exists in many places, but haven't seen it yet (and the network was intermittent at best, so didn't find any this evening). I will look at Stony Brook, SCCC, BNL, and a few other places. Hopefully somebody has the data in a nice format that I can use.
• Graph the pressure data in a way similar to how I graph the cosmic ray data.
• We have talked about how an increase in pressure will lead to a decrease in number of cosmic rays detected, so I should expect an inverse relationship between pressure and number of cosmic rays. Dima suggested that I "normalize" my countrate data by multiplying it by a factor of (p/po), where po is a standard pressure, and p is the pressure at the time that matches my countrate data. This "normalized" countrate data may (should?) take pressure variations out of the cosmic ray data, so I should be able to see other anomalies in the data, and start to find interesting stuff. Or maybe I'll look to see if the 4-fold and 5-fold coincidences, which should be caused by higher energy cosmic rays than the cosmic rays that cause the 2-fold coincidences, behave the same way with pressure as the 2-fold coincidences.
• And when I've done that, maybe I should do the whole thing over again using the (free) R statistical package. It should be easier to manipulate the data using R than using Excel. The Excel version of data manipulation would be more suitable to my regular physics students, while the R version of data manipulation would be more appropriate for research students. So maybe I should find a copy of R and learn how to use it. By next week?

Graphing Counts

I put 1 week of data together on one graph. I chose the week of 3/3/08-3/9/08. Actually, I used John Hover's "basic web analysis tool" (thank you John!) to pick a recent week that showed some variation in the number of counts. I wanted something recent so as to use data since the detectors were calibrated, and I wanted data that showed some variation so that when I start playing with the barometric pressure I will have some fluctuations that may (or may not) be due to pressure. Here are graphs of the same data. The one on the left is generated by John's code and I put together the one on the right using Excel. I used the following address to pick up the graph using John's code: http://www.mariachi.stonybrook.edu/mariachi-ws/dataquery/query?site=smithtown&start=2008-03-03T12:01:30&end=2008-03-09T17:01:30&graph=1&width=640

The first and most comforting thing I noticed is that they look similar, so I'm fairly confident that I'm picking up the same data in both cases. I looked at other data and found different variations, so this looks like the same data. Dima was right that there is too much data. I will average over 30 minute blocks of time to cut the number of data points. In class we had talked about error bars. The vertical error bars on this data should be about . The chart, however, looks as though the error bars should be about . Maybe the discrepancy is because our calculated error bar is just for the 1σ, and the large data points and huge number of data points makes it hard to visualize where the 1σ point is. I guess I could graph a histogram of the number of times we measure each number of counts, and from that figure out the 1σ point, but I don't think I'll do that now.

Here (below) I have averaged the countrate data for 30-minute intervals. The variations are a lot easier to see:

Barometric Pressure

Now I need to find some barometric pressure data in order to compare the pressure with countrate data. I found Weather Underground, a site that links to weather stations. Mount Sinai has barometric pressure and I can create comma-delimited files with the relevant data. I'm not quite sure yet how to get the time intervals to match the time intervals from the countrate data, but that will come. I Googled "weather station" and found a number of weather stations that measure pressure. I like the Mount Sinai site, which is not quite the closest, but appears to be more reliable about recording data.

I grabbed the weather data from Mount Sinai station KNYMT.SI1 in a comma-delimited file, and imported it into Excel. Actually, I grabbed 7 days of data in 7 different files, and imported them all into one Excel file. The biggest problem with the data is that, although the station records data approximately every 5 minutes, it doesn't do it always exactly every 5 minutes. So I had to massage the data file a little to get it into a form that I would then be able to use to compare data with the countrate data. I chose to average pressure readings and record an average in 30-minute increments. Like the countrate data, I converted the timestamp into GMT time, and recorded the time at the end of the 30-minute interval. And I converted the pressure from inches of mercury (inches of mercury??? how archaic is that unit?) to Pascals. The variations in barometric pressure over the interval 3/3/08-3/9/08 are shown in the graph that follows. Not that the variations look similar to the variations in countrate, just opposite, as expected. An increase in pressure means that there are more molecules in the atmosphere between where a cosmic ray enters our atmosphere and where we detect it on earth, so the cosmic ray has a greater chance of interacting with particles in the atmosphere (note: Prof. Marx points out here the difference between a cosmic ray decaying and interacting with another particle. Decaying is spontaneous, and is statistical in nature. Interactions occur between cosmic rays and other particles and are not spontaneous). Higher pressure should lead to lower number of cosmic rays, and it does appear to.

Comparing Number of Cosmic Rays and Barometric Pressure

In order to compare the countrates and barometric pressure, I graphed countrates and pressure on the same graph. The vertical axis for countrates (the lower set of data) is on the left; the vertical axis for pressure (the higher set of data) is on the right in units of Pascals. Since an increase in pressure lead to a decrease in countrate, I inverted the pressure axis, graphing from high to low pressure instead of from low to high. Countrates are the number of coincidences between detectors 1 and 2, which are superposed, and the number is averaged over approximately 30-minute time intervals. Barometric pressure is in Pascals, and is the average over approximately 30-minute intervals, massaged to coincide with the countrate time intervals. I love this graph - it shows that there is excellent correlation (by eye - no statistics yet to back my hand-waving) between the shape of countrates and barometric pressure. The pressure data is on top. It has less variation than the countrates, the lower line of data. I have to admit to having played with the vertical scales to make the similarity obvious.

Pressure Dependence of Cosmic Ray Data

The graph above showed that an increase in pressure leads to a decrease in number of cosmic rays detected, so I should expect an inverse relationship between pressure and number of cosmic rays. Dima suggested that I "normalize" my countrate data by multiplying it by a factor of (p/po), where po is a standard pressure, and p is the pressure at the time that matches my countrate data. This "normalized" countrate data may (should?) take pressure variations out of the cosmic ray data. Standard pressure is 101325 Pa, so that is the value that I used for po. If the measured barometric pressure is high (and cosmic ray count is low) then the ratio p/po will be high, and multiplying the countrate by p/po gives a higher normalized countrate. Conversely, if the measured barometric pressure is low (and cosmic ray count is high) then the ratio p/po will be low, and multiplying the countrate by p/po gives a lower normalized countrate.

I tried normalizing the countrates as described (multiplying by a factor of p/po), and found that, indeed, there is less pressure variation after the normalization. But there is still a noticeable trend of high pressure = low countrate (still no statistics to back up my hand-waving, but it looks real). So I tried normalizing the original countrates by a factor of (p/po)^2, and that made a huge difference. By eye (my eye, anyway), it looks as though the countrate has a square dependence on the pressure. I don't know why that would be. Maybe I'll have to look for some equations somewhere to support that conclusion. The graphs are below.

So I managed to do quite a lot this week:

• I graphed 1 week of count rate data together on one graph, and averaged it over approximately 30-minute intervals.
• I found a source of data for local barometric pressure, available in comma-delimited files.
• I graphed the pressure data together with cosmic ray data of the same time interval for comparison.
• I "normalize" my countrate data by multiplying it by a factor of (p/po), and was able to reduce the pressure dependence further by multiplying countrate by a factor of (p/po)^2, where po is a standard pressure, and p is the pressure at the time that matches my countrate data.

What's next?

• Use some statistics to back some of my hand-waving statements.
• See if the number of 4-fold coincidences and 5-fold coincidences, which should be caused by higher energy cosmic rays, behave the same as the 2-fold coincidences that I was working with.
• After the pressure "normalization" there are still variations in the data - maybe take a closer look at some of these anomalies.
• Look into using the (free) R statistical package to do the same analyses all over again (but hopefully more easily).

Go on to next week's class.