Skip to main content.
Welcome to the Virtual Visitor Center at SLAC

Virtual Visitor Center at SLAC

Cosmic Ray Detector - Data Center Guided Tour Stop 2

Flux: a detector-independent quantity

Suppose you want to compare your results to those found by someone else with another apparatus at another time and/or place. This is easy if the other experimenter used exactly the same kind of detector with exactly the same dimensions and other properties as yours. But usually this is not the case. For example, the other person might have a detector with bigger scintillator panels: it would count a higher rate of muons per second because his panels are bigger. On the other hand, the panels might be further apart, which would cause the measurement to give a different answer (higher or lower rate?). So it would be useful to have a quantity that one could compare that is independent of the details of the detectors measuring it.

FluxDiagram showing the two scintillation panels, area A and distance d

Our counter consists of pairs of panels that must both register the passage of a muon for a count to be recorded. Let's look at the sketch of the layout of the detector at the right, with just two of its six panels shown. The red lines indicate the range of directions the muons can come from to traverse the top panel and a small area A in the bottom panel. We can, of course, move the area A around and see that there are more possible ways for muons to cross both scintillator panels. Clearly, changing the area of either of the two panels or the distance between them will change the count rate. The angular range in three dimensions through which the muons may come in for a given location (such as the location of the small area A) on one of the detector panels is called the "subtended solid angle".

The standard way to compare rates between different detectors is to calculate what is called the "flux", which in this case is the rate of cosmic ray muons divided by the subtended solid angle and also divided by the area of the detector. This flux measurement is independent of the details of the detector. The formula to convert count rates to flux is:

F sub mu = (count rate x d squared)/(area of top panel x area of bottom panel)

where d is the distance between the two scintillator panels.

The control panel on the Data Center has options to show the flux rather than the count rates for making comparisons with other measurements. For example, select Vertical (90 deg) Flux Graph in the control panel, and click on Retrieve Data. You will see something like this:

Example 5: 90 degree Flux, 10 hours, 10 1-hour intervals
 Example 5: 90 degree Flux, 10 hours, 10 1-hour intervals

The graph looks the same as the vertical count rate graph in the previous section, but the vertical scale is different. Note the x10-3 in the top left of the vertical scale: this means multiply all numbers on that axis by 0.001. From the chart in Example 5, we can read that in the last hour the flux was roughly 0.52 counts per minute per square centimeter per steradian. A steradian (abbreviated "sterad") is the unit of "stereo angle" or solid angle, the angle in three dimensions, related to the radian which is the unit of angle in two dimensions.

Now, this allows us to compare our measurement to other measured values. For example, the Particle Data Group lists nominal values for cosmic ray fluxes at sea level on their web site (look for Cosmic Rays on this alphabetical list of reviews, labels, and plots. In the Cosmic Ray PDF file, you will find that the flux of "penetrating" cosmic rays (muons) at sea level is roughly 80 counts per second per square meter per steradian. To convert it to our units of counts per minute per square cm per steradian, we multiply by 60 (seconds/minute) and divide by 10,000 (cm2/m2).

(80 counts/sec/m2/sterad x 60 sec/min)/10000 cm2/m2

= 0.48 counts/min/cm2/sterad

So, after conversion, we find that this value is 0.48 counts/minute/cm2/sterad, which is indeed pretty close to our measurement of 0.52 counts/minute/cm2/sterad. Also, our detector is not exactly at sea level. It is actually at an altitude of 262 ft above sea level.

Long term changes

Let us now look at the somewhat longer term.

  1. In the top panel of the Data Center select a time period of roughly one year by adjusting the From and To dates and times.
  2. Set (or leave) the Show option to Vertical (90 Deg) Flux Graph.
  3. Set the number of intervals to 200 (the maximum).
  4. Now click on Retrieve Data.

After a little while (it takes a bit of time to compute) you will see a graph like this:

Example: One year of 90 Flux data
Example chart showing one year of 90 Flux data

There are a number of things to note about this graph.

  1. The size of the vertical error bars is truly tiny now.
  2. There is an obvious step in the data. It starts at about 0.50 counts/minute/cm2/sterad and after about two months suddenly jumps to 0.55 counts/minute/cm2/sterad.
  3. There are gaps in the data. For example, there is one right in the middle of the graph that spans a period of almost two weeks.
  4. Aside from the step mentioned in point 2, there is structure to it that cannot be explained by statistics alone. For example, there is a period in the last quarter of the graph where the flux rises to about 0.58 /sec/cm2/sterad, before it goes back down to 0.50 /sec/cm2/sterad at the end.

Systematic uncertainties

While the statistical uncertainties in this graph are tiny, it should be noted that statistics are not the only source of uncertainties. The step in the data is a good example of this. When the cosmic ray detector was completed and attached to the computer in March of 2000, the detector was located in a particular laboratory at SLAC, which is known to have a very thick concrete ceiling, sufficiently thick, probably, to shield against the very lowest energy muons. Between 27 and 29 July 2000, the detector was moved to its current location, the SLAC visitor center, which has a much thinner roof. This probably explains the difference in the measured flux. We say "probably", because we didn't actually check that this is the reason. In any case, the fact that before 27 July we measured a different value of the flux is an example of a systematic error. Here we can really call it an "error", since the true flux should probably be measured without a concrete roof above the detector - or at the very least one should mention that there was a ceiling, how thick it was, and what the likely consequences would be for the measurement. One can correct for some systematic errors, if one knows what they do. But such a correction usually has itself an uncertainty associated with it, which should be estimated and reported. The data presented in the data center are "raw data", without corrections, and the error bars are statistical only, no systematic effects are included.

If we look at the 45 degree and horizontal measurements for this period, we see some other interesting things: the 45 degree measurement does not seem to change as much as the vertical measurement, and the horizontal measurement shows the opposite of the vertical measurement: instead of an increase, there is a decrease in the horizontal rate. The reason for that is another thing we haven't told you: before the move, the detector was set up with the horizontal direction roughly north-south. After the move, the detector now has its horizontal direction east-west. This probably means that there is a small difference in the cosmic ray flux at non-vertical angles between the north-south and east-west directions. Again "probably", because we have at this point not bothered to find out precisely what causes this.

So we should be aware of the fact that what this detector measures is not completely comparable to other measurements without additional investigation of the possible systematic errors. There are other (smaller) sources of systematic uncertainties which we will not discuss here.

The gaps in the data

The reason there are gaps in the data is that the cosmic ray detector is not always turned on. Most often this is because there was some form of maintenance being performed on it. Sometimes it was shut off for hardware installation, other times for improvements of the software. At times, the detector was off-line for several days, though most of the gaps you see are due to short interruptions. The detector is read out by the computer once a minute. If an interruption lasts for more than a minute, one measurement of the cosmic ray rate is lost. The program that generates the graphs and tables you see in the data center is fairly conservative: whenever there is any data missing from a time interval in the graph or table, it will not show any result at all for that interval. A smarter program could do better, but it would also take a lot more computer time, so we decided not to improve it at this time.

Cosmic ray flux changes

After the step in the data, the cosmic ray flux really does seem to show some significant (in the statistical sense) changes. We already pointed out the rise during the months of January and February 2001 (as you can see by looking at the flux table using the data center). At this moment, we do not have a clear idea as to why there was this rise, but we think it was probably a real effect.

Go to Tour Stop #3
(Comparing muon count rates at different altitudes)