STEM

The Universe is Mostly Plasma

It is often convenient to calculate the arrival direction of cosmic ray showers with respect to the geographical orientation of the detector stations (e.g. angle with the zenith direction, and angle with respect to N/S direction. However for astrophysical purposes we need to know the direction with respect to the standard astronomical Right Ascension/Declination coordinate system. We therefore need to convert between the two systems easily - the fact that the Earth is rotating makes it all the more interesting!

Understanding coordinate conversion is much easier if you have done A-level maths, because you will have studied "Matrix Algebra" which, if you have understood it, make all the conversion equations look very straightforward. With GCSE maths, the trigonometry is pretty tricky to get right - though it can be done.) Fortunately, we do not really need to work through this maths every time: you just need the final equations, which are not too difficult to understand. Furthermore, in practice when we are doing computer calculations most of the time we would just call on a standard library routine that was probably written and debugged by someone else. (There is one as part of the HiSPARC Python "Sapphire" framework, and you will find them on-line in other astronomical Python libraries. One of the great things about using Python for scientific programming is finding that other expert programmers have already done a good deal of the difficult, detailed and tedious work for us.)

The HiSPARC website give guidance and calculation the arrival direction of cosmic ray showers with respect to the geographical coordinates. In our project at Marling school we attempted to calculate the arrival direction directly in terms of astronomical coordinates. This is more complex than the original HiSPARC methods, but we do not then need to do the coordinate conversion as a second, also fairly complex, step. 

Note that this solution scheme is only applicable when we have data from exactly three detectors. If a shower triggers more than three detectors, in this scheme we have to solve for all detector triplets separately. See below for a better method of solving with more than three detectors.

This is a revised set of equations for the direct calculation method, which avoids situations where the trigonometry gives ambiguous answers (because inverse tangent function can have two valid outputs) or there are "divide-by-zero" problems. (In fact, these difficult cases mostly turn up when we test the program with extreme and special cases, such as showers coming directly down the Earth rotation axis, or perhaps directly and exactly perpendicular to the plane of three detectors. Real data tends not to be so special.)

Note well: as a result of previous investigation of direction solutions, we became suspicious that some of the data in the HiSPARC database is not quite what it claims to be. See the "Investigation of HiSPARC time anomalies" project below. Until we are able to derive appropriate detector calibrations we do not believe that it is worth pursuing multi-station direction solutions.

Cosmic Shower Front Angle - more than 3 detectors

Updated 10th January 2018

All the previous methods are applicable only to showers where we use data from three detectors only. If we wish to analyse showers that trigger more than three detectors and we wish to use all the data to get more accurate answers, it is necessary to do a statistical fit for the best shower directions. This explains how it can be done by modelling the extended air shower front as a plane arriving from a certain direction and then predicting the time at which it will arrive at each of the triggered detectors. We then adjust the assumed direction iteratively (using a "least squares" minimisation procedure) until the different between our predicted arrival times and the actual arrival times is as small as possible. This allows for inevitable minor errors in the recorded arrival times which mean that it is usually impossible to find a solution that exactly predicts all the measured detector arrival times.

Investigation of HiSPARC timing anomalies.

Analysis of the result coming from the direction solution project discussed above produced some odd results (distribution of tracks on the sky that are unlikely to be real). This suggested project aims to track down the source of this issue by investigating whether there are relative timing errors in the HiSPACE data from different detector stations.

I suggest that this would be a feasible project for Yr 12s with a strong interest in space science and programming. 

Pressure Dependence of Extended Air Shower Event Rate

Updated 17th November 2019

This describes a project that uses downloaded HiSPARC data to derive a correlation between the EAS event rate and the air mass along a cosmic ray shower track. (Note that this is an extension project that goes beyond just attempting to correlate the logged EAS event rate against logged barometric pressure. Here we the arrival direction of EAS events at stations where this is available, which allows us to consider separately tracks at low and high angles with the zenith direction, corresponding to tracks that have shorter and longer lengths through the atmosphere.)

Note the revision with a correction to the geometric scaling factor for inferring the expected density of EAS events/steradian in the absence of additional absorption at higher zenith angle tracks.

This project involves a certain amount of programming to handle a relatively large amount of data, but this proved to be within the capabilities of a strongly motivated group of Yr 11s. Nevertheless, this is probably more appropriately pursued for a Gold CREST award for Yr 12s.

 download.py

A Python file that downloads a month's worth of coincidence data for a specified cluster. Note that this is in development and one has to modify the dates within the code in order to specify the dates covered by the download. It can be trivially modified with an iteration loop to download many months (or years) worth of data - providing your Internet connection will stand the data load.

The output goes to a HDF (hierarchical data format) file stored in the current directory, with a ".hd" extension. This can be read by later analysis programs multiple times without having to repeat the data download every time.

 processCoincidences.py

A Python program that reads a downloaded data file and calculates the shower arrival directions.

Note that as the program is still in development it is necessary to write the year for analysis into the main program.

The code now has the first prototypes of a multi station solution scheme. 

 solveSky.py