1. CAN WE DEDUCE THE RELATIONSHIP BETWEEN THE ANGLE OF INTERCEPT OF COSMIC RAY SHOWERS AND OTHER FACTORS? Tom Bishop and Josh Heaton

2. THE PROJECT  Our project is about calculating the angle of primary cosmic ray particles, i.e. the angle that the initial particle comes in to Earth before it splits and forms a muon shower.  We are trying to find a relationship between these angles and other factors, for example time of year.

3. ASSUMPTIONS  There are a few assumptions that need to be made in order to calculate the angles. These are: 1. The front of a cosmic ray shower is flat. 2. The altitude of each station is the same. 3. The speed of the cosmic rays are the same. This can be taken to be 2.98x10^8 m/s, which is very close to the speed of light (see references).

4. THE DETECTOR STATIONS  3 detector stations were chosen (502, 505 and 506) from the map on the HiSPARC website that form a triangular shape, are at almost the same altitude and are about 200m apart. The GPS coordinates of the stations were then converted into x/y coordinates, with detector 506 as the origin.  We will refer to 506 as ‘A’, 505 as ‘B’ and 502 as ‘C’.

5. THE ANGLES  There are two angles that need to be calculated to gain an idea of the direction of the primary particle. These are the bearing of the particle if looked at from a bird’s eye view, and the vertical angle of the particle. θ θ = vertical angle

6. THE DATA  Using the HiSPARC website data download form we took data about event coincidences recorded by each of the three detector stations.  An event was considered to be a coincidence when the stations all recorded an event at nearly the same time (within 1000ns). We then assumed that this meant one cosmic ray shower hit all three stations at once.  The data provided the time that each station recorded the event to the nanosecond, and from this the time difference between each station can be calculated, i.e. the difference in the time that the shower hit stations B and C relative to A (the origin).

7. CALCULATING THE ANGLES

8. BEARING FOR 2015  The bearing of the primary particle appears to be very evenly distributed. The gaps could be caused by station downtime.

9. VERTICAL ANGLE 2015  There appears to be a lower frequency of larger angles and smaller angles. The gaps are probably caused by the same reason as the gaps on the bearing graph.

10. BEARING FREQUENCY HISTOGRAM  Average bearing = 194

11. VERTICAL ANGLE FREQUENCY HISTOGRAM  Average vertical angle = 23

12. CONCLUSIONS  The bearing distribution is very evenly and randomly spread out, implying that the bearing of the primary particle is not affected by any factors and is random.  The average bearing of 194 implies that there are more cosmic rays coming from the east than the west.  For the vertical angle there is a lower frequency for larger angles, i.e. there appears to be fewer cosmic rays coming in at an angle closer to the ground. This shows that the showers are more likely to decay before they hit the ground if they have further to travel through the atmosphere, or they could be “curved” into steeper angles on their way down. There is also a relatively low frequency of smaller angles, meaning that there are fewer particles coming from directly overhead.  The gaps in the points are likely due to detector station downtime leading to a lack of recorded coincidences for the time that it is down.

13. PROBLEMS ENCOUNTERED  One issue we encountered was that a lot of the data from the coincidences download contained “problems with analysis” this is problematic as it render’s that data set potentially untrustworthy.  Another issue was that the data occasionally failed to adhere to the typical data structure- a non 3 set of stations, the problem with this is that this structure is the basis of our code, to solve this another program was written to identify these non adherent data sets.  The code is incapable of handling time differences of 0, as it would require dividing by 0, as such, data that contains this(a rare occurrence) has to be removed

14. PLANS FOR NEXT YEAR  We are planning to continue the project next year – we will look at the maximum vertical angle of the primary cosmic ray by considering the maximum distance that the cosmic ray muons can travel through the atmosphere without decaying before they hit the detectors.  Another idea is to use the calculated angles and GPS to try to prove or disprove that cosmic rays don’t come from the sun.

15. REFERENCES  HiSPARC website - http://www.hisparc.nl/en/  Speed of shower: ‘The Speed and Lifetime of Cosmic Ray Muons’ Author - Lulu Liu Date - November 18, 2007 URL - http://web.mit.edu/lululiu/Public/pixx/not-pixx/muons.pdf Accessed – 16/02/2016