Investigating the Statistical Significance between Latitude and Day-Night Variation on Detection

of Cosmic Rays using the HiSPARC Detectors

Mohona Datta and Fiona Connolly

Hypothesis

• We hypothesise that there will be a difference in incidences of cosmic rays detected at higher and lower latitudes, and this may be due to the Sun.

The Detectors

LATITUDE: 56.1674329°Aarhus University, Denmark

LATITUDE:53.2375489789° Netherlands, Groningen

LATITUDE:51.4579354° Bristol Grammar school, United

Kingdom

LATITUDE:51.3206534°Bouwens van der Boije College, Netherlands

LATITUDE: 51.26364162°Philips Van Horne 1, Netherlands

Method

• To find the Day Night variation, we took the Sum of the events 5 hours around Midday and 5 hours around Midnight

• This was done for one week and then the averages calculated

Method

• We worked out the Standard Deviation, Day Mean and Night Mean for each station

5778.5714295399.428571344.8481476193.8702491

ΔN: 379.142σΔ: 395.6082891

Is ΔN > 5σΔ ? No

Day Average μ2Night Average μ1

Standard Deviation (σ1):Standard Deviation (σ2):

Netherlands, Eindhoven, Weert

Results

• The Results for one week of analysis between two detectors was not statistically significant

• However we tried again for a month using the same two detectors in Denmark and the Netherlands

Results

Denmark Netherlands

0 3000 6000 9000 12000

Night Sum

Day Sum

min < 1 SD < mean > 1 SD > max, fences (1.96 SD, 2.58 SD)

Box & whisker plot 20001 Feb 2013

6800 7300 7800 8300 8800

Night Sum

Day Sum

min < 1 SD < mean > 1 SD > max, fences (1.96 SD, 2.58 SD)

Box & whisker plot 8301 Feb 2013

Results

• However this was not reproducible when tested against detectors at a slightly lower latitude, or a different month of that year.

• Although not statistically significant due to there being many other factors that play into the detection of cosmic rays detected on Earth, we noticed a trend:

Bristol- Netherlands Difference

Bristol University- Lower latitude Netherlands- Higher latitude

Computational Model

• The presence of the Sun deflects some muons away from the Earth’s surface, causing the Sun to act partially as a “shield”. However, less intuitively, the Sun’s magnetic field also causes many muons to be “lensed” towards the Earth’s surface too.

• Muons which are incident on the Sun from the approximate direction of Earth may also be deflected back towards the Earth’s surface as a result.

Computational Model

Computational Model

• Thus, it is not immediately clear which of the Sun’s effects will be greater: the “shielding” effect” or the “lensing” effect. This was the justification for building the simulation. By solving the equations of Newton and Maxwell for the case of muons within the Earth-Sun system, it indicates that the lensing effect ultimately wins out.

Computational Model

• This results in a predicted higher incidence rate of cosmic muons on the Earth’s day side than its night side - an effect which will clearly be most significant at the equator, and which should disappear near the Earth’s poles (where there is no longer any well-defined day/night side).

Secondary data: 2013 Study on the Sun’s cosmic ray shadow

Limitations and Explanations

• There was not a great difference between our highest and lowest latitude-– A difference of 5°

• We know a lot of other factors, such as atmospheric pressure, have a strong correlation with the detection of these events.

• We had no way of telling the difference between detectors that are detecting more particles, and detectors that are just more sensitive; i.e. set to pick up a greater range of voltages.

• The data we analysed was from 2013, which may be an anomalous year…

2013 Solar Maximum

New Scientist,. 'Sluggish Sun May 'Sit Out' Next Solar Cycle'. N.p., 2015. Web. 4 July 2015.

Bibliography

• Simulation by Jonathan Gorard, 2015• New Scientist,. 'Sluggish Sun May 'Sit Out' Next

Solar Cycle‘: Web.• New Scientist,. 'Sun's Cosmic Ray Shadow Is

Solar Storm Predictor‘: Web.• 'Synopsis: Catching Rays In The Sun’s Shadow'. Physics (2013): Web.

• Google Maps plotting tool, detector locations• Maria Pavlidou