1
Image Source: BBC
ABSTRACT
This experiment sought to evaluate the impact of the solar wind on the amount of
muons coming in by correlating the rate of muon flux detected in a Quarknet 6000series Scintillator detector with a) the natural day-night cycle an b) the dynamic solar
wind data from NASA's SOHO satellite.
Using two different experimental setups (each running for 64 hours), the experimenter
observed no statistically significant correlation between the day-night cycle and the
rate of muon flux. He did, however, observe a seemingly statistically significant positive
correlation between the muon flux and the real-time solar wind data; nevertheless, that
correlation was neither linear nor completely supported by the data. On the setup with
the detectors stacked atop one another and pointing directly up at the sky, a stronger
visual correlation was observed (71% of data points within one standard deviation;
94% within two). When the Pearson Equation was used to find a correlation, it gave a
value of about 0.44 (2 significant figures), which shows a mild positive correlation. On
the setup with the detectors separated by a box and pointed toward the ecliptic, the
visual correlation was not well shown (65% within one standard deviation; 88% within
two). The Pearson value on the second data run showed a very, very weak negative
correlation of -0.12.
Thus, this experiment showed no visible correlation between the day/night cycle and
the muon flux. Using all four detectors stacked directly atop one another, it showed a
mild positive correlation between the solar wind density and the measured muon flux.
Using all four detectors, pointed toward the ecliptic, with a box in between them, the
experiment showed no statistically significant correlation.
Image Source: DeviantArt (users: Nightangel/Monoxism)
2
FOCUS QUESTIONS
1. How does the rate at which muons and other particles arrive
change over time?
2. What does that demonstrate about the effects of the solar
wind?
3. What significance does this have in a greater context?
3
BACKGROUND RESEARCH
 Experiments similar to this one have, indeed, been completed in
the past.
 “Measurements of the Cosmic Muon Flux with the Willi Detector
as a Source of Information about Solar Events” (Bucharest,
2010) found that there was approximately a 5% increase in
muons during the day.
 “Solar Wind Effect on the Muon Flux at Sea Level” (Rio De
Janeiro, 2005) found that “Forbush events” in which the sun
ejects plasma, and the muon flux is decreased, are common.
Thus, solar events can sometimes be negatively correlated with
muon flux.
Image Source: Creative Commons (User: Originalwana)
4
SOLAR WIND: A QUOTIDIAN (DAILY) PATTERN?
•
Initially, this experiment will compare muon flux during the day and at night. I will
associate these day and night fluctuations with the solar wind by the following
assumptions.
•
In some cases, it takes particles from the solar wind many days to reach the
earth.
•
However, I think that those particles likely to affect my muon count will almost
certainly be traveling closer to the speed of light; ergo, there will only be eight to
ten minutes of delay between solar events and local events.
•
Furthermore, for those particles most likely to result in muon production (or for
those most likely to interfere with muon flux), it is reasonable for me to assume
that, during the night, the earth’s large mass will prevent them from reaching my
detector.
Image Source: Zastavski.com
5
HYPOTHESIS
1. When the experiment is run, slightly more muons will likely be
detected during the day, because some of them come from the
solar wind. During the night, the earth will probably shield the
detectors from those muons, so the muon flux (rate of arrival)
will decrease slightly.
However, it’s also possible that the opposite will occur: more
muons may be detected at night due to a decrease in solar wind
modulation of the cosmic ray spectrum.
6
Image Source: collidingparticles.com
HYPOTHESIS (CONTINUED)
2. If the initial portion of my hypothesis (as well as my
assumptions) is correct, a fair conclusion should be that the
solar wind bolsters, rather than attenuates, the rate of muon
flux.
3. If the first two components of my hypothesis are correct, I can
conclude that the solar wind consists partially of particles that
end up creating muons, because the modulation effect is well
known and would reduce the rate of muon flux, were it the only
variable in play.
7
Image Source: collidingparticles.com
EXPERIMENTAL TECHNIQUE OVERVIEW
After plateauing the
four scintillators
connected to a
Quarknet DAQ board, I
measure the muon flux
by looking at the times
when all four detectors
are triggered
simultaneously (within
40 ns of each other).
Image Source: Fermilab
8
DETAILED SETUP, 1ST EXPERIMENT
1) Without plugging the DAQ into a power source, connect all four scintillators’ data cables into the
DAQ. Then, plug their power cables into the voltage regulator.
2) Plug the voltage regulator cable into the DAQ. Then, plug a CAT5 cable into your GPS receiver
and your DAQ’s GPS IN port.
3) Plug the USB (type B) connector into the DAQ and into a PC. You may need to install the CP210x
Serial-to-USB driver on your PC.
4) Finally, after ensuring that each connection is tight, plug your DAQ into an electric outlet.
5) Start hyperterminal on your PC, and set up a new connection. Call it COM-3, use the port
“COM3” and set the Bits per second to 115200. Finally, set the flow control to XON/XOFF.
6) Ensure that the scintillators are stacked on top of one another in order, and properly plateaued
(see Quarknet’s Plateauing guidelines for more details). There should be no more than four
centimeters between detectors, and they should be flat, facing up.
7) Run a short test at 4 coincidences. You should get approximately 5-8 counts per second, or
400-600 per minute (WC 00 3F ; 0.770 V in daytime).
8) Ensure other variables (time delay, threshold voltage, etc.) are set to their defaults for the
Quarknet 6000 DAQ.
Image Source: NASA
9
DETAILED PROCEDURE OF BOTH EXPERIMENTS
1) Prepare experimental equipment, as discussed in previous slide (or, for second
experiment, on slides eighteen and nineteen).
2) Set up DAQ board to take data over a 24-hour (or longer) period. It should be counting
four coincidences on all four stacked detectors (WC 00 3F via the COM/USB
interface; http://quarknet.fnal.gov/toolkits/ati/det-user.pdf for assistance).
3) Capture the text data using the Quarknet guidelines.
4) After 64 hours, finish the data collection, following the Quarknet guidelines. Run a
Flux analysis.
5) From this raw data, make a more detailed result and propose an explanation (e.g.,
muon flux was 5% higher during the day, perhaps because some muons came from
the solar wind).
6) Attempt to identify trends in the data. Also, check to see if the data correlate with
real-time measurements of the solar wind using a visual standard deviation test and
a Pearson (PPMCC) statistical correlation test.
7) Document findings, procedures, and potential sources of error.
Image Source: NASA
10
11
Image Source: Sydney Electrical Contractors
To reduce noise and ensure the detectors’
functionality, I plateau the detectors by
adjusting their voltage and comparing it to
the count rate.
Plateauing for all 4 coincidences
18
Counts (Hz)
16
14
12
10
Plateau occurs
around 0.80 V
8
6
4
2
0
0
0.2
0.4
0.6
0.8
1
1.2
Voltage (V)
After running the detector for five days, with all the scintillators
stacked directly on top of one another, I receive the graph above.
12
INTERPRETING MY PRELIMINARY RESULTS
What do these data tell
us?
Peaks
Irregular Curve
Outlier!
 No discernible daily
pattern.
 Fluctuations are
generally not terribly
statistically significant,
at least with a bin width
of four hours (1-3 error
bars)
 Further investigation is
needed!
13
INTERPRETING RESULTS (CONTINUED)
Visually, however, we can correlate our muon flux pattern (outlier omitted) to realtime solar wind data from NASA’s SOHO satellite!
How does this
impact our
interpretation of the
focus questions &
hypothesis?
 Ultimately, we can’t conclude
that the day/night cycle has a
direct impact on the rate of
muon arrival (flux)
 This probably denies our
hypothesis.
 Once again, further
investigation is needed.
Image Sources: NASA, NOAA
14
NOTES ON MY DATA FIT
15
Of course, this graph was not produced without a few statistical adjustments (see
below).
 With these adjustments, 23 of my 32 (71%) 2-hour averages appear to be within
one standard deviation of the SOHO data. Seven are within two standard deviations.
Only two lie outside two standard deviations.
Proton density
is measured
logarithmically
But muon flux’s y-axis is
measured linearly, from a
flux of 8100 to 8600
events/m2/minute.
The scale is also offset by one
hour, because these protons
take longer to reach the earth
than the satellite
PEARSON TEST OF STATISTICAL CORRELATION
We can calculate the degree of similarity between the two data sets by comparing the
expected correlation (none) with the observed correlation. An R-value substantially
greater than zero means a positive correlation; an R-value substantially less than zero
means a negative correlation.
𝑹=
𝒏
𝒊=𝟏(𝑿𝒊 −𝑿)(𝒀𝒊 −𝒀)
𝒏 (𝑿 −𝑿)𝟐 ∗
𝒊=𝟏 𝒊
𝒏(𝒀 −𝒀)𝟐
𝟏 𝒊
𝑾𝒉𝒆𝒓𝒆 𝑿𝒊 𝒊𝒔 𝒕𝒉𝒆 𝒉𝒆𝒊𝒈𝒉𝒕 𝒐𝒇 𝒕𝒉𝒆 𝒄𝒖𝒓𝒓𝒆𝒏𝒕 𝒅𝒂𝒕𝒂 𝒑𝒐𝒊𝒏𝒕 𝒊𝒏 𝒎𝒚 𝒔𝒆𝒕; 𝒀𝒊 𝒊𝒔 𝒕𝒉𝒆 𝒉𝒆𝒊𝒈𝒉𝒕 𝒐𝒇
𝒕𝒉𝒆 𝒄𝒖𝒓𝒓𝒆𝒏𝒕 𝒅𝒂𝒕𝒂 𝒑𝒐𝒊𝒏𝒕 𝒊𝒏 𝒕𝒉𝒆 𝑺𝑶𝑯𝑶 𝒅𝒂𝒕𝒂, ; 𝑿 𝒂𝒏𝒅 𝒀 𝒂𝒓𝒆 𝒕𝒉𝒆 𝒂𝒗𝒆𝒓𝒂𝒈𝒆 𝒉𝒆𝒊𝒈𝒉𝒕𝒔
𝒐𝒇 𝒎𝒚 𝒅𝒂𝒕𝒂 𝒂𝒏𝒅 𝒕𝒉𝒆 𝑺𝑶𝑯𝑶 𝒅𝒂𝒕𝒂, 𝒓𝒆𝒔𝒑𝒆𝒄𝒕𝒊𝒗𝒆𝒍𝒚; 𝒂𝒏𝒅 𝒏 𝒊𝒔 𝒕𝒉𝒆 𝒏𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝒃𝒊𝒏𝒔.
Equaion source: Wikipedia
16
Bottom
Avg
PPMCC Value
122
107
91.35714286
92.42857143
2558
17
1
2
INTERPRETING THE PEARSON VALUE
77
95
91.35714286
92.42857143
-14.35714286
2.571428571
-36.91836735
206.127551
6.612244898
99
96
91.35714286
92.42857143
7.642857143
3.571428571
27.29591837
58.41326531
12.75510204
3
118
99
91.35714286
92.42857143
26.64285714
6.571428571
175.0816327
709.8418367
43.18367347
4
103
105
91.35714286
92.42857143
11.64285714
12.57142857
146.3673469
135.5561224
158.0408163
5
93
104
91.35714286
92.42857143
6
100
104
91.35714286
92.42857143
7
106
97
91.35714286
92.42857143
8
122
105
91.35714286
92.42857143
9
107
101
91.35714286
92.42857143
10
82
94
91.35714286
92.42857143
11
117
86
91.35714286
92.42857143
12
91
91
91.35714286
92.42857143
13
94
92
91.35714286
92.42857143
14
66
89
91.35714286
92.42857143
15
97
95
91.35714286
92.42857143
16
84
94
91.35714286
92.42857143
17
87
87
91.35714286
92.42857143
18
89
89
91.35714286
92.42857143
19
78
84
91.35714286
20
75
81
21
66
83
22
82
23
94
24
25
Sqrt(total sum)
1.642857143
11.57142857
19.01020408
2.698979592
133.8979592
8.642857143
11.57142857
100.0102041
74.69897959
133.8979592
14.64285714
4.571428571
66.93877551
214.4132653
20.89795918
30.64285714
12.57142857
385.2244898
938.9846939
158.0408163
15.64285714
8.571428571
134.0816327
244.6989796
73.46938776
-9.357142857
1.571428571
-14.70408163
87.55612245
2.469387755
25.64285714
-6.428571429
-164.8469388
657.5561224
41.32653061
-0.357142857
-1.428571429
0.510204082
0.12755102
2.040816327
2.642857143
-0.428571429
-1.132653061
6.984693878
0.183673469
-25.35714286
-3.428571429
86.93877551
642.9846939
11.75510204
5.642857143
2.571428571
14.51020408
31.84183673
6.612244898
-7.357142857
1.571428571
-11.56122449
54.12755102
2.469387755
-4.357142857
-5.428571429
23.65306122
18.98469388
29.46938776
-2.357142857
-3.428571429
8.081632653
5.556122449
11.75510204
92.42857143
-13.35714286
-8.428571429
112.5816327
178.4132653
71.04081633
91.35714286
92.42857143
-16.35714286
-11.42857143
186.9387755
267.5561224
130.6122449
91.35714286
92.42857143
-25.35714286
-9.428571429
239.0816327
642.9846939
88.89795918
85
91.35714286
92.42857143
-9.357142857
-7.428571429
69.51020408
87.55612245
55.18367347
84
91.35714286
92.42857143
2.642857143
-8.428571429
-22.2755102
6.984693878
71.04081633
80
82
91.35714286
92.42857143
-11.35714286
-10.42857143
118.4387755
128.9846939
108.755102
97
72
91.35714286
92.42857143
5.642857143
-20.42857143
-115.2755102
31.84183673
417.3265306
26
72
96
91.35714286
92.42857143
-19.35714286
3.571428571
-69.13265306
374.6989796
12.75510204
27
100
100
91.35714286
92.42857143
8.642857143
7.571428571
65.43877551
74.69897959
57.32653061
28
82
98
-9.357142857
5.571428571
91.35714286
92.42857143
-52.13265306
87.55612245
31.04081633
29
91.35714286
92.42857143
0
0
0
30
91.35714286
92.42857143
0
0
0
31
91.35714286
92.42857143
0
0
0
32
91.35714286
92.42857143
0
0
0
91.35714286
92.42857143
0
0
0
1491.714286
5972.428571
1892.857143
77.28148919
43.50697809
91.35714286
Total sum
Image Source: “Skbekas”
• Putting all of the data into the
Pearson equation, I receive a
value of approximately 0.44. For
my sample size (thousands of
points; only 32 bins), I think this
means that there is a statistically
significant correlation between
the two data sets.
92.42857143
0
Denominator
3362.284057
Final result
0.443660994
Image Source: NASA
18
ALTERING THE PROCEDURE
• Experimental changes may add precision to my data and thus
make it easier to confirm the observed trend in a second data
run.
• It’s possible that orienting the detectors directly toward the
ecliptic will de-munge (reveal the true patterns in) the data.
By placing the detectors further apart, and pointing them at
the ecliptic (72 degrees in July), I’ll be able to reduce the
solid angle of the sky and reduce the disparity in terms of
units and scale between the two data sets. This may also
increase my R-value from the PPMCC test, helping confirm
my correlation; or, it could make a false correlation
disappear.
19
Image Source: collidingparticles.com
EXPERIMENTAL SETUP, SECOND EDITION
Box height = 21 cm
Top scintillator
Central box to reduce
solid angle
Angle of 72 degrees
to point toward
ecliptic.
20
Image Source: collidingparticles.com
After running the detector for three days, with all the scintillators
stacked according to the 2nd Edition Experimental Setup, I
receive the graph above. It also shows no day/night cycle.
21
INTERPRETING RESULTS – 2ND EXPERIMENT
How well do our data correlate this time?
Flux Density
Flux Speed
Flux Temperature
Image Sources: NASA, NOAA
22
NOTES ON MY 2ND DATA FIT
23
The data do not seem to support as strong a correlation this time.
Visually, my adjusted data gives the following conclusions: 21 of my 32 (66%) 2-hour averages appear to be
within one standard deviation of the SOHO data; seven are within two standard deviations; and four lie
outside two standard deviations.
Once again, this graph was not produced without a few statistical adjustments (see below).
Proton density
is measured
logarithmically
(same scale as
before)
But muon flux’s y-axis is
measured linearly, from a
flux of 2600 to 2750
events/m2/minute. (Yes, the
flux went down.)
The scale is offset once again
by one hour, because these
protons take longer to reach
the earth than the satellite
PEARSON TEST, 2ND EXPERIMENT
𝑹=
𝒏
𝒊=𝟏(𝑿𝒊 −𝑿)(𝒀𝒊 −𝒀)
𝒏
𝟐
𝒊=𝟏(𝑿𝒊 −𝑿) ∗
𝒏(𝒀 −𝒀)𝟐
𝟏 𝒊
on the data set gives us a value of about -0.12, which is not
all that statistically significant for my sample size, and definitely does not indicate
a positive correlation. It could indicate a very, very slight negative correlation.
Image Source: “Skbekas”
24
The second experiment (euphemistically) doesn’t look as well
correlated as the first did.
• It’s possible that the first result was unusual and that a re-run of the
first experiment would not indicate a correlation with the solar wind
density.
• It’s also possible that the second half of the second experiment was
atypical due to unexplained phenomena.
• It’s possible that poorly controlled variables in the second
experiment impacted the results. From a visual inspection, the
experimental setup may have sagged by about 2 cm over time,
which could have put the detectors out of alignment and caused the
steady downward trend in flux during the second half of the data
run. I wasn’t able to verify if that occurred or not.
• In the second experiment, increasing the distance between
detectors reduced the overall flux by about 2/3; it likely reduced the
signal-to-noise ratio by that amount.
25
Image Source: NASA
FURTHER RESEARCH
This experiment’s conclusion is not terribly strong: a correlation observed using
one experimental technique disappeared when the technique was altered. If I had
more time and resources, I would do more data runs using the first experimental
setup to see if the correlation observed was a statistical blip or whether it was a
consistent finding. Then, I would do more data runs using the second
experimental setup (but perhaps one manufactured to greater precision) to see if
I could verify the disparity between the two setups.
Image Source: NASA
26
CONCLUSION
•
I cannot yet make a conclusion about whether the terrestrial muon flux is
correlated with the solar wind density in space, because I found contradictory
results.
•
I can conclude that there is no direct correlation between the terrestrial muon flux
and the day/night cycle, at least as observed in this experiment.
27
THANKS FOR WATCHING!
Special thanks to:
Stuart Briber
Vicki Johnson
Jason Nielsen
Tanmayi Sai
Brendan Wells
the speakers
& my fellow interns
28
Image Source: DeviantArt (user: TrekkieTe