Our
objectives were to determine whether the sun without sunspots effects the
production of muons in the ionosphere and to determine if increases in solar
activity (as measured by observation of sunspots) increases muon production or
disrupts the geomagnetic field.
We collected our muon data from alternating periods of day and night to test
the sun's influence on the number of muons produced. We assume that during
night hours, muons are produced at a constant rate from cosmic rays created as
a result of events in space such as supernovas, etc. We call this constant
Rb. During daytime, the total uv and cosmic radiation incident on
the earth's atmosphere is Rb plus the additional radiation with
sufficiently high energy from by the sun. This additional solar radiation is
Rs. Our goal, then, is to find Rs. What effect does the
sun have on the amount of particles entering our atmosphere? We found the
answer by using the following equation (Equation 4).
| N = T*Rb + D*Rs | (Equation 4) |
In
Equation 4, N is the total number of muons counted in T number of total
recording minutes, Rb is the constant rate of muons being created
by extra-solar events, D is the number of daylight recording minutes and
Rs is the rate of muons created by solar radiation.
So, to find Rs, we must first define our constant Rb. To
do this we ran a "night only" trial where muon production cannot be affected by
the sun. To obtain this value for Rs, we recorded muons for a
period of 8 hours during one night and 6 hours the next. We found a total
number of 4540 muons. We then divided by the total recording time (839
minutes) to find Rb (5.4 muons/minute). We then used this value to
calculate Rs for each recording period.
We correlate the planetary A index in a similar way. However, Rb
represents the background flux of charged particles (not necessarily cosmic
radiation) and background uv radiation. Rs likewise represents the
flux of charged particles from the sun (solar wind) and the amount of uv
radiation from the sun.
| Ap = y*Fb + x*Fs | (Equation 5) |
In
Equation 5, Ap is the planetary A index, Fb is the rate
that extra-solar occurrences influence the Ap index for y total
recording minutes and Fs is the rate solar radiation affects the
Ap index for
x number of daylight minutes.
For planetary A index evaluation, we do not need to discern differences between
day and night because the planetary A index is recorded on a 24-hour interval.
The same holds for the Sunspot number. If we record the muon flux for a period
that spans two days, we use the
A index associated with the day in which
most muons were counted (e.g. if we record from
8 p.m. on July 24 to 6 a.m.
July 25, we use the A index and Sunspot Number for July 25).
For
every muon counting interval with N events, the error associated with our
measurement is given by
.
Thus, the precision of our measurements increase as the square root of the
number of events recorded. Because Rs and Rb are rates
of muon flux, we give the error [sigma] as a rate where T1 is the
total minutes of the first recording and T2 is the total minutes
from the second. We then calculate the error through standard error
propagation techniques.
[sigma]rb=
|
(Equation 6) |
Likewise, every event that we measure has an error of
[sigma]rs+rb=
|
(Equation 7) |
Equation 7 was used to calculate the error in our combined rate measurements.
We
plotted the daytime rate of muon production (Rs), the Planetary A
index and Sunspot Number versus time to look for correlation between these
quantities.
The error bars in our muon flux measurements were determined from our error
equations (see equations).
The
graph in Figure 4 shows the sunspot number versus time for the time duration of
our experiment. We gathered the sunspot data from The National Oceanic and
Atmospheric Administration at www.sec.noaa.gov. Because of poor weather in
Pittsburgh, especially heavy cloud cover, we were unable to directly observe
any sunspots with our telescope during the program.
In Figure 5, we plotted sunspot number and Planetary A index vs. time in order
to find whether there is a meaningful correlation between sunspot activity and
Planetary A index.
The
muon levels used to calculate flux in Figure 6 on the pervious page were
gathered by our muon counter which ran continuously and was checked twice a day
throughout the weeks of our experiment. Flux for a given date calculated by
dividing the number of muons detected by the number of minutes the counter was
running. We observed no significant differences in muon fluxes in day and
night. This implies that the muon production is not influenced by the presence
of the sun.
The flux expansion in Figure 7 is simply the values we obtained for muon flux multiplied by a factor of 15 and displaced so we could more easily see and compare variations in flux with variations in sunspot number.
Because there was no way to establish quantitative correlation between our variables, we had to rely on qualitative estimates of one variable's effect on another. We conclude that sunspots do not influence the Planetary A index in any consistent way. We also observe no correlation between sunspots and muon flux. This analysis is based on two graphs: one plotting sunspots and muon flux (Figure 7) and one comparing the muon flux during the day and during the night (Figure 6). Since there was no effect of sun on muon flux values, we were able to conclude that sunspots do not influence muon flux. Furthermore, since the sun itself did not influence muon levels, it follows that sunspots would not have any effect on muon production.