USE OF NEURAL NETWORKS TO CLASSIFY COSMIC-RAY
SHOWERS ACCORDING TO THEIR MUON/EM RATIO*
H. SALAZAR AND L. VILLASEÑOR†
Facultad de Ciencias Físico-Matemáticas, BUAP,
Puebla Pue., 72570, México
The ratio of muon/EM (/EM) in extensive air showers (EAS) is an
important parameter to measure the primary mass of cosmic rays.
The existence of very strong correlations among amplitude, charge
deposition, 10%-90% and 10%-50% rise-times for isolated electrons,
isolated muons and extensive air showers in a water Cherenkov
detector allows one to separate cleanly these components by using
simple cuts in the bi-dimensional parameter space of amplitude vs
rise-time. We used these signals to form artificial traces for EAS by
adding pre-determined numbers of real electron and muon traces to
form showers with known values of /EM. Real EAS data were best
reproduced this way by using exponential arrival times for electrons
and muons with decay values narrowly distributed around 15 ns for
muons and 25 ns electrons. The artificial EAS were in turn used to
train Kohonen neural networks with the aim to classify EAS events
according to their /EM ratio. We found that neural networks are able
to classify EAS in a better-than- random way, encouraging further
work along this direction.
1. Introduction
The measurement of /EM, i.e., the muon contents relative to the
electromagnetic (electrons, positrons and photons) contents of extensive air
showers, at each of the ground stations of giant arrays of water Cherenkov
detectors, such as the Pierre Auger Observatory [1], allows in principle a
measurement of the composition of primary cosmic rays. Simulation of EAS of
ultra high energy show that extensive air showers initiated by Fe nuclei have
*
†
This work was partially supported by Coordinación de la Investigación Científica-UMSNH,
Vicerectoria de Investigación-BUAP and CONACyT projects G32739-E and G38706-E.
On leave of absence from Instituto de Física y Matemáticas, Universidad Michoacana de San
Nicolás de Hidalgo, Morelia Mich., 58040, México.
around 50% more muons at ground level than proton-initiated EAS of cosmicray primaries of the same energy; in turn gamma primaries produce less muons,
for the same energy of the primary cosmic rays. In the case of a hybrid cosmicray detector, such as the Pierre Auger Observatory, /EM, along with the shower
maximum of the EAS, as measured with fluorescence telescopes, are the main
parameters for measuring composition of cosmic rays with energies around 10 20
eV.
2. Results and Discussion
In previous papers we have reported on the charge deposition of electrons from
muon decays in a water Cherenkov detector [2], and we have demonstrated that
by doing precise measurements of the amplitude, charge and rise-time of the
signals taken with the same detector in an inclusive sample of secondary cosmic
rays, we can easily identify isolated electrons, isolated muons and extensive air
showers [3], see Figure 1. Identification of the signals for isolated electrons and
muons, see Fig. 2, permits one to form artificial signals for EAS by adding predetermined numbers of real electron and muon traces to form shower traces with
known values of /EM. These artificial signatures for EAS can in turn be used to
train specific neural networks with the aim to use them to classify real EAS
according to their /EM ratio. The obvious advantadge of using real electron and
muon signals is that one does not have to rely on simulations of the detector
response to muons, electrons and EAS.
By summing the real signal traces of electrons and muons, an example of
which is shown in Fig. 2, for varying numbers of electrons and muons we formed
artificial EAS with known contents of muons and electrons. For the purpose of
using a specific set of EAS, we selected a real EAS data sample with a mean
charge of 8 VEM from our inclusive muon data, see Fig. 1. Then we formed
artificial EAS in three categories: 8+0e, 4+33e and 0+66e by using 8, 4 or 0
muon and 0, 33 or 66 electron traces from a database formed with thousands of
real traces of isolated electrons and isolated muons as shown in Fig. 1. The
number of muons and electrons in the artificial EAS were chosen to make the
mean values of these artificial EAS equal to the 8 VEM value of real EAS. The
mean values for the amplitude, 10-50% and 10-90% rise-times were 1.160.08
V, 16.7 a 0.9 ns and 50.82.0 ns, respectively. We found out that the mean
values of the amplitude, 10-50% and 10-90% rise-times for the signals of the
artificial EAS formed were very sensitive to the arrival time distributions used to
combine the electron and muon signals. The corresponding values of real data
were reproduced best by using exponential arrival times for electrons and muons
with decay values narrowly distributed around 15 ns for muons and 25 ns
electrons.
Figure 1. Amplitude vs rise-time from 10% to 50% for signals from a water Cherenkov detector
taken with an inclusive trigger with an amplitude threshold of 30 mV. Simple cuts on this plot allow
one to separate isolated electrons and isolatated muons whose traces are subsequently used to form
artificial shower signals which, in turn, are used to train neural networks to classify EAS acording to
their /EM ratio.
Figure 2. Typical oscilloscope traces for an isolated electron, with a typical charge of around 0.12
VEM and rise time 10-50% of around 5 ns; an isolated muon with typical charge of around 1 VEM
and rise time 10-50% of around 12 ns; and an extensive air shower with a charge of 8.2 VEM and a
rise time 10-50% of 15 ns.
1
2
This first result is in agreement with the known fact that on average muons
arrive first than electrons. Since the charge was matched in the artificial and real
EAS, we used only the 10-50% rise time, 10-90% rise time, amplitude and
AC/DC, as the primary features in the classification process of EAS. We used
Kohonen neural networks with these four features as input parameters and
different numbers of dimensions and of neurons per dimension. We found that
the network that gives the highest rate of correct classification has two
dimensions with 8 neurons in the first dimension and 4 neurons in the second
dimension. We trained each of such neural networks with sets of 100 artificial
traces for each category and then measured the rate of correct identification on
different sets of 100 traces. Table 1 shows the results for the classification into
two distinct categories labeled 8+0e and 4+33e. Likewise, table 2 shows the
results for the classification into two distinct categories labeled 8+0e and
0+66e. As seen from these tables, neural networks classify in a way which is
better than random, i.e., the diagonal numbers are higher than 50% and the offdiagonal lower than 50%. In addition, we get the result that real data samples run
into the trained neural networks are classified as containing mostly muons.
Table 1. Classification results of EAS trained by using artificial EAS
with 8+0e and 4+33e. The numbers correspond to the percentage of
times an EAS of the type given by the first raw is identified as an EAS
of the type given by the left colum.
EAS Type
8+0e
4+33e
8+0e
68%
32%
4+33e
36%
64%
Data
75%
25%
Table 2. Classification results of EAS trained by using artificial EAS
with 8+0e and 0+66e. The numbers correspond to the percentage of
times an EAS of the type given by the first raw is identified as an EAS
of the type given by the left colum.
EAS Type
8+0e
0+66e
8+0e
84%
16%
0+66e
17%
83%
Data
84%
16%
Table 3 shows the results for the classification into three distinct categories
labeled 8+0e, 4+33e and 0+66e. In this case the neural network has a worse
than average value for the classification of events of the intermediate category,
4+33e, although it stills works reasonably well for the other extreme categories,
i.e., 8+0e and 0+66e. Again the real EAS data run into the trained neural
3
network are classified as containing mostly events of the muon-rich 8+0e
category.
Table 3. Classification results of EAS trained by using artificial EAS
with 8+0e, 4+33e and 0+66e. The numbers correspond to the
percentage of times an EAS of the type given by the first raw is
identified as an EAS of the type given by the left colum.
EAS Type
8+0e
4+33e
0+66e
3.
8+0e
70%
16%
14%
4+33e
36%
25%
39%
0+66e
7%
15%
78%
Data
70%
19%
11%
Conclusion
We have used simple cuts in the bi-dimensional parameter space of amplitude vs
rise-time, see Fig. 1, to identify signals due to isolated electrons and isolated
muons, as well as low energy EAS, see Fig.2. We have used these signals to form
artificial traces for EAS by adding pre-determined numbers of real electron and muon
traces to form shower traces with known values of /EM. These artificial signatures for
EAS were in turn used to train Kohonen neural networks with the aim to classify EAS
events according to their /EM value. We found out that the mean values of the
amplitude, 10-50% and 10-90% rise-times for the artificial EAS formed were very
sensitive to the arrival time distributions used to combine the electron and muon traces.
The real data values were best reproduced by using exponential arrival times for electrons
and muons with decay values narrowly distributed around 15 ns for muons and 25 ns
electrons. We found that the network that gives the highest rate of correct classification
has two dimensions with 8 neurons in the first dimension and 4 in the second. As shown
in tables 1-3, neural networks classify in a way which is better than random and
encourage further work along this direction.
References
1. Pierre Auger Project Design Report, http://www.auger.org/admin/
DesignReport/index.html, 230 p (revised 1997).
2. Y. Jeronimo, H. Salazar, C. Vargas and L. Villaseñor, Proc. of the Tenth
Mexican School on Particles and Fields, U. Cotti et al. (eds.), AIP Conf.
Proc. 670, 479-486 (2003).
3. M. Alarcón et al., Nucl. Instr. and Meth. in Phys. Res. A. 420 [1-2], 39-47
(1999).