Simulation for CHICOS (California HIgh school Cosmic ray ObServatory) Kwan-yuet Ho Department of Physics, the Chinese University of Hong Kong Supervisor: Professor Robert D. McKeown Kellogg Radiation Laboratory, California Institute of Technology September 2003 Abstract CHICOS (California HIgh school Cosmic ray ObServatory) is a project that detect the air shower particles in the atmosphere that is caused by the cosmic rays of energy greater than 1020 eV. I report on my simulation work for the project in summer 2003, including the statistical pattern for CIT1000 array and the energy spectrum of the detected showers. On the other hand, I have also calculated the neutron flux detected by a detector which is placed 20 m away from the axis of a vertical proton shower.

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Contents 1 Introduction

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2 Simulation of Showers without Thinning

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3 Energy Spectrum of the Detected Number of Showers for CIT1000 4 Statistics of CIT1000 4.1 Single Triggers for CIT1000 . . . . . . . . . . . . . . . . . . . . . 4.2 Double Triggers for CIT1000 and Caltech03 . . . . . . . . . . . .

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5 Neutron flux due to vertical proton shower

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6 Conclusion

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7 Acknowledgement

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Introduction

There are a lot of energetic particles coming from the universe into the Earth’s atmosphere every day. After invading into the atmosphere, they interact with the particles in the atmosphere and generate other particles which we call the secondary particles. Since they are numerous and spread over an area, we say these particles forming an extended air shower. The shower includes particles like protons, electrons, positrons, pions (π + , π − , π 0 ), muons (µ) etc. [7] The CHICOS (California HIgh school Cosmic ray ObServatory) project is collaborated by the California Institute of Technology (Caltech), University of California, Irvine (UC Irvine), California State University, Northwridge (CSUN) and the students and teachers in the Los Angeles high schools. Detectors are installed in the high school infrastructure in the San Fernando Valley and the San Gabriel Valley. There are computers connected with each detector site and data collected every day are sent to the server at Caltech regularly for analysis. [1] [2] [4] I worked on the project in the Kellogg Radiation Laboratory in Caltech from 16th June, 2003 to 21st, August, 2003. My work was mainly on simulation. I study mainly study the detected patterns for a CHICOS detector array called CIT1000, which is formed by a 4x3 arrays of shmoo (CHICOS detector), each separated by 3 m.

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Simulation of Showers without Thinning

A simulation program called AIRES (Air Shower Extension Simulation), developed by S. J. Sciutto, was used. It takes in some parameters such as the primary particles, primary energies, thinning energies (for optimization of the simulation), zenith angles etc. of the incoming showers coming to the Earth, and simulates how the showers evolve in the Earth’s atmosphere. The interactions that are considered in the simulation are: • Electrodynamical processes: 1. Pair production and electron-positron annihilation 2. Bremsstrahlung (electrons and positrons) 3. Muon bremstrahlung and muonic pair production 4. Emission of ”knock-on” electrons (δ rays) 5. Comptom and photoelectric effects 6. LPM effect and dielectric suppression • Hadronic processes: 1. Inelastic collisions hadron-nucleus 2. Photonuclear reactions 3. Nuclear fragmentation, elastic and inelastic • Unstable particle decays • Particle propagation 1. Medium energy losses (ionization) 2. Coulomb and multiple scattering The atmospheric model applied here is the Linsley’s model, which has been studied over many years in the research field. The simulation of AIRES is computationally expensive, and optimization algorithm are included in the simulation, where this algorithm is called thinning [3]. The hadronic model used here is the QGSJET model (quark-gluon-string jet model). In our simulation, collarated with Chao Zhang (a graduate student in Caltech) and Barbara Falkowski (a graduate student in CSUN), thinning is turned off. In short, we have simulated showers with primary particles, namely proton and iron atom, with energies 1.0 × 1013 , 2.0 × 1013 , 5.0 × 1013 , 1.0 × 1014 , 2.0 × 1014 , 5.0 × 1014 , 1.0 × 1015 , 2.0 × 1015 , 5.0 × 1015 , 1.0 × 1016 , 2.0 × 1016 , 5.0 × 1016 , 1.0 × 1017 , 2.0 × 1017 and 5.0 × 1017 eV (if you take log on the energies, they lie on a linear line), and with zenith angles (in degrees) 0.0, 25.8, 36.9, 45.6 and 53.1 (with their cosines equal to 1.0, 0.9, 0.8, 0.7 and 0.6 respectively). After simulation, a program (written by M. Takeda) was used to extract data from the simulation result to look at its distribution of particles in a region of 600 m × 600 m due to that shower. The particles that we are looking at are γ photons, electrons, positrons, positive muons (µ+ ), negative muons (µ− ) and hadrons (including pions (π + , π − , π 0 ), Kaons (K), eta particles (η), neutrons and protons [3]). [8] 4

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Energy Spectrum of the Detected Number of Showers for CIT1000

The observed spectrum of primary cosmic rays is given by the following formulae [1] [5] [6]: d4 N n E −2.7 = { 1 −3 n2 E dEdΩdtdA

(1)

where n1 is 1.58489 × 1020 and n2 is 1 × 1025 , which have appropriate units. N is the number of primary particles reaching the ground, E is the energy of the primary particles, Ω is the solid angle that is occupied by the shower, t is the time and A is the area that we are considering. It gives the number of primary particles hitting on the ground per m2 area per steradian per second per eV. We were interested also in the formula that gives the detected (using CIT1000) number of primary particles hitting on the ground per day per eV. Therefore, we have to calculate the following integral: d2 N measured = 2π dEdt

Z

Z

1

0

Z

∞

d cos θ

∞

dx −∞

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dyP (E, θ, x) −∞

d4 N dEdΩdtdA

(2)

d N where the factor dEdΩdtdA is the flux given by equation (1). N measured is the number of detected primary particles by CIT1000 and P (E, θ, x) is the probability of the shower triggering any pair of CIT1000 detectors, where by trigger we means both in the pair of CHICOS detector (shmoo) have 2 events or more. After calculating the integral for different energies specified in section 2 measured 2, the energy spectra of d N dEdt for proton shower and iron shower are as shown in figures 1 and 2. Two graphs were put together as shown in figure 3 for comparison. It is shown that for proton and iron showers with primary particles with lower energies (1013 or 1014 eV) differ more in the detected numbers, but both kind of showers differ less for those with primary particles are of higher energies (above 1016 eV).

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Figure 1: Energy spectrum of

d2 N measured dEdt

Figure 2: Energy spectrum of

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for proton shower

d2 N measured dEdt

for iron shower

Figure 3: Energy spectrum of

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d2 N measured dEdt

for both proton and iron showers

Statistics of CIT1000

There are many air showers every day that trigger the central pair of CIT1000 array (this pair of detectors is named as CIT1001). Studies of the statistical patterns in CIT1000 if all showers are proton showers or iron showers have been done extensively.

4.1

Single Triggers for CIT1000

We have used all the data from the simulation described in section 2, and simulated what the statistical pattern of the showers that trigger CIT1001 in one day will be like if the numbers of showers of different energies and zenith angles follow the power law (equation 1). Figures 4 and 5 are the scatter plots of all the data that trigger CIT1001 for proton and iron showers respectively. The horizontal axis is called nsum, which is the sum of the events of all the 12 detectors in CIT1000, while the vertical axis is the standard deviation of the number of events of the 12 detectors divided by the corresponding mean (usually called the sigma over mean, or nσ ). From the two scatter plots, it is evident that the number of proton showers that can trigger CIT1001 is larger than that of iron showers. It is suspected that it is because iron atoms start to decompose in higher atmosphere than the protons do, or the 56 nucleons in an 1 of that of iron atom with same energy of a proton have only approximately 56 a proton, causing it to be less energetic to trigger CIT1001. It is better to do the comparison between proton and iron showers using the profile plots, with vertical axis the mean of the sigma over mean for the same nsum, as shown in figures 6 and 7. The error bars are the standard deviation of the sigma over mean for that bunch of nsum. You can see that there is correlation between the average of the sigma over mean and the values of nsum between the profile plots for proton shower and that for iron shower. Or to put this conclusion more quantitatively, the data for the two profile plots (figures 6 and 7) are subtracted (that for proton shower minus that for iron shower) to give figure 8, and the corresponding percentage difference is plotted as shown in 7

Figure 4: Scatter plot for the proton shower of primary energy from 1013 eV to 1017 eV

Figure 5: Scatter plot for the iron shower of primary energy from 1013 eV to 1017 eV

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Figure 6: Profile plot for the proton shower of primary energy from 1013 eV to 1017 eV for single trigger of CIT1001 figure 9. (The percentage difference means the difference divided by the average of the sigma over mean of proton and iron showers. There are some data of value 2.0 because for those nsum, there are data for proton showers but not for iron showers.)

4.2

Double Triggers for CIT1000 and Caltech03

In the previous section we were considering the trigger of CIT1001 only. It is regarded as single trigger for CIT1001 if both detectors of the pair of shmoo of CIT1001 only have two events or above. And we have also studied the double trigger for CIT1001 and Caltech03 (a pair of detector which is 96.48 m north and 51.03 m east of CIT1001 [2]), which means both pairs of CIT1001 and Caltech03 are triggered. Figures 10 and 11 are the scatter plots (similar to those in section 4.1)of the proton and iron showers respectively for double triggers for CIT1001 and Caltech03 for 100 days. Their corresponding profile plots are made as shown in figures 12 and 13 for proton and iron showers respectively. You can see that there is no correlation between the average of the sigma over mean and the values of nsum between the profile plots for proton shower and that for iron shower. It seems to be a random fluctuations only. Or to put this conclusion more quantitatively, the data for the two profile plots (figures 12 and 13) are subtracted (that for proton shower minus that for iron shower) to give figure 14, and the corresponding percentage difference is plotted as shown in figure 15.

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Figure 7: Scatter plot for the iron shower of primary energy from 1013 eV to 1017 eV for single trigger of CIT1001

Figure 8: Difference of the average of the sigma over mean between the proton and iron showers of primary energy from 1013 eV to 1017 eV for single trigger of CIT1001

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Figure 9: Percentage difference of the average of the sigma over mean between the proton and iron showers of primary energy from 1013 eV to 1017 eV for single trigger of CIT1001

Figure 10: Scatter plot for the proton shower of primary energy from 1013 eV to 1017 eV for double trigger for CIT1001 and Caltech03

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Figure 11: Scatter plot for the iron shower of primary energy from 1013 eV to 1017 eV for double trigger for CIT1001 and Caltech03

Figure 12: Profile plot for the proton shower of primary energy from 1013 eV to 1017 eV for double trigger for CIT1001 and Caltech03

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Figure 13: Profile plot for the iron shower of primary energy from 1013 eV to 1017 eV for double trigger for CIT1001 and Caltech03

Figure 14: Difference of the average of the sigma over mean between the proton and iron showers of primary energy from 1013 eV to 1017 eV for double trigger for CIT1001 and Caltech03

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Figure 15: Percentage difference of the average of the sigma over mean between the proton and iron showers of primary energy from 1013 eV to 1017 eV for double trigger for CIT1001 and Caltech03

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Neutron flux due to vertical proton shower

This section has little relationship with the stuff that is discussed in the previous sections. For sake of this section, I have generated a number of proton showers again using AIRES with region of radius 100 m considered for primary energies 1.0 × 1015 , 2.0 × 1015 , 5.0 × 1015 , 1.0 × 1016 , 2.0 × 1016 , 5.0 × 1016 , 1.0 × 1017 and 2.0 × 1017 eV (all vertical). The radial distributions γ photons of energies between 20 MeV and 26 MeV (the function is denoted as nγ (r), the number of neutrons due to one shower per unit area) are plotted as shown in figures 16 23. The neutron flux can be evaluated from the radial distribution of γ photons within the energy range by the following integral: Z

Nneutrons (r0 ) = =

Z

∞

Z

∞

2π

6 × 102 3 nγ (r)r − λR e n σnγ · 10−3 (3) 2 4πR 14 0 0 0 Z ∞ Z ∞ Z 2π nγ (r)r − λR −6 4.1 × 10 dz dr dθ e n (4) R2 0 0 0 dz

dr

dθ

where σnγ = 12mb = 1.2 × 10−26 cm2 and λn = 200m (All numerical values in the above integral are in SI units), and R is defined by p R = ρ2 + z 2 (5) and ρ is got from the cosine formula q ρ = r2 + r02 − 2rr0 cos θ

(6)

where r0 is taken to be 20 m, which is the distance between the detector and the shower axis.

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Figure 16: Radial distribution of γ photons due to a vertical proton shower with primary energy 1.0 × 1015 eV

Figure 17: Radial distribution of γ photons due to a vertical proton shower with primary energy 2.0 × 1015 eV

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Figure 18: Radial distribution of γ photons due to a vertical proton shower with primary energy 5.0 × 1015 eV

Figure 19: Radial distribution of γ photons due to a vertical proton shower with primary energy 1.0 × 1016 eV

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Figure 20: Radial distribution of γ photons due to a vertical proton shower with primary energy 2.0 × 1016 eV

Figure 21: Radial distribution of γ photons due to a vertical proton shower with primary energy 5.0 × 1016 eV

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Figure 22: Radial distribution of γ photons due to a vertical proton shower with primary energy 1.0 × 1017 eV

Figure 23: Radial distribution of γ photons due to a vertical proton shower with primary energy 2.0 × 1017 eV

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The neutron fluxes due to each proton shower is calculated using the integral in equation 3 and also the result of the AIRES simulation, and the result is tabulated below. The second column is the neutron flux detected at a location 20 m away from the axis of the vertical proton shower of primary energy given by the first column. The flux are in general very small. Primary energy (eV) Neutron flux (m−2 ) 1.0 × 1015 0.00291542 2.0 × 1015 0.00518402 5.0 × 1015 0.02633306 1.0 × 1016 0.05706257 2.0 × 1016 0.20165373 5.0 × 1016 0.50940608 1.0 × 1017 1.05327981 2.0 × 1017 1.97554670

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Conclusion

In this report, I have reported the simulation of proton and iron showers using AIRES without thinning, and using the simulated data to get the energy spectrum of the detected number of showers (using CIT1000) in one day and the statistical patterns of detected data in CIT1000 for single trigger for CIT1001 arrays and also that for double trigger for CIT1001 and Caltech03. And I have also reported the calculation of neutron flux due to γ photons of energies between 20 MeV and 26 MeV from the vertical proton shower.

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Acknowledgement

I would like to thank Professor Robert Mckeown for offering me such a good opportunity to learn to do research and broaden my horizon throughout this project. I would like to also thank Chao Zhang, who has spent so much valuable time to teach me about the knowledge of this project and to guide me whenever I encounter any difficulties. I would thank Dr. Michelle Larson, who is really a good project coordinator, for cheering up our morale and encouraging us. I would thank Dr. Christopher Jillings for giving me useful advice for some calculation puzzles. Finally, I would like to thank the Department of Physics of the Chinese University of Hong Kong, the organizer of SURE (Summer Undergraduate Research Exchange) Programme, offering me the opportunity to come to Caltech and financially supporting me.

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References [1] M. Swanson, Observing Ultra High Energy Cosmic Rays: The California HIgh school Cosmic ray ObServatory (CHICOS), May 2002. [2] Webpage: http://www.chicos.caltech.edu/ [3] S. J. Sciutto, AIRES: A system for air shower simulations, User’s guide and reference manual Version 2.4.0, October 2001. [4] R. D. McKeown, Technical Specifications for Detector Sites, September 2001. [5] M. Nagano, A. A. Watson, ”Observations and implications of the ultrahigh-energy cosmic rays” Rev. Mod. Phys. 72, 689-732, July 2000. [6] J. W. Cronin, ”Cosmic rays: the most energetic particles in the universe” Rev. Mod. Phys. 71: S165-S172 Sp. Iss. (March 1999) [7] R. D. Mckeown, Cosmic Rays: From Stellar Explosions to Biological Diversity. [8] K. Y. Ho, Documentation on the Simulation Work for CHICOS, Aug 2003.

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