LATERAL DISTRIBUTION FUNCTIONS OF EXTENSIVE AIR SHOWERS

1
LATERAL DISTRIBUTION FUNCTIONS OF EXTENSIVE AIR
SHOWERS

• A.Geraniosa, E. Fokitisb, S. Maltezosb, I.
  Antoniadoua and D. Koutsokostac
• (a) Physics Department, Nuclear and Particle
  Physics Section, University of Athens, Ilissia
  15771, Greece.
• (b) Physics Department, National Technical
  University of Athens, Zografos 15780, Greece
• (c) Physics Department, Section of Astrophysics,
  Astronomy and Mechanics, University of Athens,
  Ilissia 15771, Greece.

2
Introduction

• Ultra High Energy Cosmic Rays are a rare
  component of the cosmic ray spectrum
• Our aim is to study these cosmic rays and bring
  out their main characteristics (energy,
  composition, direction)
• Difficulties very low rate (1 particle per
• 1 Km2 per century)
• Solution development of detection
  techniques with large
• acceptance possibility
• PIERRE AUGER OBSERVATORY

3
Energy Estimation

• Determination of the primary energy of a UHECR
  particle is achieved by
• using the ground array (cherenkov chambers) .
• Each surface detector measures the energy
  deposit of charged particles penetrating the
  detector
• Primary energy of a cosmic particle is
  proportional to the total number of particles in
  the EAS
• Difficulties This number can not be
  measured directly!
• Second thought was to use the number of particles
  at the maximum of the shower
  6
  
  
• 
  (1)
• where Nmax the number of particles at showers
  maximum and 1.4 GeV
• the energy of each particle at maximum

4
Energy Estimation

• Difficulties We must always determinate the EAS
  maximum
• Most of the times the showers reach the
• observing levels after their maximum
• Fluctuations from event to event of equal showers
  
• Technical difficulties for the estimation of N
  particles close to the core
• Introduction of a method less sensitive to
  the position of maximum
• Hillas suggestion The fluctuations of the
  particle densities far from the core are
  smaller!! 7
• Density far from the core is quite stable ( 600
  1000 m )

5
Energy Estimation

• For the energy estimation we used the following
  equations
• 8
• 
  (2) used for the Akeno
  experiment
• conversion factor of density at 600m
• E the primary energy
• S(600) muons density at 600m from shower core
  for vertical showers
• For inclined showers the muons density at 600m is
  given by
• 
  (3)
• where Xo is the atmospheric depth and equals to
  870 g/m2 for Auger
• Experiment

6
Energy Estimation
PRIMARY PARTICLE PROTON
Figure 1
Figure 2

• LDFs are intersecting at the distance of 1100 m
  (except for zenith angle of 20 degrees)
• At this distance the LDF has not great dependence
  on the zenith angle of the shower

7
Energy Estimation
PRIMARY PARTICLE PROTON
Figure 3
Figure 4

• For logarithmic scale it seems that the LDFs
  converge at the distance of 2000m
• Far from the core and farther more than 1100m the
  dependence on the zenith angle is less
• The LDFs for electrons and positrons do not seem
  to converge

8
Energy Estimation
PRIMARY PARTICLE IRON

• The LDFs for primary particle iron show
  convergence at 1100m for only three zenith angles
  (0, 20 and 30 degrees) .

Figure 5
9
Energy Estimation
Table I PROTON
Mean Energy 1E20 eV
Table II IRON
Mean Energy 6E19 eV
10
Conclusions

• A lower primary energy has been found for iron
  than for protons (This is in agreement with the
  Alan Watson presentation in Santa Barbara,
  stating that For S(600), the energy estimates
  are LOWER if iron is assumed)
• Using the well tested expression for the AKENO
  experiment we have obtained primary energy values
  approaching the energy set by the AIRES
  simulations of 1020 eV.

11
Acknowledgements The project is co-funded by the
European Social Fund and National Resources
(EPEAEK II)Pythagoras. References 1 AUGER
Design Report (1995) 2 Greisen, K., Phys. Rev.
Lett. , 16, 748 (1966). 3 AIRES, A System for
Air Shower Simulations. S. J. Sciutto, GAP-Note
1998-005. 4 Billoir, P. GAP-Note
2002-75. 5Geranios, A., Fokitis, E., Maltezos,
S., Malandraki, O., and Antoniadou, I. Proc. 29th
ICRC 7, 155-158, (2005). 6 Hillas, A. Cosmic
Rays, Pergamon Press Oxford N. York, (1972) 7
Hillas A. et al., Proc. 12th ICRC, Hobart 3
1001 (1971). 8 Yoshida, S. Energy
Determination of trans-EeV Cosmic Rays, C. R.
Physique 5 , 483 (2004). 9 Kutter, T. The Water
Cherenkov Detector in the Auger Experiment,
Wissentschaftliche Berichte FZKA 6396,
Forschungszentrum Karlsruhe, (1999). 10 Watson,
A., KITP 5 May 2005, (conference
talks) astro-ph/0312475, 0408110, 0410514.