Signatures for showers:
             Shower Characteristics

                                 R. Vazquez, USC



Trasgo me...
Extensive Air Showers iniated by Cosmic Rays have
intrinsic characteristics:

Size, timing, energies, densities, and rates...
Cosmic ray showers: Heitler model
                    Energy Number of particles Depth

                      E          1...
This simple model works well even for realistic MC.

 If the multipliticy depends on energy

          µ = KE       δ



 ...
For a nucleus primary one may apply the superposition model

     Nucleus of energy E, mass A = A nucleons of energy E/A

...
Number of charged particles as a function of energy




Nmax ~ E
           Differences between composition and hadronic m...
Kascade

                                                          Auger



                                              ...
Longitudinal profile


Near the maximum fluctuations
are smaller. Fluctuations do not
scale with energy




              ...
π0 →γγ
                 Muonic component                                     π± →µ ν
π0 decay instantly              π± co...
Seen in realistic
MC

QGSJET Proton




    Slope ≈0.9
    independent of θ
Casa-Mia
Data



           AGASA
Lateral Spread of the Shower




Shower shape depends on the development stage
t = log(x)
y = log(E)
Timing



For muons timing is
well understood. It is
related to the height
production distribution    <t> = 250 ns σ= 210 ...
Muon height production depends on the composition. It could be used,
in principle, as a handle to determine composition.

...
For electrons, the arrival time distribution is poorly understood

              Structure
              on µs
           ...
Timing II: Uncertainties   Core uncertainties
                           induce timing uncertainties




                 ...
Relativistic effects


A muon with E ~ 1 GeV
has γ ~ 10 and 1-β ~ 5
10-3
                                    Then after x ...
Rates


Accidental trigger rate
                                      The rate of accidental triggers
Assume a time window...
dN = KE −γ
dE

γ~ 2.7




             Cosmic ray spectrum compilation
Rates
                                     F ~ E-γ+1
The shower rate is given by
R ~ Flux d2

R = B E-γ+1 d2

R ~ 7.4 108 ...
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R Vazquez Showers Signatures

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R Vazquez Showers Signatures

  1. 1. Signatures for showers: Shower Characteristics R. Vazquez, USC Trasgo meeting, February 2010. Santiago de Compostela
  2. 2. Extensive Air Showers iniated by Cosmic Rays have intrinsic characteristics: Size, timing, energies, densities, and rates are intrinsic to the shower and must be taken into account in the design of cosmic ray detectors. The ability to determine physical parameters from extensive air showers depends on the correct interpretation of these characteristics. Arrival direction Energy Chemical composition Hadronic interactions
  3. 3. Cosmic ray showers: Heitler model Energy Number of particles Depth E 1 0 E/2 2 λ E/4 4 2λ After n steps Ec= E/2n 2n Xmax= n λ Then : Xmax = λ log(E/Ec) and N~E
  4. 4. This simple model works well even for realistic MC. If the multipliticy depends on energy µ = KE δ Then X max = A(1− δ ) log(E / Ec ) + B However: Assuming perfect scaling. -Only forward region is relevant
  5. 5. For a nucleus primary one may apply the superposition model Nucleus of energy E, mass A = A nucleons of energy E/A X max (E , A) = λ log(E /( AEc )) = λ log(E ) + B Hadronic model dependence Composition dependence J. Knapp
  6. 6. Number of charged particles as a function of energy Nmax ~ E Differences between composition and hadronic models
  7. 7. Kascade Auger Argo The altitude of the experiment determine the energy range!!!
  8. 8. Longitudinal profile Near the maximum fluctuations are smaller. Fluctuations do not scale with energy 15 % 4%
  9. 9. π0 →γγ Muonic component π± →µ ν π0 decay instantly π± continue the cascade N 2N N= total π0 π± 3 3 multiplicity N (1+ 2 N ) 3 3 π0 π± ( 2N ) 2 γ 3 N2 After n steps, charged pions decay N ± = ( 2N )n E 3 Where E c = n N N µ = ( E )1+ log(2 / 3 ) / log(N ) ∝ E β E c β ≅ 0.8 − 0.9 1− β β For nucleus N µ (E , A) = AN (E / A) = A E
  10. 10. Seen in realistic MC QGSJET Proton Slope ≈0.9 independent of θ
  11. 11. Casa-Mia Data AGASA
  12. 12. Lateral Spread of the Shower Shower shape depends on the development stage
  13. 13. t = log(x) y = log(E)
  14. 14. Timing For muons timing is well understood. It is related to the height production distribution <t> = 250 ns σ= 210 ns dN/dt ~ dN/dz But has an additional R dependence 1019 eV Protons <t> = 700 ns σ= 350 ns
  15. 15. Muon height production depends on the composition. It could be used, in principle, as a handle to determine composition. However fluctuations are large. Max = 306 gr/cms 1019 eV Shower Max = 337 gr/cm2 σ= 158 gr/cm2 @ 60 deg. Max = 448 gr/cm2 σ= 172 gr/cm2
  16. 16. For electrons, the arrival time distribution is poorly understood Structure on µs scale E=89 EeV Θ = 31 deg.
  17. 17. Timing II: Uncertainties Core uncertainties induce timing uncertainties For r ~ 1000 m h ~ 10 km d ~ 100 m
  18. 18. Relativistic effects A muon with E ~ 1 GeV has γ ~ 10 and 1-β ~ 5 10-3 Then after x = 1000 m Same effect for relativistic electrons
  19. 19. Rates Accidental trigger rate The rate of accidental triggers Assume a time window T, and a single station accidental rate of r is R ~ r2 T T must account for inclined shower, for instance T~ d/c The flux of random muons is given by Φ ~ 100 1/(m2 s sr) Then R ~ (Φ A)2 d/c for A ~ 1 m2 d ~ 100m R ~ 300 events/day
  20. 20. dN = KE −γ dE γ~ 2.7 Cosmic ray spectrum compilation
  21. 21. Rates F ~ E-γ+1 The shower rate is given by R ~ Flux d2 R = B E-γ+1 d2 R ~ 7.4 108 1/s (Eth/1 GeV)-γ+1 R ~ 4 103 events/day Eth = 106 GeV R ~ 80 events/day Eth = 107 GeV
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