First energy estimates of giant air showers with help of the hybrid scheme of simulations

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First energy estimates of giant air showerswith
help of the hybrid scheme of simulations

• L.G. DedenkoM.V. Lomonosov Moscow State
  University,119992 Moscow, Russia

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CONTENT

• Introduction
• 5-level scheme
• - Monte-Carlo for leading particles
• - Transport equations for hadrons
• - Transport equations for electrons and gamma
  quanta
• - The LPM showers
• - The primary photons
• - Monte-Carlo for low energy particles in the
  real atmosphere
• - Responses of scintillator detectors
• The basic formula for estimation of energy
• The relativistic equation for a group of muons
• Results for the giant inclined shower detected at
  the Yakutsk array
• Conclusion

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ENERGY SCALE
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SPACE SCALE
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Transport equations for hadrons

• here k1,2,....m number of hadron types
• - number of hadrons k in bin
  EEdE and depth bin xxdx ?k(E)
  interaction length Bk decay constant
  Wik(E',E) energy spectra of hadrons of type k
  produced by hadrons of type i.

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The integral form

• here
• E0 energy of the primary particle Pb (E,xb)
  boundary condition xb point of interaction
  of the primary particle.

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• The decay products of neutral pions are regarded
  as a source function S?(E,x) of gamma quanta
  which give origins of electron-photon cascades in
  the atmosphere
• Here a number of
  neutral pions decayed at depth x dx with
  energies E?dE?

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• The basic cascade equations for electrons and
  photons can be written as follows
• where ?(E,t), P(E,t) the energy spectra of
  photons and electrons at the depth t ß the
• ionization losses µe, µ? the absorption
  coefficients Wb, Wp the bremsstrahlung and
• the pair production cross-sections Se, S? the
  source terms for electrons and photons.

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• The integral form
• where
• At last the solution of equations can be found by
  the method of subsequent approximations. It is
  possible to take into account the Compton effect
  and other physical processes.

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• Source functions for low energy electrons and
  gamma quanta
• xmin(E0E/e)

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Balance of energy by 1 - the primary photon 2 -
electrons 3 - photons and 4 - under threshold in
e-ph shower 5 - sum of 1,2,3 6 - total sum
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Balance of energy by 1 - the primary photon 2 -
electrons 3 - photons and 4 - under threshold in
e-ph shower 5 - sum of 1,2,3 6 - total sum
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Balance of energy by 1 - the primary photon 2 -
electrons 3 - photons and 4 - under threshold in
e-ph shower 5 - sum of 1,2,3 6 - total sum
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Balance of energy by 1 - the primary photon 2 -
electrons 3 - photons and 4 - under threshold in
e-ph shower 5 - sum of 1,2,3 6 - total sum
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Balance of energy by 1 - the primary photon 2 -
electrons 3 - photons and 4 - under threshold in
e-ph shower 5 - sum of 1,2,3 6 - total sum
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Balance of energy by 1 - the primary photon 2 -
electrons 3 - photons and 4 - under threshold in
e-ph shower 5 - sum of 1,2,3 6 - total sum
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Balance of energy by 1 - the primary photon 2 -
electrons 3 - photons and 4 - under threshold in
e-ph shower 5 - sum of 1,2,3 6 - total sum
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Balance of energy by 1 - the primary photon 2 -
electrons 3 - photons and 4 - under threshold in
e-ph shower 5 - sum of 1,2,3 6 - total sum
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Balance of energy by 1 - the primary photon 2 -
electrons 3 - photons and 4 - under threshold in
e-ph shower 5 - sum of 1,2,3 6 - total sum
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Balance of energy by 1 - the primary photon 2 -
electrons 3 - photons and 4 - under threshold in
e-ph shower 5 - sum of 1,2,3 6 - total sum
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Balance of energy by 1 - the primary photon 2 -
electrons 3 - photons and 4 - under threshold in
e-ph shower 5 - sum of 1,2,3 6 - total sum
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Balance of energy by 1 - the primary photon 2 -
electrons 3 - photons and 4 - under threshold in
e-ph shower 5 - sum of 1,2,3 6 - total sum
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Balance of energy by 1 - the primary photon 2 -
electrons 3 - photons and 4 - under threshold in
e-ph shower 5 - sum of 1,2,3 6 - total sum
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Balance of energy by 1 - the primary photon 2 -
electrons 3 - photons and 4 - under threshold in
e-ph shower 5 - sum of 1,2,3 6 - total sum
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Balance of energy by 1 - the primary photon 2 -
electrons 3 - photons and 4 - under threshold in
e-ph shower 5 - sum of 1,2,3 6 - total sum
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Energy by under threshold 1 - by electrons 2 -
by photons 3 - by pair 4 - sum of 1, 2, 3
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Energy by under threshold 1 - by electrons 2 -
by photons 3 - by pair 4 - sum of 1, 2, 3
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Energy by under threshold 1 - by electrons 2 -
by photons 3 - by pair 4 - sum of 1, 2, 3
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Energy by under threshold 1 - by electrons 2 -
by photons 3 - by pair 4 - sum of 1, 2, 3
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Energy by under threshold 1 - by electrons 2 -
by photons 3 - by pair 4 - sum of 1, 2, 3
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Energy by under threshold 1 - by electrons 2 -
by photons 3 - by pair 4 - sum of 1, 2, 3
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Energy by under threshold 1 - by electrons 2 -
by photons 3 - by pair 4 - sum of 1, 2, 3
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Energy by under threshold 1 - by electrons 2 -
by photons 3 - by pair 4 - sum of 1, 2, 3
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Energy by under threshold 1 - by electrons 2 -
by photons 3 - by pair 4 - sum of 1, 2, 3
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Energy by under threshold 1 - by electrons 2 -
by photons 3 - by pair 4 - sum of 1, 2, 3
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Energy by under threshold 1 - by electrons 2 -
by photons 3 - by pair 4 - sum of 1, 2, 3
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Energy by under threshold 1 - by electrons 2 -
by photons 3 - by pair 4 - sum of 1, 2, 3
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Energy by under threshold 1 - by electrons 2 -
by photons 3 - by pair 4 - sum of 1, 2, 3
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Energy by under threshold 1 - by electrons 2 -
by photons 3 - by pair 4 - sum of 1, 2, 3
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B-H SHOWERS
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Cascade curves - NKG - LPM
lines - individual LPM curves
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Cascade curves______ - NKG ______ - LPM
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Cascade curves - NKG - LPM
lines - individual LPM curves
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Cascade curves ______ - NKG ______ - LPM
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Cascade curves ______ - NKG ______ - LPM
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Cascade curves_____ - NKG ______ - LPM
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Muon density in gamma-induced showers______ -
BH ______ - LPM Plyasheshnikov,
Aharonian - our individual points
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Muon density in gamma-induced showers1 - AGASA
2 - Homola et al. 3 - BH 4 - Plyasheshnikov,
Aharonian 5, 6 - our calculations 7 - LPM
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• For the grid of energies
• Emin Ei Eth (Emin1 MeV, Eth10 GeV)
• and starting points of cascades
• 0XkX0 (X01020 gcm-2)
• simulations of 2108 cascades in the atmosphere
  with help of CORSIKA code and responses (signals)
  of the scintillator detectors using GEANT 4 code
• SIGN?(Rj,Ei,Xk)
• SIGN?(Rj,Ei,Xk)
• 10mRj2000m
• have been calculated

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• Responses of scintillator detectors at distance
  Rj from the shower core (signals S(Rj))
• Eth10 GeV
• Emin1 MeV

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• Source test function
• S?(E,x)dEdxP(E0,x)/E?dEdx
• P(E0,x) a cascade profile of a shower
• ?dx?dES?(E,x)0.8E0
• Basic formula
• E0a(S600)b

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Energy spectrum of electrons
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Energy spectrum of photons
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Estimates of energy with test functions
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AGASA simulation
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Model of detector
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Detector response for gammas
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Detector response for electrons
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Detector response for positrons
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Detector response for muons
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Comparison of various estimates of energy

• Experimental data
• Test source function with ?1
• Coefficient 4.8/3.21.5
• Source function from CORSIKA
• Coefficient 4.8/31.6
• Thinning by CORSIKA (10-6)
• Coefficient 4.8/2.61.8

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• Direction of muon velocity is defined by
  directional cosines
• 
  
• All muons are defined in groups with bins of
  energy EiEi?E angles ajaj?aj,
• dm dm? dm and height production hk hk ?hk.
  The average values have been used , ,
  and . Number of muons and
  were regarded as some weights.

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The relativistic equation

• here mµ muon mass e charge ? lorentz
  factor t time geomagnetic field.

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The explicit 2-d order scheme

• here
• Ethr , E threshold energy and muon energy.

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assuming aerosol-free air more typical air gt E
200 EeV (atmospheric monitoring not yet
routine in early 2004 )
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Summary Air Fluorescence Yield Measurements

• Kakimoto et al., NIM A372 (1996)
• Nagano et al., Astroparticle Physics 20 (2003)
• Belz et al., submitted to Astroparticle Physics
  2005 astro-ph/0506741
• Huentemeyer et al., proceedings of this
  conference usa-huentemeyer-P-abs
  2-he15- oral

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Altitude dependence
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Lateral width of shower image in the Auger
?uorescence detector.
Figure 1. Image of two showers in the
photomultiplier camera. The reconstructed energy
of both showers is 2.2 EeV. The shower on the
left had a core 10.5 km from the telescope, while
that on the right landed 4.5 km away. Note the
number of pixels and the lateral spread in the
image in each shower.
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Figure 2. FD energy vs. ground parameter S38.
These are hybrid events that were recorded when
there were contemporaneous aerosol measurements,
whose FD longitudinal pro?les include shower
maximum in a measured range of at least 350 g
cm-2, and in which there is less than 10
Cherenkov contamination.
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CONCLUSION

• In terms of the hybrid scheme with help of
  CORSIKA
• The energy estimates for the Yakutsk array are a
  factor of 1.5-1.8 may be lower.
• The energy estimates for the AGASA array have
  been confirmed.
• Estimates of energy of the most giant air shower
  detected at the Yakutsk array should be
  checked.
• The LPM showers have a very small muon content.

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Acknowledgements

• We thank G.T. Zatsepin for useful discussions,
  the RFFI (grant 03-02-16290), INTAS (grant
  03-51-5112) and LSS-5573.2006.2 for financial
  support.