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Fluctuation in EAS development and
estimates
of energy and composition
of the primary radiation
by L. Dedenko, SINP, MSU
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Yakutsk array1) surface scintillation detectors (SD)
2) detectors of the Vavilov-Cherenkov radiation (VCR)
3) underground detectors of muons (UD)
(with the threshold energy ~1 GeV).
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18.05.2011. IWS. SINP. MOSCOW
Detectors readings
• The various particles
• of Extensive Air Showers (EAS)
• at the observation level
• hit detectors
• and induce some signals sampled as
• detector readings in (SD), (VCR)
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Detectors readings
• Some particles (muons, gammas)
• penetrate through some depth h of soil, hit underground detectors
• and induce some signals sampled as
• detector readings• in underground detectors of muons
(UD) (with the threshold energy ~1 GeV).
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Standard approach of energy estimation
• Signal s(600) in SD
• at 600 m from the EAS core
• in the vertical EAS
• is used to estimate • energy E of EAS.
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18.05.2011. IWS. SINP. MOSCOW
Standard approach of energy estimation
• DATA:
• 1. The CIC method is used to estimate s(600) in vertical EAS from data for the inclined EAS.
• 2. The signal s(600) for the vertical EAS is calibrated with the help of the
• Vavilov-Cherenkov radiation
• 3. E=4.6·1017· s(600), eV
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18.05.2011. IWS. SINP. MOSCOW
Standard AGASA approach:Like AGASA:• 1. The CIC method to estimate s(600) for
the vertical EAS from data for the inclined EAS.
• 2. Calculation s(600) for the vertical EAS with energy E:
• 3. E=3·1017·s(600), eV
• 1. L.G. Dedenko et al., Phys. of Atom. Nucl., 2007, vol. 70, No 1, pp. 170-174.
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Spectrum•Energy spectra are different for these approaches
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points ─ Yakutsk data, stars ─ PAO circles ─ Yakutsk like AGASA
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18.05.2011. IWS. SINP. MOSCOW
The CIC method
• The constant intensity cut (CIC) method:
• may be systematic error!
• For Yakutsk array the absorption length
• 458 g/cm2
• (to be compared with the simulated average value)
• 340 g/cm2
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18.05.2011. IWS. SINP. MOSCOW
New approach• All detectors readings
• are suggested to be used to study
• the energy spectrum
• and
• the chemical composition
• of the primary cosmic radiation
• at ultra-high energies
• in terms of some model of hadron interactions.
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The new approach• For the each one individual EAS
• 1) the energy E and
• 2) the type of the primary particle, (atomic number A), which induced EAS,
• 3) parameters of model of hadron interactions,
• 4) peculiar development of EAS in the atmosphere
• are not known
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The new approach• The goal is to find estimates of
• 1) energy E,
• 2) atomic number A,
• 3) parameters of model of hadron interactions,
• 4) peculiar development of EAS in the atmosphere
• for each individual shower
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The new approachIt has been suggested
for the every one observed EAS
to use all detector readings which should be compared with the simulated ones
• for many simulated individual showers,
• induced by 1) various primary particles
• with 2) different energies
• in terms of 3) various models.
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The new approach• The best estimates of
• the energy E,
• the atomic number A and
• parameters of model and
• peculiar development of EAS in
• the atmosphere are searched by the χ2 method.
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The new approach• The best estimates of the
• 1) arrival direction
• and
• 2) core location
• are also searched by the χ2 method.
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18.05.2011. IWS. SINP. MOSCOW
Simulations• Simulations of the individual shower
development in the atmosphere
• have been carried out with the help of
• the code CORSIKA-6.616 [8]
• in terms of the models QGSJET2 [9] and Gheisha 2002 [10]
• with the weight parameter ε=10-8 (thinning).
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Simulations• The program GEANT4 has been used
• to estimate signals in the scintillation detectors
• from electrons, positrons, gammas and muons
• in each individual shower.
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Detector model
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Signals in scintillation detector
• Signals ∆E in MeV in detectors as functions of
• 1) energy E
• and
• 2) the zenith angle θ (cos(θ))
• of various incoming particles:
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Electrons
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Positrons
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Gammas
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Muons
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18.05.2011. IWS. SINP. MOSCOW
Minimum of the function χ2• Readings of all scintillation
detectors
• have been used to search for the
• minimum of the function χ2
• in the square with the width of 400 m and a center determined by data with a step of 1 m.
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Minimum of the function χ2 These readings have been compared with
calculated responses for E0=1020 eV (201*201 signals) multiplied by the coefficient C.
•
• This coefficient C changed from 0.1 up to 4.5 with a step of 0.1.
• (45 values)
• L.G. Dedenko et al., JETP Letters, 2009, vol.90, No 11, pp. 691-696.
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18.05.2011. IWS. SINP. MOSCOW
Minimum of the function χ2
• Thus, it was assumed, that the energy of a shower and signals in the scintillation detectors are proportional to each other in some small interval.
• New estimates of energy
• E =C·E0 , eV
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18.05.2011. IWS. SINP. MOSCOW
Results of energy estimations
• 16*45=720 • of energy estimates for simulated
showers induced by
• protons, He, O and Fe nuclei
• have been obtained
• for the same sample of the 31 experimental readings of the
• one observed giant shower.
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Best estimates: 10**20 eVNuclei № s(600,Θ) C=E/10**20 eV x, m y, m min χ2
1
P 1 27.48 2.04 941 -374 0.88 2 29.64 2.00 965 -406 0.945 3 32.18 1.805 948 -425 1.019 4 27.77 2.27 1011 -421 1.03 He 1 25.11 2.37 956 -408 0.895 2 33.56 1.755 947 -421 0.996 3 27.88 2.085 942 -389 0.949 4 31.33 1.93 955 -439 1. O 1 30.73 1.78 909 -363 0.97 2 31.03 1.86 943 -387 0.942 3 29.90 1.94 940 -393 0.904 4 31.66 1.75 912 -428 0.997 Fe 1 34.12 1.6 905 -353 1.081 2 36.23 1.66 969 -429 1.042 3 33.05 1.745 935 -437 1.051 4 35.02 1.69 975 -389 1.01 DATAYakutsk 53.88 1.1 1055 -406
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18.05.2011. IWS. SINP. MOSCOW
Simulations• New estimates of energy E
• of the giant air shower observed at YA
• have been calculated
• in terms of the QGSJET2 and Gheisha 2002 models:
• E≈2.·1020 eV for the proton primaries
• and
• E≈1.7·1020 eV for the primary iron nuclei
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18.05.2011. IWS. SINP. MOSCOW
Minimum of the function χ2
• Coordinates of axis
• and
• values of the χ2
• have been obtained
• for each individual shower
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18.05.2011. IWS. SINP. MOSCOW
Results of energy estimations• The energy estimates are minimal for
the iron nuclei primaries
• and change inside the interval
• (1.6−1.75)· 1020 eV
• with the value of the χ2 ~ 1.1
• per one degree of freedom.
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18.05.2011. IWS. SINP. MOSCOW
Results of energy estimations• For the proton and helium nuclei
primaries
• energy estimates are maximal and
• change inside the interval
• (1.8−2.4)·1020 eV
• with the value of the χ2 ~ 0.9
• per one degree of freedom.
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18.05.2011. IWS. SINP. MOSCOW
Results of energy estimations• For the oxygen nuclei primaries the
• energy estimates are in the interval
• (1.8−2)·1020 eV
• which is between intervals for proton and iron nuclei primaries
• with the value of the χ2 ~ 0.95
• per one degree of freedom.
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Results of energy estimations• Dependence of the χ1
2
• per one degree of freedom
• on the coefficient
• C=E/(1020 eV)
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protons
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helium nuclei
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oxygen nuclei
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iron nuclei
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18.05.2011. IWS. SINP. MOSCOW
Reality of the Yakutsk DATA
• The time of sampling signal in the scintillation detectors
• τ=2000 ns
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Fraction of sampled signal: 1-100 m, 2-600 m, 3-1000 m, 4-1500 m
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18.05.2011. IWS. SINP. MOSCOW
Energy spectrum
• The HiRes data are used to construct
• 1) the base spectrum
• Jb(E)= A·(E)-3.25,• and
• 2) the reference spectrum
• Jr(E)
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Energy spectrum
• Using new variable y=lgE
• in four energy intervals of yi
• (i=1, 2, 3 and 4)
• 1) 17.<y1<18.65,
• 2) 18.65<y2<19.75,
• 3) 19.75<y3<20.01 and
• 4) y4>20.01
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Spectrum Jr(E) has been approximated by the following exponent functions
• J1(E)=A·(E)-3.25,
• J2(E)=C·(E)-2.81,
• J3(E)=D·(E)-5.1,
• J4(E)=J1(E)=A·(E)-3.25
• Constants C and D may be expressed through A and equations for Jr(E) at the boundary points.
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Spectrum Jb(E) has been approximated by the following exponent function
•
• Jb(E) = J1(E)=A·(E)-3.25,
• L.G. Dedenko et al., Phys. of Atom. Nucl.,
2010, vol. 73, No12, pp. 2182-2189.
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Spectrum
• The reference spectrum
• is assumed as•
• lgzi=lg(Ji(E)/J1(E)),
• where i=1, 2, 3, 4.
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Spectrum• Results of the spectra J(E)
• observed at various arrays
• have been expressed as
• lg z=lg (J(E)/Jb(E))• and are shown
• in comparison with
• the reference spectrum.
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HiRes
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PAO
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AGASA
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Yakutsk
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TA
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Tibet, Tunka-25, Cascade-Grande
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Study of the chemical composition
• Muon density for the primary protons with the energy E:
• ρμ(600)=a·Eb
• b<1• Decay processes are decreasing for higher
energies E.
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Study of the chemical composition
• Muon density for the primary nuclei with atomic number A
• ρμ(600)=a·Ac·Eb
• c>0 (c=1-b)• QGSJET2: b=0.895, c=0.105
• For Fe:
• A0.105=1.53
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Study of the chemical composition
• QGSJET2:
• Signal in SD
• s(600)=∆E·(E/3·1017 eV)
• Signal in UD
• k·∆E·ρμ(600)
• Coefficient k=1.3
• Average signal ∆E=10.5 MeV
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Study of the chemical composition
• Muon fraction at 600 m:
• α=k·∆E·ρμ(600)/s(600)• Coefficient k=1.3 takes into account
the difference in the threshold energies and signals in UD
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Signal ∆ Е in underground muon detectors for deph h = 2.5 m: о– 0о, stars– 45о,
solid – 10.5 МeV,dashed – 14.85 МeV.
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18.05.2011. IWS. SINP. MOSCOW
Signal ∆ Е in underground muon detectors for deph h = 2.5 m: о– 0о, stars– 45о,solid
– 10.5 МeV,dashed – 14.85 МeV.
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18.05.2011. IWS. SINP. MOSCOW
Signal ∆ Е distributions in underground muon detectors for deph h = 3.2 m
a – Еμ = 1.05 GeV, b – Еμ = 1.5 GeV, c – Еμ = 10 GeV.
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Mean signal ∆ Е in underground muon detectors from gammas with various energies for deph h :
● – h = 2.3 м , ○ – h = 3.2 м.
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Signal ∆ Е distributions in underground muon detectors from gammas for deph h =2.3 m:
a – Еγ = 5 GeV, b – Еγ = 10 GeV.
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Composition: solid-p, dashed-Fe, points-data
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Conclusion
• Fluctuations in EAS development should be
taken into account to get estimates of
• energy E and • composition (atomic number A) of the primary particles.
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•Thank you for attention
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