yakutsk array
DESCRIPTION
Study of the Energy Spectrum and the Composition of the Primary Cosmic Radiation at Super-high Energies. By L.G. Dedenko 1 , A.V. Glushkov 2 , G.F. Fedorova 1 , S.P. Knurenko 2 , a.A. Makarov 2 , M.I. Pravdin 2 , T.M. Roganova 1 , I.Ye. Sleptzov 2 - PowerPoint PPT PresentationTRANSCRIPT
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Study of the Energy Spectrum and the Composition of the Primary Cosmic Radiation at Super-high Energies
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By L.G. Dedenko1, A.V. Glushkov2, G.F. Fedorova1, S.P. Knurenko2, a.A. Makarov2, M.I. Pravdin2, T.M. Roganova1, I.Ye. Sleptzov2
1. M.V. Lomonosov Moscow State University, Faculty of Physics and D.V. Skobeltzin Institute of Nuclear Physics, Moscow, 119992, Leninskie Gory, Russian Federation
2. Insitute of cosmic rays and aeronomy. Yakutsk, Russian Federation
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Yakutsk array
The Yakutsk array includes the surface scintillation detectors (SD)
and detectors of the Vavilov-Cherenkov
radiation and underground detectors of muons
(UD) with the threshold energy ~1 GeV.
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Detectors readings induced by EAS particles
The various particles of Extensive Air Showers (EAS) at the observation level hit detectors and induce some signals sampled as detector readings
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Standard approach of energy estimation
s(600) – signal at 600 m in the vertical EAS used to estimate energy E of EAS.
DATA: 1. The CIC method to estimate s(600)
from data for the inclined EAS. 2. The signal s(600) is calibrated with help of the Vavilov-Cherenkov radiation E=4.6·1017· s(600), eV
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Standard AGASA approach
Like AGASA: 1. The CIC method to estimate s(600)
from data for the inclined EAS. 2. Calculation s(600) for EAS with energy E: E=3·1017·s(600), eV
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Spectrum
Energy spectra are different for these approaches
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points ─ Yakutsk data circles ─ Yakutsk (calculation like AGASA) stars ─ PAO
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The CIC method
The constant intensity cut (CIC) method:
systematic error! For Yakutsk array the absorption
length 458 g/cm2 (to be compared with 340 g/cm2)
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Yakutsk array. 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 method
For the individual EAS the energy E and the type of the primary particle, (atomic
number A), which induced EAS, parameters of model of hadron
interactions, peculiar development of EAS in the
atmosphere are not known
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The new method
The goal: to find estimates of the energy E and atomic number A, parameters of model of hadron
interactions, peculiar development of EAS in the
atmosphere for each individual shower
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The new method
It has been suggested for the one observed EAS to estimate all detector readings for many simulated individual showers, induced by various primary particles with different energies in terms of various models.
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The new method
All these detector readings for all simulated individual
showers should be compared with detector readings of one observed EAS
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The new method
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 method
The best estimates of the arrival direction and core location are also searched by the χ2
method.
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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 [11] 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 as functions of energy E and the cos( teta) (teta – the zenith angle) of incoming particles
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Electrons
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Positrons
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Gammas
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Отклики от мюонов Muons
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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. These readings have been compared with
calculated responses for E0=1020 eV multiplied by the coefficient C. This coefficient changed from 0.1 up to 4.5 with a step of 0.1.
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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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Results of energy estimations
The 16 various values of energy estimates for 16 individual simulated showers induced by
protons, He, O and Fe nuclei have been obtained for the same sample
of the 31 experimental readings of the observed giant shower with different values of the function χ2.
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Results for the most energetic shower observed at the Yakutsk array
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Nucleus № s(600) E0/1020 x y χ12
P 1234
27.4829.6432.1827.77
2.042.001.8052.27
9419659481011
-374-406-425-421
0.880.9451.0191.03
He 1234
25.1133.5627.8831.33
2.371.7552.0851.93
956947942955
-408-421-389-439
0.8950.9960.9491.
O 1234
30.7331.0329.9031.66
1.781.861.941.75
909943940912
-363-387-393-428
0.970.9420.9040.997
Fe 1234
34.1236.2333.0535.02
1.61.661.7451.69
905969935975
-353-429-437-389
1.0811.0421.0511.01
Experiment 53.88 1 1055 -406
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Simulations
New estimates of energy 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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Minimum of the function χ2
Coordinates of axis and values of the function χ2 have been obtained for each individual shower
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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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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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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 value χ2 per one degree of freedom on the coefficient C=E/(1020 eV)
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Reality of the Yakutsk DATA
The sampling time of signal in the scintillation detetor
τ=2000 ns
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Fraction of signal: 1-100 m, 2- 600 m, 3- 1000 m, 4-1500 m
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Energy spectrum
The base spectrum
Jb(E)= A·(E)-3.25, and the reference spectrum
Jr(E) are introduced on the base of the HiRes
data
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Energy spectrum
New variable y=lgE In four energy intervals yi (i=1, 2, 3 and 4) 17.<y1<18.65, 18.65<y2<19.75, 19.75<y3<20.01 and 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
we assume the reference spectrum as
lgzi=lg(Ji(E)/J1(E)),
where i=1, 2, 3, 4.
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Spectrum
This reference spectrum is represented as follows
lgz1=0, lgz2=0.44·(y -18.65), lgz3=0.484-1.85·(y -19.75)
lgz4=0
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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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Spectrum
Data lgz=lg(J(E)/Jb(E)) observed at various arrays are shown in Fig. as follows:
(a) − HiRes2 (open circles), HiRes1 (solid squares),
(b) − PAO (solid circles), (c) − AGASA (solid triangles), (d) − Yakutsk (solid pentagons). The reference spectrum is also shown on
all Figures (solid line).
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HiRes
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PAO
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AGASA
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Yakutsk
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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=1.15
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Study of the chemical composition
Muon fraction at 600 m:
α=k·∆E·ρμ(600)/s(600) Coefficient k=1.15 takes into
account the difference in the threshold energies and signals in UD
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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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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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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Gammas
Possible signals in UD from gammas
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Energy spectra of gammas in vertical EAS inside 100 m. 1 – Е = 1017 eV, 2 – Е = 1018 eV.
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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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Muon fraction α at 600 m in vertical EAS. Points – [19], solid– protons, dashed – iron nuclei.
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Results
1. Primary protons above 1018 eV 2. Heavier primary nuclei below
1018 eV
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At energies E>1020 eV
No definite conclusion
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χ21 vs E. Solid – protons, dashed – iron nuclei.
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Conclusions are model dependent
The most energetic EAS observed at the Yakutsk array may be induced by the primary particles with energy 2·1020 eV.
The primary protons may dominate at energies
1018 – 3·1019 eV. Heavy primary particles are possible at
energies below 1018 eV.
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Conclusions are model dependent
The Coulomb scattering of charged particle (electrons, positrons)
and the pt distribution of hadrons (for muon scattering) should be taken into account precisely in calculations of lateral distributions of these particles.
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Acknowledgements.
Authors thank RFBR (grant 08-02-00348), LSS (grant 959.2008.2) and
Federal Agency on Science (State contracts 02.740.11.5092, 02.518.11.7173, 02.740.11.0248)
for support.
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Proton, SIBYLL (AIRES)
Proton, QGSJET (AIRES)
Proton, GEISHA, QGSJET (CORSIKA)
Proton, FLUKA, QGSJET (CORSIKA)
Proton, GEISHA, QGSJET2 (CORSIKA)
Proton, FLUKA, QGSJET2 (CORSIKA)
Iron, SIBYLL (AIRES)
Iron, QGSJET (AIRES)
50
34
(VEM)
SD+MC Average ( 18%)
FD Average ( 30%)
Fixed Beta
Floating Beta
Proton, SIBYLL (AIRES)
Proton, QGSJET (AIRES)
Proton, GEISHA, QGSJET (CORSIKA)
Proton, FLUKA, QGSJET (CORSIKA)
Proton, GEISHA, QGSJET2 (CORSIKA)
Proton, FLUKA, QGSJET2 (CORSIKA)
Iron, SIBYLL (AIRES)
Iron, QGSJET (AIRES)
Summary of S(1000) at 38o and 10 EeV
Proton
Iron