Yakutsk array

QUARKS-2010, Kolomna

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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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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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Coordinates of axis and values of the function χ2 have been obtained for each individual shower


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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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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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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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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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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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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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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)

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(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

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