Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://tunka.sinp.msu.ru/en/presentation/Dedenko.pdf Äàòà èçìåíåíèÿ: Sun May 22 11:46:33 2011 Äàòà èíäåêñèðîâàíèÿ: Mon Feb 4 18:35:21 2013 Êîäèðîâêà:

Fluctuation in EAS development and estimates of energy and composition of the primary radiation by L. Dedenko, SINP, MSU


1) surface scintillation detectors (SD) 2) detectors of the Vavilov-Cherenkov radiation (VCR) 3) underground detectors of muons (UD) (with the threshold energy ~1 GeV).

Yakutsk array


Detectors readings

· 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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in (SD), (VCR)


Detectors readings

· Some particles (muons, gammas) · penetrate through some depth h of soil, hit underground detectors · and induce some signals sampled as

·

detector readings
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· in underground detectors of muons (UD) (with the threshold energy ~1 GeV).


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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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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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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The CIC method
· The constant intensity cut (CIC) method: · may be systematic error! · For Yakutsk array the absorption length ·

458

2 g/cm

· (to be compared with the simulated average value) ·

340 g/cm
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2


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 approach
It 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 2 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 2 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 =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 (cos()) · 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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· · · ·

Minimum of the function 2 Readings of all scintillation detectors have been used to search for the minimum of the function 2 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 2
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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Minimum of the function 2

· 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

·

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 eV Nuclei s(600,) C=E/10**20 eV P 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 27.48 29.64 32.18 27.77 25.11 33.56 27.88 31.33 30.73 31.03 29.90 31.66 34.12 36.23 33.05 35.02 53.88 2.04 2.00 1.805 2.27 2.37 1.755 2.085 1.93 1.78 1.86 1.94 1.75 1.6 1.66 1.745 1.69 1.1 x, m 941 965 948 1011 y, m -374 -406 -425 -421 min
2 1

0.88 0.945 1.019 1.03 0.895 0.996 0.949 1. 0.97 0.942 0.904 0.997 1.081 1.042 1.051 1.01

He

956 -408 947 -421 942 -389 955 -439 909 943 940 912 905 969 935 975 1055 -363 -387 -393 -428 -353 -429 -437 -389 -406

O

Fe

DATA Yakutsk

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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: · E2.·1020 eV for the proton primaries · and · E1.7·1020 eV for the primary iron nuclei

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Minimum of the function 2

· · · · ·

Coordinates of axis and values of the 2 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 2 ~ 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 2 ~ 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 2 ~ 0.95 · per one degree of freedom.

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Dependence of the 1 · per one degree of freedom · on the coefficient 20 eV) · C=E/(10
·

Results of energy estimations

2

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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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Reality of the Yakutsk DATA

· The time of sampling signal in the scintillation detectors · =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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Energy spectrum

· The HiRes data are used to construct
· 1) the base spectrum

·

Jb(E)= A·(E)
Jr(E)

-3.25

,

· and · 2) the reference spectrum ·

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Energy spectrum · Using new variable y=lgE · in four energy intervals of yi · (i=1, 2, 3 and 4) · 1) 17.20.01
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Spectrum Jr(E) has been approximated by the following exponent functions

· · · ·

J1(E)=A·(E)J2(E)=C·(E) J3(E)=D·(E)

3.25,

-2.81, -5.1

,
3.25

J4(E)=J1(E)=A·(E)-

· Constants C and D may be expressed through A and equations for Jr(E) at the boundary 18.05.2011. IWS. SINP. points. MOSCOW


Spectrum Jb(E) has been approximated by the following exponent function

·

·

Jb(E) = J1

-3.25, (E)=A·(E)

· 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:

·

·

(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

· ·

(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·(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:
·

=k·E·(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 in underground muon detectors for deph h = 2.5 m: ­ 0, stars­ 45, solid ­ 10.5 eV,dashed ­ 14.85 eV.

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Signal in underground muon detectors for deph h = 2.5 m: ­ 0, stars­ 45,solid ­ 10.5 eV,dashed ­ 14.85 eV.

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Signal distributions in underground muon detectors for deph h = 3.2 m a ­ = 1.05 GeV, b ­ = 1.5 GeV, c ­ = 10 GeV.

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Mean signal in underground muon detectors from gammas with various energies for deph h : ­ h = 2.3 , ­ h = 3.2 .

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Signal distributions in underground muon detectors from gammas for deph h =2.3 m: a ­ = 5 GeV, b ­ = 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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