fluctuation in eas development and estimates of energy and composition

Fluctuation in EAS development and

estimates

of energy and composition

of the primary radiation

by L. Dedenko, SINP, MSU

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).

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)


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).


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.


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


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.


Spectrum•Energy spectra are different for these approaches


points ─ Yakutsk data, stars ─ PAO circles ─ Yakutsk like AGASA


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


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.


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


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


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.


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.


The new approach• The best estimates of the

• 1) arrival direction

• and

• 2) core location

• are also searched by the χ2 method.


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).


Simulations• The program GEANT4 has been used

• to estimate signals in the scintillation detectors

• from electrons, positrons, gammas and muons

• in each individual shower.


Detector model


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:


Electrons


Positrons


Gammas


Muons


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.


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.


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


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.


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


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


Minimum of the function χ2

• Coordinates of axis

• and

• values of the χ2

• have been obtained

• for each individual shower


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.


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




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




Results of energy estimations• Dependence of the χ1

2

• per one degree of freedom

• on the coefficient

• C=E/(1020 eV)


protons


helium nuclei


oxygen nuclei


iron nuclei


Reality of the Yakutsk DATA

• The time of sampling signal in the scintillation detectors

• τ=2000 ns


Fraction of sampled signal: 1-100 m, 2-600 m, 3-1000 m, 4-1500 m


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)


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


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.


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.


Spectrum

• The reference spectrum

• is assumed as•

• lgzi=lg(Ji(E)/J1(E)),

• where i=1, 2, 3, 4.


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.


HiRes


PAO


AGASA


Yakutsk


TA


Tibet, Tunka-25, Cascade-Grande


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.



• 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



• 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



• 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


Signal ∆ Е in underground muon detectors for deph h = 2.5 m: о– 0о, stars– 45о,

solid – 10.5 МeV,dashed – 14.85 МeV.


Signal ∆ Е in underground muon detectors for deph h = 2.5 m: о– 0о, stars– 45о,solid

– 10.5 МeV,dashed – 14.85 МeV.


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.


Mean signal ∆ Е in underground muon detectors from gammas with various energies for deph h :

● – h = 2.3 м , ○ – h = 3.2 м.


Signal ∆ Е distributions in underground muon detectors from gammas for deph h =2.3 m:

a – Еγ = 5 GeV, b – Еγ = 10 GeV.


Composition: solid-p, dashed-Fe, points-data


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.


•Thank you for attention

fluctuation in eas development and estimates of energy and composition

Documents

energy e of eas

vertical eas

eas development

inclined eas

eas core

observed eas

peculiar development

estimates of energy