Properties of giant air showers and the problem of energy

estimation of initial particles

M.I. Pravdin for Yukutsk CollaborationYu.G. Shafer Institute of Cosmophysical Research and

Aeronomy, 31 Lenin Ave., 677980 Yakutsk, Russia

THE GZK PROBLEM

• AGASA - Super GZK-particles exist11events above 1020 eV. No GZK cutoff

• HiRes – Steeping of the spectrum above 1019.8 eV. GZK cutoff is observed

• Yakutsk – 4 events above 1019.99 eV. Statistics is insufficient

• Auger SD – No events above 1020 eV. But no steeping of the spectrum

Research of the GZK problem is started for a long time, but the exact answer is not received yet. Results of different experiments in the GZK cutoff region of the energy spectrum will not be coordinated:

Differential Energy Spectrum at E0 > 1017 eV

1017 1018 1019 1020

1024

1025

Yakutsk AGASA HiRes Auger

J E

o3 , m-2s-1

sr-1eV

2

Eo, eV

THE GZK PROBLEM

Energy spectra obtained in different experiments correspondquite well in shape but differ in intensity. The data from the Yakutsk array near 1019 eV are higher by a factor of 2.5 than HiRes data and 30% than AGASA’s.

Problem of a agreement of energy estimation in different experiments

Estimation of shower energy E0 in Yakutsk

The calorimetric method The relation between parameters S300 or S600 and primary particle energy E0 for showers close to the vertical has been determined by the calorimetric method. For the average showers with different S300 or S600 E0 is estimated as the sum separate a components:

E0 = Ei + Eel + Eμ+ Eμi + Eν + Eh

Ei is the energy lost by a shower over the observation level.

Eel is the energy conveyed below the array level.

E is the energy of the muon component.

Ei and E are the energy of muon losses on ionization and the neutrino

Eh is the energy on nuclear reactions in the atmosphere.

Red color allocates components are added on the basis of model calculation results

.

Ei = k is estimated by measurements of total Cerenkov light flux , and

k = 2.16104 / (0.37 + 1.1(Xm /1000) in the interval of waves 300-800nm. In view of mean atmospheric transmittance

For E0 1019 eV : Ei / E0 74%; Eel / E0 15%; Eμ / E0 3.6%;

(Eμi + Eν + Eh) / E0 7.4%

Ratio between shower energy E0 and S600(0º) determined by the calorimetric method

EO = (4.6 1.2)1017S600(0)0.98 0.03

10 100

1E18

1E19

Experiment 4.6e17*S^0.98 Yakutsk 3.48e17*P^1.0 Kalmykov & Sleptsova

E0,

eV

S600

(0o), m-2

Zenith-Angular Dependence of S300 and S600

We assume that S300 (S600) dependence on the atmospheric depth must be

described as

S(θ) = S(0º)·{(1-β)·exp((X0-X)/λE) + β·exp((X0-X)/λM)}

X0 = 1020 g·cm-2, X=X0/cos(θ)

β is a portion of the «muon» component in the total response of S(0º) at the depth

of X0 = 1020 g·cm-2

for S300 λE = 200 g·cm-2, λM = 1000 g·cm-2

β300 = (0.368 + 0.021) ·(S300(0º)/10)–(0.185 + 0.02)

for S600 λE = 250 g·cm-2, λM = 2500 g·cm-2

β600 = (0.39 + 0.04) ·S600(0º)–(0.12 + 0.03)

β600 versus the shower parameter S600(0º)

0 20 40 60 80 1000,15

0,20

0,25

0,30

0,35

0,40

0,45

600 = 0.39 * S600(0o)- 0.12

600

S600

(0o)

S600 versus the atmospheric depth X for different energies. The red lines are the change of S600 depending on X by using formula with 2 exponents

1000 1200 1400 1600 1800 2000 2200 2400 2600 2800

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0

1,2

1,4

1,6

1,8

2,0

Lo

g(S

600)

X g cm-2

Errors of energy estimation in giant air showers

The relative error in energy estimation for individual event δE/E depends on several factors: -Errors in determination of S600(θ) (δS/S(θ)) and zenith angle (δθ)-Errors in parameters for zenith angular dependence (δβ)-Errors in parameters for calorimetric formula E0=(E1 ± δE1 )S600(0o) k ± δk

Errors of energy estimation in EAS with E0>4x1019 eV(only δS/S(θ), δθ, δβ)

0 10 20 30 40 50 600,15

0,20

0,25

0,30

0,35

0,40

0,45

0,50

- inner area of the array S/S()=0.15, =2 - additional area S/S()=0.35, =3.5E

0/E

0

o

Errors of energy estimation in giant air showers

Errors in parameters for calorimetric formula - systematic errors of energy spectrum

E0=(E1 ± δE1 )S600(0o) k ± δk

Relative error δE1/E1 = 25% is mainly connected with absolute calibration of Cherenkov light detectors and results in systematic shift of estimated energies of all events.

δk = 0.03 increases errors of an estimation with energy rise. For 1020 uncertainty makes 30 %

Comparison of the Yakutsk array Spectrum with accounts from AGNBerezinsky V.S., Gazizov A.Z., Grigorieva S.I. // preprint 2002,

hep-ph/0204357

1019 1020

1024

1025

Inner Area Max Area, E/E = 30%

g=2.7

g=2.5

J E

o3 , m-2s-1

sr-1eV

2

Eo, eV

Comparison of the Yakutsk spectrum at reduction E0 by the factor 1.6 with the HiRes data

1017 1018 1019 1020

1024

1025

Yakutsk E0/1.6

HiRes

J E

o3 , m-2s-1

sr-1eV

2

Eo, eV

Muon Component of EAS

In Yakutsk array experimental data about increase of muon fraction in giant air showers are received

We have

- 5 muon detectors: Area = 20 m2; Threshold energy of muons – 1/cosθ GeV

- Big Muon Detector: Area = 180 m2

Threshold – 0.5/cosθ GeV

A plan of the location of detector stations of the Yakutsk EAS Array

Lateral Distribution

For the description of lateral distribution muons and all particles function is used as

ρ(R) (R/R0)a (1 + R/R0)

a-b (1 + R/2000)-g

for all particles:

R0 - Molier unit (70 m), a=1.3, g=1

for muons:

R0=280 m, a=0.75, g=6.5

Lateral Distribution of muons and all particles in EAS with θ=12

Open circles – muons, close one – all particles

Lateral Distribution of muons and all particles in EAS with θ=55

Open circles – muons, close one – all particles

10000,1

1

10

100

1000

EAS 18-02-04 22:20:38 UT =47.7 Log(E

0)=20.16

B2=16.3 L2=140.2

Charged particles Muons

Den

sity

, m

-2

R, m

100 10000,1

1

10

100

1000

EAS 7-05-89 22:03 UT =58.7 Log(E

0)=20.14

B2=2.7 L2=161.5

Charged particles muons

De

nsi

ty,

m-2

R, m

Energy dependence of the parameter

b in different zenith angle intervals

Energy dependence of the parameters b

and bs in vertical showers (cosθ>0.9)

The muon fraction at R=300m and R=600m (cosθ>0.9)

Open circles – R=600m; close one – R=300m

The muon fraction in full number of particles at distances from 100m up to 1000m (cosθ>0.9)

Conclusions

• The muon contribution in the response scintillation detectors at Е0 near 1019 eV starts to grow. Models predict reduction.

• Probably it reflects existence of unknown processes in nuclear interactions. The energy fraction of EAS transmitted in muons becomes essentially more and increases with growth of energy. Fluorescent detectors do not see the contribution muon component and can underestimate energy of a gain showers.

• For a correct energy estimation of showers and the decision of GZK problem it is necessary to carry out complex researches of EAS properties including muon component.