The Cosmic Ray Spectrum at Ultrahigh Energies
M.I. Pravdin for Yakutsk Collaboration
Yu.G. Shafer Institute of Cosmophysical Research
and Aeronomy, 31 Lenin Ave., 678980 Yakutsk,
Russia
Estimation of EAS Energy by a Calorimetric
Method
M.I. Pravdin for Yakutsk Collaboration
Yu.G. Shafer Institute of Cosmophysical Research
and Aeronomy, 31 Lenin Ave., 678980 Yakutsk,
Russia
-2
-1
0
1
2
2
X, km 3
1
0
-1
Y,
km
-2
TRIGGER STATIONS have
2
2 x 2 m scintillation detectors
- operate from 1973
- operated from 1973 to 1990
- operate from 1991
- CERENKOV LIGHT DET.
- MUON DETECTORS S=20 m
2
2
- additional scintil. detectors S=2 м
2
- Big Muon Detector, S=180 м
A plan of the location of detector stations of the
Yakutsk EAS Array
Cerenkov light
detector
55
Sinchr. reciv.
Scintillation
detector 2 m2
1.5 m
Station of Yakutsk EAS Array
to Centrer
The diagram of the trigger of the Yakutsk EAS
array
2000
1500
1000
Y
500
0
-500
-1000
-1500
-2000
-3000
-2000
-1000
0
1000
2000
3000
X
Each trigger station has 2 scintillator detectors (Sdet=2 m2). The
coincidences within a resolving time 2.0 - 2.2 μs is required.
EAS is selected when an event is registered simultaneously by
three neighboring stations forming a triangle. Resolving time
in this case equals 40 μs
Red triangles - trigger-500 (now - 63 cells, SII=7.2 km2; up to
1992 - 19 cells SI =2.5 km2)
Blue ones trigger-1000 (now - 24 cells, SII = 10.5 km2)
Green circle - 10 stations of the trigger-1000, working from
1973 up to 1990 (24 + 16=40 cells, SI = 17.3 км2)
Estimation of shower energy E0
The calorimetric method
The relation between parameters S300 or S600 and primary
particle energy E0 for EAS 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 = k
is the energy lost by a shower over the observation
level. It is estimated by measurements of total Cerenkov light
flux , and k = 2.16104 / (0.37 + 1.1(Xm /1000)
in the interval of light waves 300-800 nm, In view of mean
atmospheric transmittance.
Eel = 2.2106NsN
is the energy conveyed below the
array level. It is estimated by the attenuation length N of the
number of charged particles Ns through the atmosphere
depth;
E = N is the energy of the muon component. It is
estimated by the total number of muons N and average
9
energy on one muon  = 10.610 eV
Ei + E = 0.76E is the energy of muons losses on
ionization and the neutrino
Eh = 0.06Ei is the energy on nuclear reactions in the
atmosphere.
Red components are added on the basis of model calculation
results.
For
E0  1019 eV –
Ei / E0  74%;
Eel / E0  15%;
Eμ / E0  3.6%;
(Eμi + Eν + Eh) / E0  7.4%
Lateral distribution of EAS Cerenkov light,
<30, 1015 <E0 < 31019 eV
The red lines correspond to approximation
Q(R) = Q150((62+R)/212)-1((200+R)/(350))1-m,
m = (1.150.05) + (0.300.06)log(Q150)


2R  Q(R )  R
-1
-1
Ф(Е0,R)E , (photon MeV )
16
19
14
- Е0=10 eV
12
- E0=10 eV
18
17
- E0=10 eV
10
16
- E0=10 eV
8
6
4
2
0
1
2
3
4
5
6
7
8
9
10
lnR, (m)
Interval of distances for real measurements of Cerenkov light
in the average EAS
From lateral distribution and atmospheric transmittance -
  12-15%
But we have a regular error connected to absolute calibration
of cerenkov light detectors. It is 20%
We have the similar data on lateral distribution of the charged
particles and muons
In result we have obtained:
EO = (5.66  1.4)1017(S300(0)/10)0.94  0.02
EO = (4.6  1.2)1017S600(0)0.98  0.03
21017 < E0 <21019 eV
EO = (5.66  1.4)1017(S300(0)/10)0.94  0.02
17
E0=(5.66 + 1.4)*10 *(S300/10)
(0.94 + 0.02)
E0, eV
1E19
1E18
1E17
10
100
o
-2
S300(0 ), m
Ratio between shower energy E0 and S300(0º) determined by
the calorimetric method
EO = (4.6  1.2)1017S600(0)0.98  0.03
17
E0 = (4.6 + 1.2)*10 *S600
(0.98 + 0.03)
E0, eV
1E19
17
E0 = 3.48*10 *ch, 600
(1.0 + 0.01)
QGSJet
1E18
10
100
o
-2
S600(0 ), m
Ratio between shower energy E0 and S600(0º) determined by
the calorimetric method
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)
λE = 200 g·cm-2, λM = 1000 g·cm-2
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
β300 = (0.368 + 0.021)(S300(0º)/10)–(0.185 + 0.02)
β300 = (0.33 + 0.017) ·(E0/1018) –(0.19 + 0.02)
for S600
β600 = (0.62 + 0.06) ·S600(0º)–(0.076 + 0.03)
β600 = (0.58 + 0.05) ·(E0/1018)–(0.077 + 0.03)
S1
S2
S3
S4
S5
S6
S7
Q1
Q2
Q3
Q4
Q5
Q6
S300, m
-2
100
10
1
1000
1200
1400
X, g cm
1600
1800
-2
S300 versus the atmospheric depth X for different energies.
Black indices (S1 - S7) are equi-intensity method data,
blue indices (Q1 - Q6) are data by Q400 method. The lines
are the change of S300 depending on X by using formula
1
equi-intensity method
Q400 method
18 -0.19 + 0.02
300
(0.33 + 0.01)*(E0/10 )
0,1
1E17
1E18
1E19
E0 ,eV
β300 versus the showers energy. β300 is a portion of the hard
component in the total response of S300(0º) at the depth of
1020 g·cm-2
S1
S2
S3
S4
S5
Q1
Q2
Q3
Q4
S600, m
-2
100
10
1
1000
1200
1400
X, g cm
1600
1800
-2
S600 versus the atmospheric depth X for different energies.
Black indices (S1 – S5) are equi-intensity method data, blue
indices (Q1 – Q4) are data by Q400 method. The lines are the
change of S600 depending on X by using formula
Largest events
N
Date
1
2
3
4
18-02-04
07-05-89
21-12-77
15-02-78
Time
θ
22:20:38 47.7
22:03:00 58.7
18:45:00 46.0
03:35:00 9.6
Log(E0)
20.16
20.14
20.01
19.99
Error
E0 %
42
46
40
32
Galactic Galactic
latitude longitude
16.3
140.2
2.7
161.6
50.0
220.6
15.5
102.0
2
25
10
24
3
-2 -1
-1
J Eo , m s sr eV
10
- Yakutsk
- AGASA
- HiRes
10
17
10
18
10
19
10
20
Eo, eV
Differential Energy Spectrum at E0 > 1017 eV
25
2
-2 -1
-1
I Eo , m s sr eV
2
10
10
24
- Trigger-500
- Trigger-1000
- Trigger-1000, max. area
10
18
10
19
10
20
Eo, eV
Integral Energy Spectrum of the Yakutsk Array
Last largest Event
EAS 7-05-89 22:03 UT
 =58.7 Log(E0)=20.14
B2=2.7 L2=161.5
1000
Density, m
-2
100
10
Charged particles
muons
1
0,1
100
1000
R, m
25
3
-2 -1
-1
J Eo , m s sr eV
2
10
10
24
10
23
Trigger-500
Trigger-1000
g=2.7
g=2.5
E/E = 25%
10
17
10
18
10
19
10
20
Eo, eV
Comparison of the Yakutsk array Spectrum with
accounts from AGN
Berezinsky V.S., Gazizov A.Z., Grigorieva S.I. // preprint 2002,
hep-ph/0204357
The conclusion. The Spectrum obtained on the Yakutsk
array will be agree with the assumption, that the particles
with E0 > 1019 eV are mainly formed in extragalactic sources