Yakutsk results: spectrum
and anisotropy
M.I. Pravdin for Yukutsk Collaboration
Yu.G. Shafer Institute of Cosmophysical Research and
Aeronomy, 31 Lenin Ave., 677980 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
- additional scintil. detectors S=2 м
2
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
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
from 1992 - 63 cells,
SII=6.8 km2
up to 1992 - 19 cells
SI =2.6 km2
2000
1500
1000
Y
500
Blue ones trigger-1000
from 1990 - 24 cells
SII = 10.5 km2
0
-500
Green circle - 10 stations
of the trigger-1000, working
up to 1990
24+16 = 40 cells
SI = 17.3 км2
-1000
-1500
-2000
-3000
-2000
-1000
0
X
1000
2000
3000
Estimation of shower energy E0
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 = 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 waves 300-800nm
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
through the atmosphere depth
E = N
N of the number of charged particles Ns
is the energy of the muon component. It is estimated by the total
number of muons
N and average energy on one muon  = 10.6109 eV
Ei and E are the energy of muon losses on ionization and the neutrino
Ei + E = 0.76E
Eh = 0.06Ei is the energy on nuclear reactions in the atmosphere.
Red color allocates 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%
E0, eV
1E19
Experiment
4.6e17*S^0.98 Yakutsk
3.48e17*P^1.0 Kalmykov & Sleptsova
3.2e17*S^1.08 Fedunin, Theses
6.5e17*S^1.08 Fedunin, Theses
1E18
10
100
o
S600(0 ), m
-2
Ratio between shower energy E0 and S600(0º) determined by the
calorimetric method
EO = (4.6  1.2)1017S600(0)0.98  0.03
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
for S600
λE = 200 g·cm-2, λM = 1000 g·cm-2
β300 = (0.368 + 0.021) ·(S300(0º)/10)–(0.185 + 0.02)
λE = 250 g·cm-2, λM = 2500 g·cm-2
β600 = (0.39 + 0.04) ·S600(0º)–(0.12 + 0.03)
0,45
0,40
o - 0.12
600 = 0.39 * S600(0 )
600
0,35
0,30
0,25
0,20
0,15
0
20
40
60
80
100
o
S600(0 )
β600 versus the shower parameter S600(0º)
2,0
1,8
1,6
1,4
Log(S600)
1,2
1,0
0,8
0,6
0,4
0,2
0,0
-0,2
-0,4
-0,6
1000
1200
1400
1600
1800
2000
X g cm
2200
2400
2600
2800
-2
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
Dependence S600 on temperature
• Molier unit
R0  75  ((T  273) / 273)  (1000 / P), m
• S600(R0) is recalculated on R0 = 68 m. The formula is
received from the assumption, that full number of particles
equally for different R0
Ktmr  (68 / R0 )(b  2)  ((600  R0 ) / 668)(b 1)
• R0 = 68 corresponds T = -25°C - average temperature of
the periods for Cerenkov light experiment.
Dependence Ktmr on temperature
=0
1,2
o
 = 60
o
Ktmr
1,1
1,0
0,9
0,8
0,7
-60
-40
-20
0
o
T, C
20
40
Cosθ > 0.95; Tyan= -37, Pyan=1008; Tmay= 8, Pmay=992
Cos >0.95
Jan without correction
May without correction
Jan with correction
May with correction
-10,8
-11,0
2
2
-1
2
Log(I*S600 , (m *s*sr) *eV )
-10,6
-11,2
-11,4
0,0
0,5
1,0
1,5
-2
Log(S600, m )
2,0
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 and δX)
-Errors in parameters for calorimetric formula
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.
Area for events with E0 > 4·1019 eV
2500
2000
33
24
23
34
22
1500
1000
32
12
21
13
25
35
500
31
0
20
11
8
1
26
14
-500
30
19
10
27
15
9
-1000
-1500
29
18
-2000
-1000
17
16
28
-2000
-2500
-3000
0
1000
2000
3000
Errors of energy estimation in EAS with E0>4x1019 eV
- inner area of the array S/S()=0.15, =2
- additional area S/S()=0.35, =3.5
0,50
0,45
E0/E0
0,40
0,35
0,30
0,25
0,20
0,15
0
10
20
30

40
o
50
60
10
25
10
24
- Yakutsk
- AGASA
- HiRes
3
-2 -1
-1
J Eo , m s sr eV
2
Differential Energy Spectrum at E0 > 1017 eV
10
17
10
18
10
19
Eo, eV
10
20
Integral Energy Spectrum of the Yakutsk Array
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
Eo, eV
19
10
20
Largest events
N
Date
Time
θ
E0
1
2
3
4
18-02-04
07-05-89
21-12-77
15-02-78
22:20:38
22:03:00
18:45:00
03:35:00
47.7
58.7
46.0
9.6
1.6e20
1.5e20
1.1e20
9.8e19
Error
E0 %
46
40
27
36
Galactic Galactic
latitude longitude
16.3
140.2
2.7
161.6
50.0
220.6
15.5
102.0
On the Yakut EAS array four events with energy greater GZKcutoff are registered. It specifies absence of such cutoff in
cosmic rays spectrum. But because of small statistics and
errors of energy estimation in individual events reliability of
such conclusion while is insufficient.
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 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
Anisotropy. Harmonic analysis.
For an estimation of cosmic ray anisotropy it is possible to
use the harmonious analysis of showers distribution on a
sidereal time or on right ascension. We carried out such
analysis for different intervals on energy
Interval about 1017 eV is near to the threshold of the trigger – 500
of Yakutsk array.
In [MikhaÏlov and Pravdin, JETP Lett. 66, 305 (1997)] we studied
the data in the energy range of 3·1016 <E0 <3·1017 eV with respect
to the right ascension and obtained a probably significant
amplitude of the first harmonic
r1 = (1.35±0.36)% and the phase φ1 = 123°±15° .
On the Haverah Park: r1 = (1.7±0.4)% but φ1 = 218°±14°
[R. N. Coy, et al., in Proc. 17th ICRC, Paris, 1981, Vol. 9, p. 183.].
Harmonic analysis. Interval about 1017 eV
The further analysis shown, that on results near to a threshold
essential are influenced inhomogeneous sky survey and
seasonal variations of shower frequency.
The reasons resulting in the inhomogeneous sky survey by array:
-Short-term switching-off of operation (most often in the daytime)
-Temporary failure of certain trigger station (varies the collection
area)
To estimate inhomogeneity of the sky survey we calculate relative
distribution of the effective area of array on minutes of day (for
each time - solar, sidereal and antisidereal)
Near threshold the effective area is proportional to the number of
triangles in the trigger that actually register the events
The Influence of the inhomogeneity of the sky survey on
parameters of a solar vector for events of the trigger - 500.
H
1
2
Without regard
to survey
With regard to
survey
Without regard
to survey
With regard to
survey
R,%
4.19 ± 0.14
, h
22.2 ± 0.13
1.66 ± 0.14
20.4 ± 0.33
1.35 ± 0.14
4.2 ± 0.2
0.70 ± 0.14
4.0 ± 0.4
The contribution of seasonal variations to sidereal vector
(VAR) is determined from an antisidereal vector. Analogical
contribution on right ascension is determined from an
antisidereal vector and zenith- angular distribution of events
Parameters of anisotropy vectors for the trigger-500 at E0 ~ 1017 eV
Vector
Solar
Events
984582
Sidereal
without Nov.
892362
984582
Antisidereal
SiderealVAR
without Nov.
892362
984582
without Nov.
892362
984582
without Nov.
892362
H
1
2
1
2
1
2
1
2
1
2
1
2
1
2
1
2
R,%
R0.95, %
1.66 ± 0.14
0.70 ± 0.14
1.58 ± 0.15
0.65 ± 0.15
0.65 ± 0.14 0.87
0.55 ± 0.14 0.77
0.98 ± 0.15 1.22
0.40 ± 0.15 0.62
0.69 ± 0.14
0.30 ± 0.14
0.75 ± 0.15
0.41 ± 0.15
0.43 ± 0.2
0.72
0.76 ± 0.2
1.07
0.30 ± 0.21 0.59
0.34 ± 0.21 0.64
, h
20.4 ± 0.33
4.0 ± 0.4
20.6 ± 0.36
4.6 ± 0.44
10.1 ± 0.84
5.0 ± 0.5
10.1 ± 0.58
4.5 ± 0.72
9.3 ± 0.79
7.2 ± 0.9
8.0 ± 0.76
6.2 ± 0.7
15.0 ± 1.8
5.6 ± 0.5
12.5 ± 2.7
6.8 ± 1.2
Harmonic analysis. Interval about 1017 eV
The inhomogeneity of the sky survey is essential to the Yakutsk
EAS array. Its account considerably decreases amplitudes of
anisotropy vectors
Taking account distorting factor, the statistical significant
anisotropy of the first and second harmonics is not observed:
By sidereal time
amplitude of the first harmonic is smaller than
0.6% with the probability 0.95 and for second
harmonic it is 0.65%;
In the analysis samples of previous work (1997) the amplitude
of the first harmonic with respect to the RA with regard to the
perturbing factors is (0.45 ± 0.55)%. (Instead of 1.35)
Harmonic analysis. Interval about 1018 eV
Parameters of anisotropy vectors for the trigger-1000. In a
column R0.95 95 % confidence limit are given. 34596 events
Vector
Solar
Sidereal
Antisidereal
Sidereal-VAR
H
1
2
1
2
1
2
1
2
R,%
2.66 ± 0.76
0.99 ± 0.76
1.63 ± 0.76
1.77 ± 0.76
1.23 ± 0.76
1.31 ± 0.76
0.58 ± 1.1
1.23 ± 1.1
R0.95, %
2.7
2.9
2.3
2.8
, h
19.4 ± 1.1
4.9 ± 1.5
8.0 ± 1.8
2.0 ± .85
5.7 ± 2.4
6.6 ± 1.1
5.5 ± 7.2
0.4 ± 1.7
Harmonic analysis. Interval about 1018 eV
RA 18.0<Log(E0)<18.5, Events: 27301, r1 = (0.7 ± 0.9)%
At ≈1018 eV the statistically significant anisotropy is not
observed.
Our results do not confirm given AGASA. The Yakutsk array
cannot observe the center of the Galaxy.
Events with E0 > 1019 eV
Harmonic analysis RA: 19.0 <Log(E0)< 19.5, events 312,
r1 = (26.4 ± 8.0), α1 = (2.3 ± 1.2) h , P = 0.004
This result specifies existence anisotropic components of
cosmic rays in the given interval of energy
Distribution of cosmic rays on galactic latitude
RNSA = (nN-nS)/ (nN+nS) - parameter of asymmetry where nN number of particles from northern hemisphere, nS from southern.
Points - experimental data of the Yakutsk array. Curves - results of
model calculations for a mix of isotropical extragalactic protons
with nucleus (Nu) and protons (P) from a disk of the Galaxy
Two-dimensional Marr wavelet on the
equatorial sphere (’Mexican Hat’)
Two-dimensional wavelet amplitude as a function of energy and
declination.
Events with E0 > 1019 eV
Two-dimensional Marr wavelet:
In an energy bin 19.0 < Log(E) < 19.5 eV the observed
amplitude is significantly greater than isotropic one:
Wobserved / Wisotropic = 2.83 ± 0.51;
αmax = (2.3 ± 1.3) h; δmax = 52.50 ± 7.50
Events with E0 > 1019 eV
Direction of the increased intensity on a map
Map of distribution on arrival directions of cosmic rays with
Е0 > 8·1018 eV in galactic coordinates on Yakutsk data and
SUGAR. Intensity - in terms of a standard deviation of a
difference of observable number and expected average for
an isotropic flux. A bold line - a plane of the Supergalaxy
Events with E0 > 1019 eV
For showers with energy E0 >1019 eV the
deviation of experimental distribution on arrival
directions from isotropic one is observed.
Probably it is caused by some excess of events
from a Supergalaxy plane.