Post on 04-Jan-2016
Yakutsk results: spectrum and anisotropy
M.I. Pravdin for Yukutsk CollaborationYu.G. Shafer Institute of Cosmophysical Research and
Aeronomy, 31 Lenin Ave., 677980 Yakutsk, Russia
A plan of the location of detector stations of the Yakutsk EAS Array
1 .5 m to C en tre r
5 5
C eren k o v lig h td e tec to r
S c in tilla tio nd e tec to r 2 m 2
S in ch r. re c iv.
Station of Yakutsk EAS Array
The diagram of the trigger of the Yakutsk EAS array
-3000 -2000 -1000 0 1000 2000 3000
-2000
-1500
-1000
-500
0
500
1000
1500
2000
Y
X
Red triangles - trigger-500 from 1992 - 63 cells, SII=6.8 km2
up to 1992 - 19 cellsSI =2.6 km2
Blue ones - trigger-1000 from 1990 - 24 cells SII = 10.5 km2
Green circle - 10 stations of the trigger-1000, working up to 1990 24+16 = 40 cells SI = 17.3 км2
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.
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 = 2.16104 / (0.37 + 1.1(Xm /1000) in the interval of waves 300-
800nm In view of mean atmospheric transmittance
Eel = 2.2106NsN 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 energy on one muon = 10.6109 eV
Ei and E are the energy of muon losses on ionization and the neutrino
Ei + E = 0.76E
Eh = 0.06Ei 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%
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 3.2e17*S^1.08 Fedunin, Theses 6.5e17*S^1.08 Fedunin, Theses
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
Dependence S600 on temperature
• Molier unit
• S600(R0) is recalculated on R0 = 68 m. The formula is received from the assumption, that full number of particles equally for different R0
• R0 = 68 corresponds T = -25°C - average temperature of the periods for Cerenkov light experiment.
)1(0
)2(0 )668/)600(()/68( bb
tmr RRK
mPTR ),/1000()273/)273((750
Dependence Ktmr on temperature
-60 -40 -20 0 20 400,7
0,8
0,9
1,0
1,1
1,2 = 0o
= 60o
Ktm
r
T, oC
Cosθ > 0.95; Tyan= -37, Pyan=1008; Tmay= 8, Pmay=992
0,0 0,5 1,0 1,5 2,0-11,4
-11,2
-11,0
-10,8
-10,6 Cos >0.95
Jan without correction May without correction Jan with correction May with correction
Lo
g(I
*S60
02 , (m
2 *s*s
r)-1*e
V2 )
Log(S600
, m-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 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
-3000 -2000 -1000 0 1000 2000 3000
-2500
-2000
-1500
-1000
-500
0
500
1000
1500
2000
2500
26
27
28 29
30
31
32
33 34
35
22
23 24
25 13 12 21
20 11 1 8 14
15 9 10 19
18 17 16
15
8
13
23
22
12
Errors of energy estimation in EAS with E0>4x1019 eV
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
Differential Energy Spectrum at E0 > 1017 eV
1017
1018
1019
1020
1024
1025
- Yakutsk - AGASA - HiRes
J E
o
3 , m-2s-1
sr-1eV
2
Eo, eV
Integral Energy Spectrum of the Yakutsk Array
1018
1019
1020
1024
1025
- Trigger-500 - Trigger-1000 - Trigger-1000, max. area
I Eo
2 , m-2s-1
sr-1eV
2
Eo, eV
Largest eventsN Date Time θ E0 Error
E0 % Galactic latitude
Galactic longitude
1 18-02-04 22:20:38 47.7 1.6e20 46 16.3 140.2 2 07-05-89 22:03:00 58.7 1.5e20 40 2.7 161.6 3 21-12-77 18:45:00 46.0 1.1e20 27 50.0 220.6 4 15-02-78 03:35:00 9.6 9.8e19 36 15.5 102.0
On the Yakut EAS array four events with energy greater GZK-cutoff 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.
1017 1018 1019 10201023
1024
1025
Trigger-500 Trigger-1000
g=2.7
g=2.5
E/E = 25%
J E
o
3 , m-2s-1
sr-1eV
2
Eo, eV
Comparison of the Yakutsk array Spectrum with accounts from AGNBerezinsky 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 R , % , hWithout regard
to survey4.19 ± 0.14 22.2 ± 0.131
With regard tosurvey
1.66 ± 0.14 20.4 ± 0.33
Without regardto survey
1.35 ± 0.14 4.2 ± 0.22
With regard tosurvey
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 Events H R , % R0.95, % , h1 1.66 ± 0.14 20.4 ± 0.339845822 0.70 ± 0.14 4.0 ± 0.41 1.58 ± 0.15 20.6 ± 0.36
Solar
without Nov.892362 2 0.65 ± 0.15 4.6 ± 0.44
1 0.65 ± 0.14 0.87 10.1 ± 0.849845822 0.55 ± 0.14 0.77 5.0 ± 0.51 0.98 ± 0.15 1.22 10.1 ± 0.58
Sidereal
without Nov.892362 2 0.40 ± 0.15 0.62 4.5 ± 0.72
1 0.69 ± 0.14 9.3 ± 0.799845822 0.30 ± 0.14 7.2 ± 0.91 0.75 ± 0.15 8.0 ± 0.76
Anti-sidereal
without Nov.892362 2 0.41 ± 0.15 6.2 ± 0.7
1 0.43 ± 0.2 0.72 15.0 ± 1.89845822 0.76 ± 0.2 1.07 5.6 ± 0.51 0.30 ± 0.21 0.59 12.5 ± 2.7
Sidereal-VAR
without Nov.892362 2 0.34 ± 0.21 0.64 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 vectorsTaking 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 H R , % R0.95, % , h1 2.66 ± 0.76 19.4 ± 1.1Solar2 0.99 ± 0.76 4.9 ± 1.51 1.63 ± 0.76 2.7 8.0 ± 1.8Sidereal2 1.77 ± 0.76 2.9 2.0 ± .851 1.23 ± 0.76 5.7 ± 2.4Antisidereal2 1.31 ± 0.76 6.6 ± 1.11 0.58 ± 1.1 2.3 5.5 ± 7.2Sidereal-VAR2 1.23 ± 1.1 2.8 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.
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
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.