1. Vasily Prosin (SINP MSU)
Tunka-133: Primary Cosmic Ray Mass Composition in the energy range of 1016 – 1018 eV
Vasily Prosin (SINP MSU)
For the Tunka Collaboration

2. Tunka Collaboration
S.F. Beregnev, S.N. Epimakhov, N.N. Kalmykov, E.E. Korosteleva, N.I. Karpov, V.A. Kozhin, L.A. Kuzmichev, M.I. Panasyuk, E.G. Popova, V.V. Prosin, A.A. Silaev, A.A. Silaev(ju),
A.V. Skurikhin, L.G. Sveshnikova, I.V. Yashin
– Skobeltsyn Inst. of Nucl. Phys. of Lomonosov Moscow State Univ., Moscow, Russia;
N.M. Budnev, A.V. Dyachok , O.A. Chvalaev, O.A. Gress, A.V. Korobchenko, R.R. Mirgazov, L.V. Pan’kov, Yu.A. Semeney, A.V. Zagorodnikov
– Inst. of Applied Phys. of Irkutsk State Univ., Irkutsk, Russia;
B.K. Lubsandorzhiev, B.A. Shaibonov(ju)
– Inst. for Nucl. Res. of Russian Academy of Sciences, Moscow, Russia;
V.S. Ptuskin
– IZMIRAN, Troitsk, Moscow Region, Russia;
Ch. Spiering, R. Wischnewski
– DESY-Zeuthen, Zeuthen, Germany;
A. Chiavassa
– Dip. di Fisica Generale Universita' di Torino and INFN, Torino, Italy.
D. Besson, J. Snyder, M. Stockham
– Department of Physics and Astronomy, University of Kansas, USA

3. Irkut river
Tunka-133
Tunka-25

4. Experimental data 2 winter seasons 2009-2010 and 2010-2011
102 clean moonless nights
~ 600 h of data acquisition with trigger rate ~ 2 Hz
events
Zenith angle θ ≤ 45°, Rcore < 450 m:
~ events with E0 > 6·1015 eV – 100% efficiency
~ events with E0 > 1016 eV
~ 400 events with E0 >1017 eV

5. CORSIKA: Simulated lateral distributions and fitting function (LDF)
E0 ~ Q
LDF has a single variable parameter of shape - steepness: P=Q(100)/Q(200)
0 < R < 700 m
Q(R) = Qkn·exp((Rkn-R)·(1+3/(R+3))/R0)
Q(R) = Qkn·(Rkn/R)2.2
Qkn
R0 = ·P [m]
Rkn = ·(P-4) [m]
b = ∙log10(6.5-P)
Rkn
1 - P= – P= – P=3.2
Q175
Q(R) = Q(200)·((R/200+1)/2)-b

6. Primary energy reconstruction
Q175
E for every event
The details of this procedure and the primary energy spectrum will be reported by Leonid Kuzmichev at the next session after the tea break (# 250).

7. Primary nucleus E0 , A? Xmax X0
Xmax(model independent): Xmax = Xp – δXmax/δlnE∙lnA Two methods:
θ, φ
Xmax
2. Pulse width: ΔX = a – b∙FWHM [g/cm2]
ΔX = X0/cosθ – Xmax
1. LDF steepness P:
Hmax= c – d·P
Hmax=T0((1-(Xmax cosθ /X0)grad(T)/C)/(grad(T)·cosθ)
T – atm. temperature °K
C=34.18 km/grad
X0=965 gcm-2 X0

8. An example of real shower of 16.03.2010
The limits for distances used now to unify Xmax analysis for all energy range:
WDF
FWHM(400) – analysis
P – analysis
LDF

9. Mean mass composition – previous experiments

10. Mean mass composition – previous data
Xmax = 560 g·cm-2
Normalization point for the phenomenological approach

11. Simulation for Tunka.
CORSIKA: Measurement of a distance to EAS maximum with the Cherenkov light LDF steepness P
Hmax, км
Simulation for QUEST 2000 m a.s.l.
480 simulated events with E0 from 1 PeV to 20 PeV and zenith angles θ from 0° to 25° P
Hmax= – 2.33·P , [km]

12. 2222 events: 16.4 < log10(E0/eV) < 16.5
PHENOMENOLOGICAL APPROACH: Experimental LDF steepness vs. zenith angle for E0 = 3·1016 eV
2222 events: 16.4 < log10(E0/eV) < 16.5 
cosθ  Hmax in [km]: Hmax=96/cosθ·(1-(Xmaxcosθ/X0)0.0739)
For t = - 30°C, X0 = 965 g·cm-2,
<Xmax> = 560 g·cm-2 for E0 = 3·1016 eV

13. PHENOMENOLOGICAL APPROACH: Hmax vs. LDF steepness parameter P
Hmax= – 2.08·P , [km]

14. PHENOMENOLOGICAL APPROACH: Hmax vs. steepness parameter P
Simulation without absorption
Simulation with absorption
Hmax= – 2.08·P , [km]

15. CORSIKA: Xmax vs. FWHM(400)

16. PHENOMENOLOGICAL APPROACH: FWHM(400) vs
PHENOMENOLOGICAL APPROACH: FWHM(400) vs. zenith angle for E0 = 3·1016 eV
cosθ  ΔXmax in [g·cm-2]: ΔXmax=X0/cosθ - Xmax
X0 = 965 g·cm-2,
<Xmax> = 560 g·cm-2 for E0 = 3·1016 eV

17. PHENOMENOLOGICAL APPROACH: ΔXmax vs. FWHM(400)
Simulation
ΔXmax= 3522 – 1700·FWHM(400)

18. Mean depth of EAS maximum
Tunka-25

19. Mean mass composition – Tunka-133
<Xmax> LnA
by interpolation between QGSJET-01 curves for
p and Fe.
Possible systematic uncertainty ± 0.25.

20. Mean mass composition – Tunka-133
Comparison with some previous experiments measured Nμ/Ne ratio:

21. Mean mass composition – Tunka-133
Comparison with some previous experiments measured Nμ/Ne ratio:

22. Mean mass composition – Tunka-133
Comparison with some previous experiments measured Nμ/Ne ratio:

23. An example of a single log bin Xmax distribution for 16
An example of a single log bin Xmax distribution for 16.4 < log10(E0 /eV) < 16.5

24. CONCLUSION
Primary mass composition changes from light (He) at the knee to heavy at 3·1016 eV
The mass composition is heavy till at least 1017 eV
More statistics is needed at the energy range 1017 – 1018 eV
PLANS
Expanding of the methods to the core distance range
R > 200 m
2. Deployment of 6 additional clusters at about 1000 m from the array center (#495, N. Budnev).
3. The new simulations and the Xmax distribution analysis.

25. Thank you!

26. Processing Decoding and store of the 19 clusters data.
Collecting of clusters data to the united events by timer inside 2 μs.
Analysis of the trigger rate.
List of good weather periods (more that 2 h).
Noise and interference analysis.
Pulse fitting and pulse parameters reconstruction.
Calibration by the data itself
EAS arrival direction (θ, φ) reconstruction .
Reconstruction of EAS core position, LDF steepness P, Q175, FWHM(400m) .

27. Further information analysis:
Xmax distributions in the narrow lgE0 bins.
Simulation of Xmax distributions for the different primary mass groups.
Comparison of the experimental and combined simulated distributions and thus estimation of the most probable primary composition for the every energy bin.
Estimation of <lnA> vs. E0 in the energy range 1016 – 1017 eV.

28. CORSIKA: Width vs. Distance Function (WDF)
ΔX=150 g/cm2
CORSIKA: Width vs. Distance Function (WDF)
ΔX=850 g/cm2
τR=FWHM(R)
WDF has a single variable -FWHM(400)
Rch
lg(τR+200)=lg(τch+200)+b2∙(R-Rch)
τch
lgτR=lgτch+b1∙(R-Rch)
b1= ∙lgτ b2= ∙lgτ Rch= ∙lgτ ∙(lgτ400)2 lgτch=lgτ400+b1(Rch-400), Rch<400m lg(τR+200)= lg(τch+200) + b2(Rch-400), Rch>400m