The primary cosmic ray mass composition around the knee of the energy spectrum

UCLEARPHYSIC~ PROCEEDINGS SUPPLEMENTS kSI.SkVlkR

Nuclear Physics B (Proc. Suppl.) 39A (1995) 235-241

T h e P r i m a r y C o s m i c R a y M a s s C o m p o s i t i o n a r o u n d the K n e e o f the E n e r g y S p e c t r u m G.B. Khristiansen, Yu.A. Fomin, N.N.Kalmykov, G.V.Kulikov, S.S.Ostapchenko, V.P.Sulakov, A.V.Trubitsyn Institute of Nuclear Physics, Moscow State University, Moscow 119899, Russia Experimental muon number distributions in EAS obtained at Moscow State University are analysed to estimate the primary mass composition at energies before and after knee. The mass composition before the knee corresponds to the normal one (as at E0-10 ~2 eV), while experimental data after the knee are in agreement with the assumption that normal composition becomes enriched slowly by heavy nuclei, as also supported by contemporary diffusion models.

1. INTRODUCTION The knowledge of the mass composition of primary cosmic rays (PCRs) is essential for the theory of generation and propagation of cosmic rays in the Galaxy. In particular, a subject of interest is to understand the nature of the well-known knee in the PCR energy spectrum at E0=3xl0 ~5 eV, the existence of which was first reported more than 35 years ago [1]. The information concerning the PCR mass composition in the energy region including the knee can only be obtained by indirect methods. Among them, the method of investigation of EAS muon number fluctuations [2,3] gives an opportunity to study the mass composition in wide energy intervals before and beyond the knee. in this paper we present a new set of experimental data obtained by the MSU EAS array with better statistics (an increase by about 1-2 orders of magnitude).

2. E X P E R I M E N T A L D A T A

Muon density p, was measured in an individual shower by an underground muon detector of 36.4 m 2 total area [4]. The threshold energy of muons is 10 GeV. The muon size of a shower N, is determined by the relation N u = p/~ / f u ( r , N e , S )

(1)

0920-5632/95/$09.50© 1995 Elsevier Science B.V. All rights reserved. SSDI

0920-5632(95)00026-7

where fg is the muon lateral distribution ftmction (LDF). Experimental data on muon LDFs were analysed in the wide range of electron size Ne=10S+5xl07, in order to find the dependence of the average muon LDF on Ne and shower age S [5]. Both dependences are rather weak. The analysis showed that if we use, as usual, our muon LDF approximation f u ~ r-n "exp(-r / R)

(2)

with R=80m, the value o f n changes from 0.6 to 0.7 at N¢= 105+5x 107 (the inaccuracy of n is about 0.03). As far as the dependence of f, on S is concerned, a noticeable deviation of the value of n from the average was observed only for young showers with S<0.9 (n=0.77+0.04 at Ne-(2-10)x105). The contribution of those showers to the total is less than 10%. Thus the inaccuracy in the determination of N , , that may arise if one applies average LDF for all showers, does not exceed 6-7%, because the lateral distribution for the bulk of showers (80-90%) does not differ significantly from average lateral distribution. Experimental muon number distributions obtained are shown in Fig.1. For better statistical accuracy we combined several intervals of Ne. The distributions presented correspond to the following regions of PCR energy spectrum: before the knee (Ne=10S-4xl05, 14238 showers), immediately after the knee (Ne=4×105-2.5×i06, 23039 showers), and far beyond the knee (Ne=107-4×107, 841 showers).

G.B. Khristiansen et al./Nuclear Physics B (Ppvc. Suppl,) 39A (I995)235-241

236

N

078 "

N,u = N u ( N e ) ( e o / N e )

(3)

Wp.

The values of Ne0 chosen are 2x105, 10 6, and 2×107, respectively. The relative dispersions x/D/ for these

0.20

distributions are equal to 0.63+0.01, 0.56+_0.01, and 0.42_+0.01, respectively. Taking into account errors due to the uncertainty of shower axis location and Poissonian fluctuations of 9~ , we find corrected relative dispersions (x/D/< N~ >).... to be 0.54+-0.01,

0.15

0.10

L

0.05

0.00

.5

-1,0

-0.5

I

0.'0

,

0.5 1.0 Lg(NJ)

Fig. 1 Experimental EAS muon number distributions at fixed values of Ne0:2 x 105 (dashed line), 106(solid line), and 2x 10 7 (dotted line). In each Ne interval muon size N~,(N~) for individual showers was recalculated to the fixed value of Neo according to the relation [6]:

WlJ. 0.20

0.50+-0.01, and 0.38+-0.02, respectively. Those are connected with shower development. From the data presented it is clear that the distributions become narrower with increasing Ne , that is, we obtained evidence that muon number fluctuations become less in the region far beyond the knee (Ne0=2×10 v) compared to the region before the knee (N~o=2X 105).

3. CALCULATION MODEL A reliable model describing hadron-nucleus and nucleus-nucleus interactions at high and superhigh energies is necessary to interpret the experimental results. Nowadays the quark-gluon string (QGS)

W~t [-i

0,2a

a)

0.15

b)

0,15 i.....

1

j-

0.10

O.lO

__2 _

0.00 150

-1.00

--0150

,

0.00

0.50

1.0C

Lg(NJ)

0.00

-1.50

-1.00

,

-0.50

0.[30

0.50

1.06

Lg(NJ)

Fig.2 The influence of experimental errors and fluctuations of muon lateral distribution functions for different nuclei on muon number distributions: a) before the knee, Ne0=2×105 ; b) far beyond the knee, Ne0=2× 107 . Solid line - including the above mentioned factors, dashed line - without these factors.

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G.B. Khristiansen et al./Nuclear Physics B (Proc. Suppl.) 39A (1995) 235 241

Table 1. Relative intensities of nuclei ~;roups (%) for different mass compositions Nuclei group

p

c~

M

H

Fe

Normal composition

32

23

21

14

10

14±9

23±4

26±12

13±8

24±10

Peters-Zatsepin model E0=1016 eV E0=1017 eV

24 14

24 14

24 25

16 24

12 23

Juliusson model E0=4× 1015 eV

2

4

10

14

70

Heavy composition Asakimori et al.. [13]) E0~4× 1014 eV

Stanev et al [ 17] Eo=10 is eV Eo=1017 eV

7 8

31 17

model can be considered as a basic model [7] which describes various experimental EAS data and explains almost all characteristics of ),-ray and hadron families [8,9]. In the present analysis we used improved version of QGS model [10] that simulates directly the configuration of nucleus-nucleus collision, and allows for fragmentation of the spectator part of the projectile nucleus. Calculations predict almost the same average EAS characteristics as the superposition model, while fluctuations appear to be approximately twice as great for EAS generated by nuclei. The increase of fluctuations in EAS generated by nuclei complicates the problem of the primary mass composition study, but we can check the sensitivity of the results to various predictions concerning the primary mass composition.

18 17

H1

H2

(Ne-S)

(CI-Mn)

23 25

8 12

13 21

Then, using a Monte-Carlo method, we studied how muon number distributions are influenced by experimental inaccuracy in the shower axis position, and by fluctuations of the muon lateral distribution for different nuclei. We assumed the Peters-Zatsepin diffusion model of PCR propagation with normal composition before the knee (see Table 1). From the calculated distributions (Fig.2) it follows that the conclusion about decreasing muon number fluctuations with increasing Ne remains true. To compare experimental data with calculations, we used the following parameters of muon number distributions. The first parameter is asymmetry, i.e. the difference between the number of events in adjacent central intervals of N ~ , / < N~, > :

As= N -0.2


<0 -

4. ANALYSIS OF EXPERIMENTAL DATA. Using the QGS model we calculated muon lateral distribution functions at fixed Ne, and they are in good agreement with experimental data [5].

N 0<_

L g < N p > -<0.2

(4)

The second parameter is the absolute value of the difference between experimental and theoretical

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G.B. Khristian,~en et al./Nuclear Physics B (Proc. Suppl.) 39,4 (1995) 235-241

numbers of events in the central part of the distribution:

Table2. As~/mmetr,/anal~csis. Before knee Far beyond knee

B = Ncexp ( L g ( N u / < Np >) _<0.2) -

(5)

Nctheor ( L g ( N p / < N . >) _<0.2)

This way we exclude the tails of muon number distributions, where statistics is poor. First of all we checked the assumption that the primary composition consists purely of protons. This assumption can be excluded by the comparison of the observed asymmetry As of muon number distributions with the calculated one. In fact we expect strictly positive As for pure protons, because the muon distribution at fixed Ne may be satisfactorily described by the log-normal law [11], and for this law the most probable value of a variable is strictly less than its average value. At the same time, experimental values of As are negative (Table 2). For the comparison of experimental and calculated muon number distributions in the case of complex PCR composition, we mainly used the absolute value of the difference between N~ ~xp and N~ th~or(parameter B, see (5)) expressed in standard deviations cy~×pof Nc exp.

Ne0

2-105

2-107

Asexp

-47+87

-63+25

ASproton

+853

+64

(Asproton- ASexp)/~exp

10.2

5.1

In the further analysis we assumed different primary mass compositions, as presented in Table 1. The normal composition is close to the mass composition at energy -1012 eV [12]. The JACEE mass composition [13] is enriched in heavier nuclei at energies >1014 eV (heavy composition). We also considered some other contemporary PCR compositions fitting experimental data. The comparison of calculated and experimental muon distributions at Neo=2xl05 (Fig.3a) shows that heavy composition is in strong contradictions with experimental data below the knee (the discrepancy is about 8~). The normal composition agrees with the

Wu

W~ @

0.20 0.15 a

b

!

0.15

0.10 0.10 0.05 0.05 @

0.00 -1.5

-1 .o

-0.5

o.o

0.5

1.o

0.00 -1.5

I

-I

.0

I

-0.5

i

0.0

i

0.5 1.0 Lg(N~)

L g ( N J < N.>) Fig 3. EAS muon number distributions at fixed values of Ne. Histograms - experimental data for Ne0=2x 10s (a) and 2x 107 (b). Calculations: (o) - normal composition, (e)- heavy composition, (×)- composition according to Peters-Zatsepin model.

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G.B. Khristiansen et al./Nuclear Physics B (Proc. Suppl.) 39A (1995) 235 241

experimental one satisfactorily (the discrepancy is less than 2cr). However, at high N¢, especially at N~0=2×107 (Fig.3b), the normal composition deviates from experimental data (the discrepancy is about 4~). Agreement at Ne0=2xl07 may be achieved if the normal composition transforms slowly into a heavier one. Thus, it is quite natural to adopt the diffusion model of PCR propagation in the Galaxy with the following energy dependence of diffusion coefficient:

D ( E o ) - Eo Ar

(6)

The dependence (6) is valid for different nuclei at

energies Eo>E~,(Z). We adopted E~,(Z) according to the Peters-Zatsepin model [14,15]:

E~(z) =

z . E~r(p)

(7)

We used the following values of parameters: for the slope of the PCR energy spectrulm before the knee 7=1.65, A),=0.5, and Eer(p)=4xl0 eV. Table 1 presents PCR mass compositions obtained in the Peters-Zatsepin model for 1016 and 1017 eV (assuming normal composition before the knee). In the region far beyond the knee (Ne0=2× 107), the normal mass composition modulated by diffusion enables us to reach a substantially better agreement (within 2or) with the experimental muon distribution. Thus it is clear that

N c exp N c theor

1.1

J~

1.0

09

0.8

0.7 I

5.0

5.5

I

6.0 Lg(Ne)

I

I

6.5

7.0

7.5

Fig 4. The dependence of ratio N~ exp/N¢theoron Ne for various mass compositions: (o) - normal, (*) - heavy, (x) -according to the Peters-Zatsepin model, (E3) - Swordy composition, (+) -Stanev et al. model, (0) Juliusson model.

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G.B. Khristiansen et al./Nuclear Physics B (Proc. Suppl.) 39A (1995) 235-241

the decreasing width of the muon distribution is due to a significant fall of proton abundance in PCRs, and to the increasing role of medium and heavy nuclei. Now we shall discuss some other possibilities to explain our data. A fit consistent with JACEE data at energies ~I014 eV was proposed by Juliusson [16]. In his model each group of nuclei changes its exponent ~'A by 0.5 at energy EA=Z.I.4×1014 eV. Although Juliusson's model describe the knee of the PCR spectrum well, the mass composition obtained is too heavy before the knee (Table 2), and is in strong disagreement with our experimental data (Fig.4). A rather complicated PCR model was proposed recently by Stanev et al [17]. In the model they proposed that cosmic rays at energies 1015-1017 eV originate mainly from two sources: a) normal supernova explosions into the approximately homogeneous interstellar medium, and b) supernova explosions into stellar winds. The authors prove that their concept allows a proper understanding of the PCR spectrum and composition at energies above 1013 eV. The special treatment of nuclei accelerated in the regions with different magnetic field topology is of great importance in this model, and gives an opportunity to fit the spectrum successfully in the knee region. The resulting mass composition at Ne0=2xl07 agrees well with our data (agreement within lc~), but at Ne0=2×105 the mass composition predicted by the model [17] is too heavy, and it is incompatible with our data (discrepancy -14~). Thus the Peters-Zatsepin diffusion model seems to describe the whole bulk of our experimental data adequately. A new diffusion model [18] which takes into account an effect of Hall diffusion also explains our data. It should be noted that our conclusion remains true if, instead of the normal composition, we use the mass composition proposed by Swordy [19] based on experimental data at E0<1014 eV. It is connected with the fact that in this composition the sum of proton and a-particle contributions is the same as in the normal composition, and fluctuations in showers initiated by protons and a-particles are namely comparable. The recent investigation of shower maximum depth distributions with the Fly's Eye array [20] also confirms our results [21 ] that the mass composition at E0-1017 eV is characterised by a greater

abundance of medium and heavy nuclei, than the normal composition.

5. CONCLUSION We would like to stress the following points. 1. The MSU array gives a possibility to investigate the PCR mass composition not only before the knee, but also beyond the knee (E0=10161017 eV). 2. The mass composition before the knee (E0-1015 eV) is close to the normal composition (and also not incompatible with the Swordy composition). 3. The analysis of the muon number distribution's asyrmnetry allows to exclude a pure proton composition. 4. The PCR mass composition's changes over the energy interval E0=1015-1017 eV are in agreement with the Peters-Zatsepin diffusion model (and also with the Hall diffusion model).

Acknowledgements. This work has been carried out under the financial support of the Russian Fund of Fundamental Researches.

REFERENCES 1.

Kulikov G.V., Khristiansen G.B., Soy. Phys. JETP, 35 (1958) 635. 2. Fukui S. et al., Progr.Theor.Phys., 6 (1960) 1. 3. Khristiansen G.B. et al., Proc. 8 ICRC. Jaipur, 3 (1963) 393. 4. Vernov S.N. et al., Proc. 16 ICRC. Kyoto, 8 (1979) 129. 5. Khristiansen G.B. et al., Astroparticle Phys., 2 (1994) 127. 6. Khristiansen G.B. et al., lzv.Akad.Nauk USSR. Ser.Fiz., 42 (1978) 1434. 7. Kaidalov A.B. et al., Izv.Akad.Nauk USSR. Ser.Fiz., 50 (1986) 2087. 8. Kalmykov N.N. et al., Yadernaya Fiz., 41 (1985) 947. 9. Dunaevsky A.M. et al., Izv.Akad.Nauk USSR. Ser.Fiz., 55 (1991) 654. 10. Kalmykov N.N.,Ostapchenko S.S., Yadernaya Fiz. 56 (1993) 105. 11. Kalmykov N.N., Yadernaya Fiz. 10 (1969) 121.

Gt~ Khristiansen et al./Nuclear Physics B (Proc. Suppl.) 39A (1995) 235-241

12. 13. 14. 15. 16.

Simon N. et al, Proc. 16 ICRC. Kyoto. 1 (1979) 352. Asakimori K. et al, (JACEE collaboration). Proc. 23 ICRC. Calgary. 2 (1993) 25. Peters B., Proc. 6 ICRC. Moscow. 3 (1959) 157. Zatsepin G.T. et al., Izv.Akad.Nauk USSR. Ser.Fiz. 26 (1962) 685. Juliusson E., 13 Europ. CR. Syrup. Geneva.. Book of Abatracts (1992) OG-6.11.

241

17. Stanev T., Biermann P.L., Gaisser T., Astron. Astroph., 274 (1993) 902. 18. Ptuskin V.S. et al., Astron. Astrophys., 268 (1993) 726. 19. Swordy S., Proc. 23 ICRC. Calgary.. Inv. and Rapp. papers, (1993) 243. 20. Bird D.J. et al., Proc. 23 ICRC, Calgary, 2 (1993) 38. 21. Kalmykov N.N. et al.., lzv.Akad.Nauk RAN. Ser.Fiz., 58 (1994) N12.