ISSN 1062-8738, Bulletin of the Russian Academy of Sciences: Physics, 2009, Vol. 73, No. 5, pp. 584–587. © Allerton Press, Inc., 2009.Original Russian Text © A.A. Petrukhin, S.Yu. Matveev, 2009, published in Izvestiya Rossiiskoi Akademii Nauk. Seriya Fizicheskaya, 2009, Vol. 73, No. 5, pp. 623–626.

584

Gamma-Rays from Magellanic Cloudsand Origin of Cosmic Rays

A. A. Petrukhin and S. Yu. Matveev

Moscow Engineering Physics Institute (State University), Moscow, 115409 Russiae-mail: AAPetrukhin@mephi.ru

Abstract

—Various calculations of the integral spectrum of

γ−

rays from the neutral pion decays generated in pp-interactions have been analyzed. The estimate of the integral

γ

-ray spectrum with allowance for the behavior ofthe cross section of

π

0

production in the pp

→

pp

+

n

π

0

+

X

reaction near the threshold for each channel and theproton spectrum at low energies (<1 GeV) proved to be much lower than those obtained in earlier calculations.

DOI:

10.3103/S1062873809050153

INTRODUCTION

Measurements of the flux of

γ

-rays with energiesabove 100 MeV from the Magellanic Clouds (MCs) isa rare possibility of finding experimental arguments forchoosing between the galactic and metagalactic modelsof the origin of cosmic rays, whose interaction withinterstellar gas is considered to be the key process in

γ

-ray generation from neutral pion decay [1]. The con-tribution of other channels (decay of hyperons and

K-

and

η

-

mesons) is approximately 10–20% of the neutralpion decay [2]; that is why only the

γ

-ray flux from neu-tral pions is considered in nearly all papers.Bremsstrahlung of electrons is considered as the sec-ond in importance process; however, its role in solutionof the problem is not evident and in many works it wasexamined only qualitatively. In this paper, influence ofvarious parameters on the estimation of

γ

-ray flux fromMC is also analyzed only for the first process.

The first theoretical estimates of

γ

-ray fluxes fromthe Small Magellanic Cloud (SMC) with energiesexceeding 100 MeV, made on the assumption that thecosmic ray density in the Universe is constant, yielded

F

γ

(>100

MeV) =

10

–7

photons s

–1

cm

–2

[3]. After obtain-ing the upper limit for the

γ

-ray flux with an energyabove 100 MeV from the SMC (

F

γ

(> 100 MeV) <

0.5

×

10

–7

photons s

–1

cm

–2

) with the Energetic Gamma RayExperiment Telescope (EGRET) [4], it was con-cluded that the observed cosmic ray flux has a galac-tic origin [5]. However, the wide spread in the resultsof calculations performed in [6–9] shows that the sit-uation is far from unambiguous, although the funda-mental quantity (the total number of

π

0

pro-duced in pp-interactions) is calculated from a simpleformula

Γpp π→

(1)

where

ζ

(

T

p

)

and

σ

π

(

T

p

)

are the multiplicity and totalcross section of neural pion production,

J

p

(

T

p

)

is the dif-ferential spectrum of primary cosmic ray (PCR) pro-tons, and

T

p

is the kinetic energy.

The purpose of this study is to analyze the ambigu-ities in the calculations of the diffuse

γ

-ray flux fromneutral pions produced in pp-interactions and deter-mine its value using the experimental data on individualchannels of neutral pion production resulting frompp

→

pp

+

n

π

reactions, up to

n

= 3 inclusive.

Γpp π0→

4π ζ T p( )σπ T p( )T pmin

∞

∫=

× J p T p( ) T p, π0 s 1– (H atom) 1–d

1

1 10

T

p

,

GeV/nucleon

10

–1

10

–2

10

–3

10

–4

J

p

(

T

p

),

cm

–2

s

–1

sr

–1

GeV

–1

Fig. 1.

Approximation of the proton spectrum near theEarth: (

�

) [6], (

�

) [7], (

�

) [8, 9], (

*

) this study, and(

�

) experimental data of [10].

BULLETIN OF THE RUSSIAN ACADEMY OF SCIENCES: PHYSICS

Vol. 73

No. 5

2009

GAMMA-RAYS FROM MAGELLANIC CLOUDS AND ORIGIN OF COSMIC RAYS 585

1. PROTON SPECTRUM

Figure 1 shows the proton spectra used in the papersanalyzed here. The closed symbols correspond to theexperimental data for protons near the Earth [10] andthe lines are spectrum approximations in different stud-ies. It can be seen in Fig. 1 that the proton flux approx-imations in the energy range 1–10 GeV, which makesthe main contribution to the

γ

-ray flux, differ by a factorof 3. The approximation [6] is the closest to the experi-mental data, whereas those used in [8, 9] give overesti-mated values. The experimental data (Fig. 1) aredescribed well by function (2) which will be used here-inafter (

m

p

is the proton mass):

(2)

It should be noted that flattening of the proton spec-trum at

T

p

< 1 GeV can be attributed to the magneticfields in the near-Earth space and probably it is morecorrect to use the spectrum in a purely power-like form.

2. CROSS SECTION OF NEUTRAL PION PRODUCTION

The cross section of neutral pion production result-ing from pp-interactions was first measured in the1950s–1960s [11]. Although half a century has passedsince that time, the precision and completeness of thedata on the production cross sections of neutral pions inpp-interactions with energies below 30 GeV leave muchto be desired, although an overwhelming majority of

γ

-rays with energies above 100 MeV are generatednamely in these interactions [6]. The cross sections of

π

0

production in the range of proton energies greaterthan 12.5 GeV and near the threshold of neutron pionproduction (0.3–3 GeV) are best studied. The statistical

J p T( ) 10 3– 1mp

T p mp+-------------------⎝ ⎠

⎛ ⎞2

–⎝ ⎠⎛ ⎞=

×T p mp+

mp

-------------------⎝ ⎠⎛ ⎞

2.73–

, cm 2– s 1– sr 1– MeV 1– .

precision of the experimental data in this energy rangeis 10–30%, with significant systematic measurementerrors (up to 50%, as was noted earlier [8]). For the pro-ton energy range of ~3–10 GeV, there are no reliableexperimental data, and different approximations areused to calculate the cross sections. It is essential thatthe cross section of π0 production, multiplied by theirmultiplicity, is approximated in this case.

However, taking into account the threshold charac-ter of the energy dependence of multiplicity, it is expe-dient to consider each channel of π0 production sepa-rately. The experimental data on the production crosssection of one π0 are taken from [12]; the experimentalproduction cross section of two π0 and one pion fromthe pp → pnπ+π0 reaction is taken from [13] and that forthree π0 and one pion from the pp → ppπ+π–π0 reactionare from [14]. Near the threshold and for the protonkinetic energy less than 3 GeV, all these cross sectionsare approximated well by the function

(3)

where a, k, and Tc are the fitting parameters listed inTable 1. The error in the experimental data approxima-tion is ~20%. A contribution of these processes to thetotal number of π0 is shown in Table 2; it is apparentfrom the table that to reliably determine a pion flux(and, correspondingly, the γ-ray flux resulting fromtheir decay), it is sufficient to use the cross sections ofproton interactions where one, two, or three pions areproduced. The contribution of the other channels adds~15%.

The sum of the cross sections of the channels underconsideration, with the multiplicity of produced pionstaken into account, is shown in Fig. 2, which also pre-sents the functions used in other studies [6, 8, 9]. Wecan clearly see a significant difference (by a factor ofabout 2) between our results and the cross sections usedin [6] and [8, 9], starting with proton energies of~700 MeV and ~2 GeV, respectively. Such a deviationis attributed to the cross section overestimation in [11]due to the incorrect consideration of the contributionfrom the pp → ppη channel [13] and the differences inthe models used to approximate the experimental datain the energy ranges for which such data are absent.

The number of π0 produced in a pp-interaction (1) withthe production of no more than 3 pions, which was obtainedin this calculation, is = 1.36 × 10–26 s–1 (H atom) –1

with an error of about 20%. Taking into account other chan-nels, as well as the collisions of heavier cosmic ray nucleiwith the interstellar gas yields ~2.3 × 10–26 π0 s–1 (H atom)–1

σπ T p( ) a1 k T p Tc–( )–( )exp+----------------------------------------------------,=

Γpp π→

Table 1. Parameters of fitting the pion production cross sec-tions for different pp-interaction channels with function (3)

Channel a, mb k, MeV–1 Tc, MeV

pp → pp + π0 3.61 0.02 595

pp → pn + π+ + π0 1.08 0.011 1232

pp → pp + 2π0 0.76 0.0093 1307

pp → pp + 3π0 0.48 0.0029 3037

pp → pp + π+ + π– + π0 0.69 0.006 2197

Table 2. Ratios of the fluxes of pions produced in different channels to the main flux y (pp → ppπ0)

Channel pp → ppπ0 pp → pnπ+π0 pp → pp2π0 pp → pp3π0 pp → ppπ+π–π0

Contribution 1 0.18 ± 0.03 0.24 ± 0.05 0.09 ± 0.02 0.07 ± 0.02

586

BULLETIN OF THE RUSSIAN ACADEMY OF SCIENCES: PHYSICS Vol. 73 No. 5 2009

PETRUKHIN, MATVEEV

or ~1.8 × 10–27 π0 s–1 sr–1 (H atom)–1 in a unit solid angle.Note that the value 7.0 × 10–27 π0 s–1 sr–1 (H atom)–1 wasused a priori in [1, 3–5].

3. γ-RAY FLUX WITH ENERGY ABOVE100 MeV PRODUCED BY NEUTRAL

PION DECAY

An integral energy spectrum of gamma rays isobtained from formula (1) by substituting the energydistributions of pions and γ-rays and a factor 2, whichtakes into account the generation of two photons froma neutral pion decay:

(4)Jγ

π >Eγ( ) 8π ζiσπi T p( )

Tth_i

∞

∫i

∑=

× ωγp >Eγ T p,( )J p T p( )dT p, s 1– H atom( ) 1– .⋅

All the channels of pion production from pp-interactionare summed up: ζi is the multiplicity of neutral pions in

the i-th channel, (Tp) is the total cross section of pionproduction in the i-th channel; Tth_i is the thresholdenergy of pion production in the i-th channel; ωγp(>Eγ,Tp) determines a probability of photon production withan energy above >Eγ from a proton with an energy Tp.This probability is a convolution of two probabilities:ωπ(Tπ, Tp) is the probability of pion production with theenergy Tπ from a proton with the energy Tp and ωγπ(>Eγ,Tπ) is the probability of photon production with anenergy above >Eγ from decay of a pion with an energyTπ:

(5)

As follows from the kinematics of two-particle decays[15], the energy distribution of γ-rays is uniformbetween minimum and maximum values, admissible ata specified pion energy. Based on the analysis of theexperimental data of [16], the pion energy distributionwas taken as a normal distribution, which is valid forproton energies up to ~2 GeV:

(6)

In formula (6), the parameters w and T0 depend on theproton energy. Processing of the experimental data of[16] yields the following dependences:

(7)

At higher energies, such a representation is only quali-tative; nevertheless, it allows one to calculate the γ-ray flux(4) with an error of 10–20%. The calculations performed

showed that (>100 MeV) = 4 × 10–26 s–1 (H atom) (withnuclei taken into account, the factor is 1.5), whichmakes 84% of the total number of produced γ-rays andagrees well with the calculations [17], where the por-tion of γ-rays with energies above 100 MeV was 76%.Table 3 compares the integral γ-ray fluxes with energiesabove 100 MeV, obtained by different researchers. Thesignificant spread (by a factor of ~4) in different calcu-lations is related to incorrect approximation of theexperimental data [18] on the neutral pion productioncross sections (which was noted in [6]) and evidentlyoverestimated proton spectrum and overestimated neu-tral pion production cross section in [6, 7] and [8, 9],respectively.

A γ-ray flux with energies above 100 MeV from aparticular galaxy is given by the expression

σπi

ωγp >Eγ T p,( )

= ωπ Tπ T p,( )ωγπ >Eγ Tπ,( ) Tπ.d

Eγ mπ– mπ2 /4Eγ+

Tπmax

T p( )

∫

ωπ Tπ T p,( ) 1

w π/2----------------- 2

Tπ T0–( )2

w2------------------------–

⎝ ⎠⎜ ⎟⎛ ⎞

.exp=

T0 0.45T p 94.7 MeV;–=

w 0.26T p 28.3 MeV.–=

Jγπ

1 10Tp, GeV

10

1

0.1

ζ(Tp) σ(Tp), mb

1 23

Fig. 2. Total neutral pion production cross section multi-plied by the pion multiplicity: (1) [6], (2) [8, 9], (3) thisstudy.

Table 3. Integral flux of γ-rays with energies above100 MeV (in 10–25 photons s–1 (H atom)–1)

Reference (>100 MeV)

Levi and Goldsmith [18] 3.2

Stecker [6] 1.0

Stephens and Badhwar [7] 1.37–1.63

Dermer [8] 1.53

Mori [9] 0.75–1.85

Pavlidou [17] 1.5

This study 0.4

Jγπ

BULLETIN OF THE RUSSIAN ACADEMY OF SCIENCES: PHYSICS Vol. 73 No. 5 2009

GAMMA-RAYS FROM MAGELLANIC CLOUDS AND ORIGIN OF COSMIC RAYS 587

(8)

where d is the distance to the galaxy, Mgas is the mass ofgas (mainly atomic hydrogen) in the galaxy, ε is theratio of cosmic ray fluxes in some galaxy and our Gal-axy. Assuming the ratio Mgas/d2 to be 2.2 × 10–5 g cm–2,we obtain (for ε = 1) a flux of γ-rays from the SMC:Fγ(>100 MeV) = 0.35 × 10–7 photons s–1 cm–2, which issomewhat lower than the available experimental limita-tion [4].

CONCLUSIONS

Thus, the performed analysis shows that the protonspectra and neutral pion production cross sections frompp-reactions, used in the calculations of diffuse γ-rayflux from the SMC differ by several times. The key rea-son is the lack of experimental data on the π0 produc-tion in the most significant range of 3–10 GeV. A situa-tion with the π0 production from the interaction ofnuclei is even worse, because there are no experimentaldata at all. Thus, the factor that takes into account thecontribution of nuclei to the π0 production (~1.5) maydrastically differ from the real value, although it mayseem to be likely. The contribution of electronbremsstrahlung to the flux of γ-rays with energiesabove 100 MeV remains vague. Here, a significantspread was also revealed: 2 × 10–26 photons s–1 (accord-ing to the data of [6]) vs 8 × 10–26 photons s–1 [17]. Tak-ing all the aforesaid into account, we can state that cur-rently the diffuse γ-ray flux from the SMC can be deter-mined only with a large error. Rejection of themetagalactic model of cosmic ray origin can be consid-ered only provided that the measured γ-ray flux from theSMC turns out to be lower than 10–8 photons/(s cm2).

ACKNOWLEDGMENTS

We are grateful to R.P. Kokoulin for constructivecritical remarks.

REFERENCES

1. Ginzburg, V.L. and Ptuskin, V.S., Rev. Mod. Phys., 1972,vol. 48, p. 161.

2. Stecker, F.W., Astrophys. J., 1968, vol. 151, p. 881.3. Ginzburg, V.L., Usp. Fiz. Nauk, 1978, vol. 124, no. 2,

p. 312.4. Sreekumar, P. et al., Phys. Rev. L., 1993, vol. 7, no. 2,

p. 127.5. Ginzburg, V.L., Usp. Fiz. Nauk, 1993, vol. 163, no. 7,

p. 47.6. Stecker, F.W., Astrophys. J., 1973, vol. 185, p. 499.7. Stephens, S.A. and Badhwar, G.D., Astrophys. Space S.,

1988, vol. 76, p. 213.8. Dermer, C.D., Astron. Astrophys., 1986, vol. 157, p. 223.9. Mori, M., Astrophys. J., 1997, vol. 478, p. 225.

10. http://pdg.ihep.su/2008/reviews/cosmicrayrpp.pdf11. Pickup, E. et al., Phys. Rev., 1962, vol. 125, no. 6,

p. 2091.12. VerWest, B.J., Phys. Rev. C, 1982, vol. 25, no. 4, p. 1979.13. Johanson, J., Nucl. Phys. A, 2002, vol. 712, p. 75.14. CELSIUS-WASA Collaboration, arXiv:nucl-ex/0602006

(2006).15. Gol’danskii, V.I., Nikitin, Yu.P., and Rozental’, I.L.,

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16. Stanislaus, S., Phys. Rev. C, 1991, vol. 44, no. 6, p. 2288.17. Pavlidou, V., Astrophys. J., 2001, vol. 588, p. 63.18. Levy, D.J. and Goldsmith, D.W., Astrophys. J., 1972,

vol. 177, p. 643.

Fγ >100 MeV( ) 1

4πd2------------

Mgas

mp

-----------εJγ >100 MeV( ),=