ISSN 1062-8738, Bulletin of the Russian Academy of Sciences: Physics, 2009, Vol. 73, No. 5, pp. 584587. 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. 623626.
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
Various calculations of the integral spectrum of
rays from the neutral pion decays generated in pp-interactions have been analyzed. The estimate of the integral
-ray spectrum with allowance for the behavior ofthe cross section of
production in the pp
reaction near the threshold for each channel and theproton spectrum at low energies (100
. After obtain-ing the upper limit for the
-ray flux with an energyabove 100 MeV from the SMC (
(> 100 MeV) <
) with the Energetic Gamma RayExperiment Telescope (EGRET) , it was con-cluded that the observed cosmic ray flux has a galac-tic origin . However, the wide spread in the resultsof calculations performed in  shows that the sit-uation is far from unambiguous, although the funda-mental quantity (the total number of
pro-duced in pp-interactions) is calculated from a simpleformula
are the multiplicity and totalcross section of neural pion production,
is the dif-ferential spectrum of primary cosmic ray (PCR) pro-tons, and
is the kinetic energy.The purpose of this study is to analyze the ambigu-
ities in the calculations of the diffuse
-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
reactions, up to
= 3 inclusive.
pp 0 4 T p( ) T p( )T p
= J p T p( ) T p, 0 s 1 (H atom) 1d
Approximation of the proton spectrum near theEarth: (
) , (
) , (
) [8, 9], (
) this study, and(
) experimental data of .
BULLETIN OF THE RUSSIAN ACADEMY OF SCIENCES: PHYSICS
GAMMA-RAYS FROM MAGELLANIC CLOUDS AND ORIGIN OF COSMIC RAYS 585
1. PROTON SPECTRUMFigure 1 shows the proton spectra used in the papers
analyzed here. The closed symbols correspond to theexperimental data for protons near the Earth  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 110 GeV, which makesthe main contribution to the
-ray flux, differ by a factorof 3. The approximation  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 (
is the proton mass):
It should be noted that flattening of the proton spec-trum at
< 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 the1950s1960s . 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
-rays with energies above 100 MeV are generatednamely in these interactions . The cross sections of
production in the range of proton energies greaterthan 12.5 GeV and near the threshold of neutron pionproduction (0.33 GeV) are best studied. The statistical
J p T( ) 10 3 1mp
T p mp+-------------------
T p mp+
1 MeV 1 .
precision of the experimental data in this energy rangeis 1030%, with significant systematic measurementerrors (up to 50%, as was noted earlier ). For the pro-ton energy range of ~310 GeV, there are no reliableexperimental data, and different approximations areused to calculate the cross sections. It is essential thatthe cross section of 0 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 0 production sepa-rately. The experimental data on the production crosssection of one 0 are taken from ; the experimentalproduction cross section of two 0 and one pion fromthe pp pn+0 reaction is taken from  and that forthree 0 and one pion from the pp pp+0 reactionare from . Near the threshold and for the protonkinetic energy less than 3 GeV, all these cross sectionsare approximated well by the function
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 0 is shown in Table 2; it is apparentfrom the table that to reliably determine a pion flux(and, correspondingly, the -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  and [8, 9], starting with proton energies of~700 MeV and ~2 GeV, respectively. Such a deviationis attributed to the cross section overestimation in due to the incorrect consideration of the contributionfrom the pp pp channel  and the differences inthe models used to approximate the experimental datain the energy ranges for which such data are absent.
The number of 0 produced in a pp-interaction (1) withthe production of no more than 3 pions, which was obtainedin this calculation, is = 1.36 1026 s1 (H atom) 1with 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 1026 0 s1 (H atom)1
T p( ) a1 k T p Tc( )( )exp+----------------------------------------------------,=
Table 1. Parameters of fitting the pion production cross sec-tions for different pp-interaction channels with function (3)
Channel a, mb k, MeV1 Tc, MeV
pp pp + 0 3.61 0.02 595pp pn + + + 0 1.08 0.011 1232pp pp + 20 0.76 0.0093 1307pp pp + 30 0.48 0.0029 3037pp pp + + + + 0 0.69 0.006 2197
Table 2. Ratios of the fluxes of pions produced in different channels to the main flux y (pp pp0)Channel pp pp0 pp pn+0 pp pp20 pp pp30 pp pp+0
Contribution 1 0.18 0.03 0.24 0.05 0.09 0.02 0.07 0.02
BULLETIN OF THE RUSSIAN ACADEMY OF SCIENCES: PHYSICS Vol. 73 No. 5 2009
or ~1.8 1027 0 s1 sr1 (H atom)1 in a unit solid angle.Note that the value 7.0 1027 0 s1 sr1 (H atom)1 wasused a priori in [1, 35].
3. -RAY FLUX WITH ENERGY ABOVE100 MeV PRODUCED BY NEUTRAL
An integral energy spectrum of gamma rays isobtained from formula (1) by substituting the energydistributions of pions and -rays and a factor 2, whichtakes into account the generation of two photons froma neutral pion decay:
>E( ) 8 ii T p( )
= p >E T p,( )J p T p( )dT p, s 1 H atom( ) 1 .
All the channels of pion production from pp-interactionare summed up: i is the multiplicity of neutral pions inthe 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; p(>E,Tp) determines a probability of photon production withan energy above >E from a proton with an energy Tp.This probability is a convolution of two probabilities:(T, Tp) is the probability of pion production with theenergy T from a proton with the energy Tp and (>E,T) is the probability of photon production with anenergy above >E from decay of a pion with an energyT:
As follows from the kinematics of two-particle decays, the energy distribution of -rays is uniformbetween minimum and maximum values, admissible ata specified pion energy. Based on the analysis of theexperimental data of , the pion energy distributionwas taken as a normal distribution, which is valid forproton energies up to ~2 GeV:
In formula (6), the parameters w and T0 depend on theproton energy. Processing of the experimental data of yields the following dependences:
At higher energies, such a representation is only quali-tative; nevertheless, it allows one to calculate the -ray flux(4) with an error of 1020%. The calculations performedshowed that (>100 MeV) = 4 1026 s1 (H atom) (withnuclei taken into account, the factor is 1.5), whichmakes 84% of the total number of produced -rays andagrees well with the calculations , where the por-tion of -rays with energies above 100 MeV was 76%.Table 3 compares the integral -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  on the neutral pion productioncross sections (which was noted in ) and evidentlyoverestimated proton spectrum and overestimated neu-tral pion production cross section in [6, 7] and [8, 9],respectively.
A -ray flux with energies above 100 MeV from aparticular galaxy is given by the expression
p >E T p,( )
= T T p,( ) >E T,( ) T.dE m m
Tmax T p( )
T T p,( ) 1w /2----------------- 2
T T0( )2w
T0 0.45T p 94.7 MeV;=w 0.26T p 28.3 MeV.=
1 10Tp, GeV
(Tp) (Tp), mb
Fig. 2. Total neutral pion production cross section multi-plied by the pion multiplicity: (1) , (2) [8, 9], (3) thisstudy.
Table 3. Integral flux of -rays with energies above100 MeV (in 1025 photons s1 (H atom)1)
Reference (>100 MeV)
Levi and Goldsmith  3.2Stecker  1.0Stephens and Badhwar  1.371.63Dermer  1.53Mori  0.751.85Pavlidou  1.5This study 0.4
BULLETIN OF THE RUSSIAN ACADEMY OF SCIENCES: PHYSICS Vol. 73 No. 5 2009
GAMMA-RAYS FROM MAGELLANIC CLOUDS AND ORIGIN OF COSMIC RAYS 587
where d is the distance to the galaxy, Mgas is the mass ofgas (mainly atomic hydrogen) in the galaxy, is theratio of cosmic ray fluxes in some galaxy and our Gal-axy. Assuming the ratio Mgas/d2 to be 2.2 105 g cm2,we obtain (for = 1) a flux of -rays from the SMC:F(>100 MeV) = 0.35 107 photons s1 cm2, which issomewhat lower than the available experimental limita-tion .
CONCLUSIONSThus, the performed analysis shows that the proton
spectra and neutral pion production cross sections frompp-reactions, used in the calculations of diffuse -rayflux from the SMC differ by several times. The key rea-son is the lack of experimental data on the 0 produc-tion in the most significant range of 310 GeV. A situa-tion with the 0 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 0 production (~1.5) maydrastically differ from the real value, although it mayseem to be likely. The contribution of electronbremsstrahlung to the flux of -rays with energiesabove 100 MeV remains vague. Here, a significantspread was also revealed: 2 1026 photons s1 (accord-ing to the data of ) vs 8 1026 photons s1 . Tak-ing all the aforesaid into account, we can state that cur-rently the diffuse -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 -ray flux from theSMC turns out to be lower than 108 photons/(s cm2).
ACKNOWLEDGMENTSWe are grateful to R.P. Kokoulin for constructive
REFERENCES1. 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. Goldanskii, V.I., Nikitin, Yu.P., and Rozental, I.L.,
Kinematicheskie metody v fizike vysokikh energii (Kine-matic Methods in High Energy Physics), Moscow:Nauka, 1987.
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.
F >100 MeV( ) 14d2------------
-----------J >100 MeV( ),=
/ColorImageDict > /JPEG2000ColorACSImageDict > /JPEG2000ColorImageDict > /AntiAliasGrayImages false /DownsampleGrayImages true /GrayImageDownsampleType /Bicubic /GrayImageResolution 150 /GrayImageDepth -1 /GrayImageDownsampleThreshold 1.50000 /EncodeGrayImages true /GrayImageFilter /DCTEncode /AutoFilterGrayImages true /GrayImageAutoFilterStrategy /JPEG /GrayACSImageDict > /GrayImageDict > /JPEG2000GrayACSImageDict > /JPEG2000GrayImageDict > /AntiAliasMonoImages false /DownsampleMonoImages true /MonoImageDownsampleType /Bicubic /MonoImageResolution 600 /MonoImageDepth -1 /MonoImageDownsampleThreshold 1.50000 /EncodeMonoImages true /MonoImageFilter /CCITTFaxEncode /MonoImageDict > /AllowPSXObjects false /PDFX1aCheck false /PDFX3Check false /PDFXCompliantPDFOnly false /PDFXNoTrimBoxError true /PDFXTrimBoxToMediaBoxOffset [ 0.00000 0.00000 0.00000 0.00000 ] /PDFXSetBleedBoxToMediaBox true /PDFXBleedBoxToTrimBoxOffset [ 0.00000 0.00000 0.00000 0.00000 ] /PDFXOutputIntentProfile (None) /PDFXOutputCondition () /PDFXRegistryName (http://www.color.org?) /PDFXTrapped /False
/Description >>> setdistillerparams> setpagedevice