Gamma-Rays from magellanic clouds and origin of cosmic rays

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<ul><li><p> 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.</p><p>584</p><p>Gamma-Rays from Magellanic Cloudsand Origin of Cosmic Rays</p><p>A. A. Petrukhin and S. Yu. Matveev</p><p>Moscow Engineering Physics Institute (State University), Moscow, 115409 Russiae-mail: AAPetrukhin@mephi.ru</p><p>Abstract</p><p>Various calculations of the integral spectrum of </p><p>rays from the neutral pion decays generated in pp-interactions have been analyzed. The estimate of the integral </p><p>-ray spectrum with allowance for the behavior ofthe cross section of </p><p>0</p><p> production in the pp</p><p>pp</p><p> + </p><p>n</p><p>0</p><p> + </p><p>X</p><p>reaction near the threshold for each channel and theproton spectrum at low energies (100</p><p> MeV) = </p><p>10</p><p>7</p><p> photons s</p><p>1</p><p> cm</p><p>2</p><p> [3]. After obtain-ing the upper limit for the </p><p>-ray flux with an energyabove 100 MeV from the SMC (</p><p>F</p><p>(&gt; 100 MeV) &lt; </p><p>0.5 </p><p>10</p><p>7</p><p> photons s</p><p>1</p><p> cm</p><p>2</p><p>) 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 [69] shows that the sit-uation is far from unambiguous, although the funda-mental quantity (the total number of </p><p>0</p><p> pro-duced in pp-interactions) is calculated from a simpleformula</p><p>pp </p><p>(1)</p><p>where </p><p>(</p><p>T</p><p>p</p><p>)</p><p> and </p><p>(</p><p>T</p><p>p</p><p>)</p><p> are the multiplicity and totalcross section of neural pion production, </p><p>J</p><p>p</p><p>(</p><p>T</p><p>p</p><p>)</p><p> is the dif-ferential spectrum of primary cosmic ray (PCR) pro-tons, and </p><p>T</p><p>p</p><p> is the kinetic energy.The purpose of this study is to analyze the ambigu-</p><p>ities in the calculations of the diffuse </p><p>-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</p><p>pp</p><p> + </p><p>n</p><p> reactions, up to </p><p>n</p><p> = 3 inclusive.</p><p>pp 0 4 T p( ) T p( )T p</p><p>min</p><p>= J p T p( ) T p, 0 s 1 (H atom) 1d</p><p>1</p><p>1 10</p><p>T</p><p>p</p><p>, </p><p>GeV/nucleon</p><p>10</p><p>1</p><p>10</p><p>2</p><p>10</p><p>3</p><p>10</p><p>4</p><p>J</p><p>p</p><p>(</p><p>T</p><p>p</p><p>), </p><p>cm</p><p>2</p><p> s</p><p>1</p><p> sr</p><p>1</p><p> GeV</p><p>1</p><p>Fig. 1.</p><p> Approximation of the proton spectrum near theEarth: (</p><p>) [6], (</p><p>) [7], (</p><p>) [8, 9], (</p><p>*</p><p>) this study, and(</p><p>) experimental data of [10].</p></li><li><p> BULLETIN OF THE RUSSIAN ACADEMY OF SCIENCES: PHYSICS</p><p>Vol. 73</p><p>No. 5</p><p>2009</p><p>GAMMA-RAYS FROM MAGELLANIC CLOUDS AND ORIGIN OF COSMIC RAYS 585</p><p>1. PROTON SPECTRUMFigure 1 shows the proton spectra used in the papers</p><p>analyzed 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 110 GeV, which makesthe main contribution to the </p><p>-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 (</p><p>m</p><p>p</p><p> is the proton mass):</p><p>(2)</p><p>It should be noted that flattening of the proton spec-trum at </p><p>T</p><p>p</p><p> &lt; 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.</p><p>2. CROSS SECTION OF NEUTRAL PION PRODUCTION</p><p>The cross section of neutral pion production result-ing from pp-interactions was first measured in the1950s1960s [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</p><p>-rays with energies above 100 MeV are generatednamely in these interactions [6]. The cross sections of</p><p>0</p><p> 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</p><p>J p T( ) 10 3 1mp</p><p>T p mp+------------------- </p><p>2 =</p><p>T p mp+</p><p>mp------------------- </p><p>2.73, cm</p><p>2s</p><p>1sr</p><p>1 MeV 1 .</p><p>precision of the experimental data in this energy rangeis 1030%, with significant systematic measurementerrors (up to 50%, as was noted earlier [8]). 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.</p><p>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 [12]; the experimentalproduction cross section of two 0 and one pion fromthe pp pn+0 reaction is taken from [13] and that forthree 0 and one pion from the pp pp+0 reactionare from [14]. Near the threshold and for the protonkinetic energy less than 3 GeV, all these cross sectionsare approximated well by the function</p><p>(3)</p><p>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%.</p><p>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 pp channel [13] and the differences inthe models used to approximate the experimental datain the energy ranges for which such data are absent.</p><p>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</p><p> T p( ) a1 k T p Tc( )( )exp+----------------------------------------------------,=</p><p>pp </p><p>Table 1. Parameters of fitting the pion production cross sec-tions for different pp-interaction channels with function (3)</p><p>Channel a, mb k, MeV1 Tc, MeV</p><p>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</p><p>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</p><p>Contribution 1 0.18 0.03 0.24 0.05 0.09 0.02 0.07 0.02</p></li><li><p>586</p><p>BULLETIN OF THE RUSSIAN ACADEMY OF SCIENCES: PHYSICS Vol. 73 No. 5 2009</p><p>PETRUKHIN, MATVEEV</p><p>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].</p><p>3. -RAY FLUX WITH ENERGY ABOVE100 MeV PRODUCED BY NEUTRAL</p><p>PION DECAY</p><p>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:</p><p>(4)J</p><p>&gt;E( ) 8 ii T p( )</p><p>Tth_i</p><p>i</p><p>= p &gt;E T p,( )J p T p( )dT p, s 1 H atom( ) 1 .</p><p>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(&gt;E,Tp) determines a probability of photon production withan energy above &gt;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 (&gt;E,T) is the probability of photon production with anenergy above &gt;E from decay of a pion with an energyT:</p><p>(5)</p><p>As follows from the kinematics of two-particle decays[15], the energy distribution of -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:</p><p>(6)</p><p>In formula (6), the parameters w and T0 depend on theproton energy. Processing of the experimental data of[16] yields the following dependences:</p><p>(7)</p><p>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 (&gt;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 [17], 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 [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.</p><p>A -ray flux with energies above 100 MeV from aparticular galaxy is given by the expression</p><p>i</p><p>p &gt;E T p,( )</p><p>= T T p,( ) &gt;E T,( ) T.dE m m</p><p>2 /4E+</p><p>Tmax T p( )</p><p> T T p,( ) 1w /2----------------- 2</p><p>T T0( )2w</p><p>2------------------------ </p><p>.exp=</p><p>T0 0.45T p 94.7 MeV;=w 0.26T p 28.3 MeV.=</p><p>J</p><p>1 10Tp, GeV</p><p>10</p><p>1</p><p>0.1</p><p>(Tp) (Tp), mb</p><p>1 23</p><p>Fig. 2. Total neutral pion production cross section multi-plied by the pion multiplicity: (1) [6], (2) [8, 9], (3) thisstudy.</p><p>Table 3. Integral flux of -rays with energies above100 MeV (in 1025 photons s1 (H atom)1)</p><p>Reference (&gt;100 MeV)</p><p>Levi and Goldsmith [18] 3.2Stecker [6] 1.0Stephens and Badhwar [7] 1.371.63Dermer [8] 1.53Mori [9] 0.751.85Pavlidou [17] 1.5This study 0.4</p><p>J</p></li><li><p>BULLETIN OF THE RUSSIAN ACADEMY OF SCIENCES: PHYSICS Vol. 73 No. 5 2009</p><p>GAMMA-RAYS FROM MAGELLANIC CLOUDS AND ORIGIN OF COSMIC RAYS 587</p><p>(8)</p><p>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(&gt;100 MeV) = 0.35 107 photons s1 cm2, which issomewhat lower than the available experimental limita-tion [4].</p><p>CONCLUSIONSThus, the performed analysis shows that the proton</p><p>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 [6]) vs 8 1026 photons s1 [17]. 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).</p><p>ACKNOWLEDGMENTSWe are grateful to R.P. Kokoulin for constructive</p><p>critical remarks.</p><p>REFERENCES1. Ginzburg, V.L. and Ptuskin, V.S., Rev. Mod. Phys., 1972,</p><p>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><p>p. 312.4. Sreekumar, P. et al., Phys. Rev. L., 1993, vol. 7, no. 2,</p><p>p. 127.5. Ginzburg, V.L., Usp. Fiz. Nauk, 1993, vol. 163, no. 7,</p><p>p. 47.6. Stecker, F.W., Astrophys. J., 1973, vol. 185, p. 499.7. Stephens, S.A. and Badhwar, G.D., Astrophys. Space S.,</p><p>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.</p><p>10. http://pdg.ihep.su/2008/reviews/cosmicrayrpp.pdf11. Pickup, E. et al., Phys. Rev., 1962, vol. 125, no. 6,</p><p>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</p><p>(2006).15. Goldanskii, V.I., Nikitin, Yu.P., and Rozental, I.L.,</p><p>Kinematicheskie metody v fizike vysokikh energii (Kine-matic Methods in High Energy Physics), Moscow:Nauka, 1987.</p><p>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,</p><p>vol. 177, p. 643.</p><p>F &gt;100 MeV( ) 14d2------------</p><p>Mgasmp</p><p>-----------J &gt;100 MeV( ),=</p><p> /ColorImageDict &gt; /JPEG2000ColorACSImageDict &gt; /JPEG2000ColorImageDict &gt; /AntiAliasGrayImages false /DownsampleGrayImages true /GrayImageDownsampleType /Bicubic /GrayImageResolution 150 /GrayImageDepth -1 /GrayImageDownsampleThreshold 1.50000 /EncodeGrayImages true /GrayImageFilter /DCTEncode /AutoFilterGrayImages true /GrayImageAutoFilterStrategy /JPEG /GrayACSImageDict &gt; /GrayImageDict &gt; /JPEG2000GrayACSImageDict &gt; /JPEG2000GrayImageDict &gt; /AntiAliasMonoImages false /DownsampleMonoImages true /MonoImageDownsampleType /Bicubic /MonoImageResolution 600 /MonoImageDepth -1 /MonoImageDownsampleThreshold 1.50000 /EncodeMonoImages true /MonoImageFilter /CCITTFaxEncode /MonoImageDict &gt; /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</p><p> /Description &gt;&gt;&gt; setdistillerparams&gt; setpagedevice</p></li></ul>

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