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VOLUME
LATE PAPERS
AUGUST 13 -ee. 1977
15* InternationalCismic Ray Conference
VOLUME
LATE PAPERS
BULGARIAN ACADEMY OF SCIENCES
PLOVDIV, BULGARIAAUGUST 13-26,197"7
I l l
PREFACE
The present publication contains the proceedings of the 15th International Cosmic Ray Confe-rence, Plovdiv, 13-26 August, 1977. This Conference is to be held under the auspices of the Inter-national Union of Pure and Applied Physics, organized by the Bulgarian Academy of Sciences.
The publication comprises \2 volumes. Volumes from 1 to 9 include the original contribu-tions, which have arrived at the Secretariat of the National Organizing Committee by May 26, 1977.Papers which have been declared but not submitted by that date have been represented by theirabstracts. Volumes from 10 to 12 include the invited and rapporteur lectures, as well as late origi-nal papers. Volume 12 contains the general contents of the volumes, an authors' index and otherreferences.
All papers included in the present publication are exact reproductions of the authors' originalmanuscripts. The Secretariat has not made any corrections or changes in the texts. The originalcontributions have been accepted and included in the programme after a decision of the Interna-tional Programme Advisory Board of the 15th ICRC on the basis of their abstracts. The full textsof the papers, however, have not been refereed by the editorial board of the present publication.
The first nine volumes have been organized in accordance with the classical headings adoptedat the cosmic ray conferences, which also coincide with the sessions.
Volume 1 - OG (Origin) SessionVolume 2 - OG (Origin) SessionVolume 3 - MG (Modulations and Geophysical Effects) SessionVolume 4 - MG (Modulations and Geophysical Effects) SessionVolume 5 - SP (Solar Particles) SessionVolume 6 - MN (Muons and Nutrinos) SessionVolume 7 - HE (High Energy Physics) SessionVolume 8 - EA (Extensive Air Showers) SessionVolume 9 - T (Techniques) SessionThe National Organizing Committee is indebted to the invited reporters and rapporteur lec-
turers, as well as to all authors of original papers, who, by their hard and highly qualified work,have contributed t» the success of the Conference and have,made possible the publication of thepresent proceedings.
We also express acknowledgement to the members of the Organizing Committee and the Se-cretariat of the Conference, as well as to the Publishing House of the Bulgarian Academy ofSciences, without whose diligent work the publication of the proceedings would have been im-possible.
Acad. Chris to Yu. Chris tovChairman of the National
Committee
IV
BULGARIAN NATIONAL ORGANIZING COMMITTEE
Honorary Chairman - Acad. A. Balevsky, President of the Bulgarian Academy of Sciences and
Member of the State Council
Executive
Chairman: Ch. Ya. Christov
Vice-Chairman: P.K.Markov
Secretary: B.L. Betev
Members: M. Borisov, I. Todorov, G. Nestorov, K. Serafimov, Ts. Bonchev, Ts. Petkov, D. Pari-
kian, N. Balabanov, J. Stamenov, L. Popova, St. Kavlakov, T. Stanev, N. Ahababian, S. Ushev,
Ch. Tchernev, T. Palev, I. Kirov, J. Georgiev, L. Katsarsky
MEMBERS OF THE COSMIC RAY COMMISSION OF IUPAP
Chairman: Professor A.J. Somogyi (Hungary)
Secretary: Professor S. Miyake (Japan)
Members: Professor A.E. Chudakov (USSR), Professor R.R. Daniel (India), Professor R. Gall
(Mexico), Professor B. Peters (Denmark), Professor K. Pinkau (FRG), Professor H. Reeves
(France), Professor CJ.Waddington (USA), Professor A.W. Wolfei dale (UK)
INTERNATIONAL PROGRAMME ADVISORY BOARD
Chairman: Professor Ch. Christov
Secretary: Dr B. Betev
Members: Professor A. Chudakov (USSR), Professor H. Elliot (UK), Professor S. Miyake
(Japan), Professor S. Nikolsky (USSR), Professor K. Pinkau (FRG), Professor A. Somogyi
(Hungary),Professor C. Waddington(USA), ProfessorG. Yodh(USA)
The 15th International Cosmic Ray Conference is organized by the Bulgarian Academy of
Sciences under the auspices of the International Union of Pure and Applied Physics.
ADDRESS OF SECRETARIATInstitute for Nuclear Research and Nuclear EnergySofia 1113,72 Blvd LeninTelephone: 73-41 Telex: SOFIA BAN 22424
T A B L E O F C O N T E N T S
VOLUME 11 - LATE PAPERS
O R I G I N
page
06-8 Comparison of High Energy Gamme 'Hays from 1/ b / > 30° v i t h the Galactic Neutral HydrogenDistr ibution jM.E. Özel, H. Ógelraan, .T. TOmer, C E . F ichte l ,R.C. Hartman, D.A. Kjrlffen and D.J. Thompson !
OG-21 COS-B Results on à Search for Pulsed Gamma-ray 7 IEmission from Radio Pulsars \G. Kanbach, K. Rennett, G.F. Bignami, G. Boel la, . . |M. Bonnardeau, R. Buccheri, N. D'Amico,W. Harmsen, J .C. Higdon, G.G. L i c h t i , J. Masnou,H.A. Mayer-Hasselwander, J.A. Paul, ! . . Scarsi ,n.N. Swanenburg, P.G. Taylor and K.D. Wills
OG-22 COS-B Observations \»f Localised Gamma-Ray ikEmission \ ^>*W. Hermeen, K. BennetV G^F7 Bignami, G. Boel la,R. Buccheri, J .C . Higdjrf; G. Kanbach, G.G.Lichti,J . L . Masnou, H.A. M^yarJHasselwander, J.A. Paul,L. Scarsi , B.N. Äwanenburgu R.G. Taylor andR.D. Wil ls , y ^ ^
OG-38 Recent Ariel V Measurements on Hard X-Ray Bursts 20and the Implications for • -Burst OriginJ . J . ijuenby, M.J. Coe ana A.R. Engel
OG-47 Observation of a Gamma-Ray Burst at Baloon 23Alt i tudeJ . Nishimura, M. F u j i i , T. Tawara, S. Miyamoto,
i / M. Oda, Y. Ogawara, T. Yamagami, M. Kajiwara,v H. Murakami, M. Yoshimori, Mj Nakagawa and
T. Sakurai
An Estimation of the Primary Proton Spectrum 29between 1()12 1 Ql4 e y >
T.K. Gaisser, F. Siohan and G,B, Yodh
OG-55 On the High Energy Proton Spectrum Measurements 37R.V. Ellsworth, A. Ito, J. MacFall, F.Siohan,R.E. Streitmatter, S.C. Tonwar, P.R. Vishwanath,G.B. Yodh and V.K. Balasubrahmanyan.
V7
OG-70 Cosmic Ray Abundances from Nitrpgen to Zinc 6oUsing a Cel lu lose NAtrate P l a s t i c DetectorG.S. Kalnth, V.S, Bhktia am^Sumaa Parut hi
06-73 Average Abundances of\GaVactic Cosmic Rays &6with Z?90 from StudieAXf Meteor i t i c Ol iv inesV.P. Pere lygin , S.G. iffietsenko, D.Lhagvaauren,0 . Otgonsuren, P.PelAaB,and B. Jakupi.
OG-79 The Method of X-Ray Efliilsion Chamber as Applied 72to Determination^of the\Chemical Composition ofPrimary Cosmic/Rays i n toe Energy range of10 - 100 TeV/per NucleusXM.D. DezhurKo, S.B. I g n a u e v , K.V. Mandritskaya,V.V. Abulova, I .V. RakoboYskaya, N.V.Sokolakaya,A.Ta. VarlEOvitskaya, G.P. >Sazhina, E.A. Zamcha-
- lOT«, ÇpiA. Ivanova and V.lA Zatsepin.
OG-93y Measurements of the I s o t o p i c Composition of 77aic-Ray Nuclei w i th Z.lO-lU
Simpson, J .C . Kish, J .A. Lezniak andW,R. Vebber.
-93 / Meaev/ Cosmd
OG-100 High Bttergy PrimarV Elect«4on Spectrum Observed • 83by the Saul s ion ChaM>ep^J . Nishlmura, M. PujW, H. Ai zu, N. Hi rai va,T. Taira , T. KobayatSbJ . K. Niu, T.A. Koss,J . J . Lord, R.J. Vl lkesVnd R.L. Golden.
\j OG-138 Transport of Cosmic Rays i n Supernova Remnants gnG.B. Morf i l l and M. Schol er
0G-1&2 Cross Sect ions for Spa l la t ion Produstion of 93kkTi : Application to Determining Cosmic Ray
J Acceleration TimeG^ff.Raisbeck and F. Yiou.
/ 3G-153 Some Thoughts on the Musala Anisotropy; 10 2(/ Pitch Angle Distribution or What Else?
J. Kote, and A.J. Somogyi
Farther Evidences of the Anisotropy observed 1 0 9at Musala StationT. Gombosi, J. K«ita, A.J. Somogyi, A. Varga,B. Betev, L. Katsarski, S. Kavlakov andI. Kirov.
OG-161 S idereal AnisoWoay^of^Cosmlc Rays 114R.M. Jacklynj^JIrtîK^ Fenton, K. Nagashlmaand S. Moi
VII
OG-172 The Formation of\a Comm±4 Ray Electron Halo 121R. Schlickeiaer add K.CT. Thlelheia
OG-175 Physical Characteristics of the Galactic 126Halo from Radio Dplft v Scan ObservationsA.W. Strong
OG-183 The Acceleration of Cosmic Rays by Shock Waves 132V.I. Axford, E. Leer and G. Skadron
OG-191 On the Origin and Propagation of Ultra HighEnergy .Cosmic RaysP. Kiraly
OG-210 The Low Energy /"-H^v/iSSxperinient Aboard theSigne III S a t e l l i t eM. Niel , A.R. B^er-^achi and G. Vedrenne
OG-216 Secondary Positrons and Electrons in theI / Cosmic Radiationl / G.D. Badhwar and S.A. Stephens
OG-218 The Proton and Helium Rigidity Spectra from 15510 to 100 GV
\f G.D. Badhwar, R.R. Daniel, T. Cleghorn,R.L. Golden, J.L. Lacy, S.A. Stephens andJ.E. Zipse
OG-283 Measuremenvyof the Cosmic Rajr Element 1 ° 1
Abundances between i 3OO and&750 MeV/N inthe Region fr\m Nickel toyKrypton UsingLexan TrackP.H. Fowler, D.fS. Henah«(v, C. O'Ceallaigh,D. O'Sullivan ana\A. Thompson
OG-284 Charge and Energy Spectra of Ultra Heavy 165Cosmic Ray NucleiP.H. Fowler, C. Al&xandore, V.M. Clap hero,D.L. Henshaw, D.yO'Sullivan and A. Thompson
OG-285 Ultra-Heavy Cojmic Ray Abtiaance Measurementswith a Large lias Sc int i l lat -Nm DetectorP.H. Fowler, /R.J. Edge, R.T. ftoses, K.O. TathamC. Thoburn, (R.N.F. Walker and V. Worley
VIII
J
MG - M O D U L A T I O N
MG-lf Energy Loss in fche^S<j>«Cr5ystem and Modulation 186of Cosmic -RadiatlojiJ . K6ta
MG-8 Kinematical Anisotropy of Non-Coherent RadiationA. Geranios and N.J. Martinic
MG-38 COsSmic Ray Modulation During Solar A c t i v i t y 197Cycle TwentyJ.AXLockwood and V.R. Webber
MG-kk The CoVnie Hay Electron Spectj/a i n 197''t and 1975 20 3and theVlmplications for Sola*- ModulationJ .H. Cal \wel l , P. Evenson, s /jordan and p. Meyer
MG-U5 The Observed Spectrum of v / r i a t i o n o f Cosmic Ray 20 SI n t e n s i t y above 1 GeV/Nuc/eon andModels of Coemic Ray ModulationR.B. Mend ell a\nd S.A. KonFf
MG-51 Cosmic Ray Rad&al Grad/ents: Hel ios 1 Results 21 between 1.0 and\D.3 KU.R. Mai ler -Mel l in \ M./Witte , H. Hempe, H. Kunov,G. Wibberenz and \ . /Green
MG-63 The Radial Evolut^bV of the Bulk Propert ies 21 yof the Solar WineD.S. Intriligato^
MG-65 Evidence for a/- Consta)it Speed of ShockPropagation bytween»0.8\AU and 2.2 AUD.S. Intr i l i /ator
MG-66 Solar Activity, Solar WinV Velocity and CosmicRay Rigidity Spectrum durxng a Solar RotationH. Takaha4hi, N. Yahagi andv T. Chiba
MG-67 Three-nfmensional Analysis oV the August 1972Cosmic/Ray Event Using Sea Le^el andUnderground DataH. TjCtahashi , T. Chiba and M.N^ada
MG-109 Sidereal Variations at 365 hg cm"2 Underground. / and Interplanetary Magnetic Field Directionsv A.G. Fenton, K.B. Fenton and J.E. Humble
MG-110 Sidereal Variations a**<6 hg.cm"2 andInterplanetary Magratic Field DirectionsJ.E. Humble .
IX
MG-117 On the CUtoff Variations During the MagneticDisturbances of 30.3. - 3.4.1973 and
13,. V 18.9.197?*H. DebrunnerNand E. Fluckiger
MG-128 The Use of Off l e t Dipole Coordinates forInterpolating Cbamic Ray Cutoff Rigidities/in Three DimensionsD.F. Smart and M\A. Shea
MG-132 Pitch Angle Diffusion Rate of Protons/in Radia-tion Belts According to Inter cosmos- 5 DataJ.-^Dubinsky and k. Vudala
MG-133 Secondary Maximum ofl Proton Integrity inRadiation Belts Near\ PlaamapaustS. Fischer, K. Kudel^, P.V. Vafculov andI.A. Yuzsyhovitch
MG-135 On the Residual Atmosphere /raversed by CosmicRays at Large Zenith A\iglo/ at Sate l l i teAltitudeN. Petrou and A. Soutouty
/MG-156 Short Period Variat ions
I n t e n s i t y at GroundM.R. A t t o l i n i , C. C/vani,M, G a l l i
Cosmic Ray
Cecchini and
MG-157 The Cosmic Ray Spectral Density in the
Ketiion 10~ - HzM.R. Atto^ini^ S. Cecchini and\M. G a l l i
MG-158 Slow and Fsfet S c i n t i l l a t i o n s i n \ h e CosmicRay Variat ionM.R. A t t ^ l i n i , S. Cecchini and M.>Galli
MG-I65 Penianb/a Structure Calculat ions andXtheirAppl icat ion to Isotope Analysis of c\smic RaysN. Lpnd and A. Sorgen
MG-183 Lolig Term Changes i n the Parameters of\y Da i ly Harmonics
US. Ahluwalia
MG-18U Do Coronal Holes Inf luence Cosmic Ray1 / Dai ly Harmonics?v H.S. Abluwalia
MG-193 The Response Function of^Cosmic-ray MuonsDeep Undergz
L.K. Ng and C.H. P>
251
2 5 6
2 6 2
267
273
27°
281
287
29 o
MG-280 Numerical Correlations Between Solar and 315Sidereal Cosmic-Rav Diurnal Variations Under-ground and the Interplanetary Magnetic, FieldV.H. Regener and R.H.St. John
SP - SOLAR PARTICLES
SP-il Event Oriented Data ColYe^tion for the Ground- 322Level Solar Cosmic Ray^twent of 30 April 1976D.B. Bucknam and M.A»/Sh«a.
SP-12 The Anomalous Component of\Lov Energy Cosmic 326 ;Rays During the/**resent SolWr Minimum - a |Comparison of J0bserva$ions with Model ICalculations ' ' V "B, Klecker./b. Hovestadt, G. (Uoeckler and .C.Y. Fan r X *
SP-26 An Example of Long Distance Propagation of 328Electrons on the Sun ?M. Oros
SP-56 Interplanetary Electrons: What i s the 334aj Strenght of the Jupiter Source ?
V. Fil l iua, V.-H. Ip and P. Knickerbocker
SP-100 Possible Mechanism £*r Enrichment of Solar 34oCosmic Rays by Helium-Three and Heavy NucleiI .A . Ibraginov anaNj.E. Kocharov
MN - MUONS AND NEUTRINOS
MN-5 The Approach tov Sca l ing and the Charge' Rat io of CoaoicStty Huons
A. Liland - ^ " ^ \
MN-6 The Muon Charge Ratio and i t s Re la t ion 354r/ to Primary Mass Composition
A.K. Lee and E.C.M. Young
MN-12 Study of the Energy Speptra of the Cosmic 35sRay Muons, 1 -Qu^ita and Hadrons in the
2 TeV Range X X
T.P.Amineva, M .A.\v»anova,K.V.Mandritslcaya,E.A.Osipova, I.V^takobolskaya, N.V.Sokol-skaya, NcI.Tulin6va\ A.Y.Varkovitskaya,L.Kuzmichev, Vya.Zat\opin and G.T.Zatsepin
MN-13 Momentum Spectrum and Charge Ratio of CoaraicRaV Muons at Zenith Angle 84T.LV Asatiani, S.V. Alchudgian, K.A. Gaiarian,L.I NlCoz l iner , A.C. Minasyan, G.Se Mar/tirosian,V.N. Rrokhorov, K.K. Prokhorova, S.V./Ter-Antoni dm, A.A. Chilingarian and A.M./Zverev
MN-14 Momen turnend Zenithal Dependence of the Enhan-cements oft Intensit ies of Cosmic Bray MuonsM.S. Abdel-Monem, A.R. Osborno, V.R. Benbrook,V.R. SheldoÀ. N.M. Duller and pjj. Green
MN-18 Predicted Cross Sections and Experimental StudyMN-19 of Direct Pair\Production (DP/) of Electron»
Positron by Higk Energy MuoniA. Paul, N.L. Karmakar and y, Chaudhuri
/MN-35 Deep underground and undeyseas Stopping
Particles and Their Possible Relation toPrimordial Superheavy ElementsS. Anderson, J . Lord, JA Albers, L. Barrett,P. Kötzer, R. Lindsayy&nd K. Stehling
MN-36 An Evaluation of Muoli-Nuclecr InteractionFormulations by Co soli c Ray ExperimentsN.L. Karmakar and p. Chaudhuri
MN-38 The Nuclear Enerdy-Loss Parameter b for Muons
V. Cons tandt, V/D. Dau and H. Jokisch
Electromagnet^ Interactions of Cosmic-RayMuonsT.L. Asatiani, S.B. Alchudzhyan, K.A.Gazaryan,L.I. Ko»liner, G. Eh. Minasyan, G.S. Martiro-syan and SJV. Ter-Antonyan
The Lateral Distribution of Muons in ExtensiveAir Showers at Sea LevelF. Ashtqii, J . Fatemi, H. Ne j abat, A. Nasri,V.S. Raâa, E. 5haat, A.C. Smith, T.R. Stewart,M.G. Thompson, M.W. Treasure auà I.A. Ward
362
368
374
379
383
MN-itO 394
1*00
Tfto
Studies on Muon Showers Underground. I I . Resultsand/DiscussionS. A l e s s i o , R. D'Ettorre Piaszoli ,G/Mar. cohi, M. Pal lotta , P. Picchi andKri Si
kok
MN-38 i)ire/L.G.
/ andf
ns in Cosmic Rays.o, VIA. Kuzsin, E.A. Taynov
Zheleznykh
kxo
X1JL
MN-67 The Cosmic Ray Neutrino-Induced Background 4l6in the Solar Neutrino ExperimentA.W. Wolfendale and E.C.M. Young / '
MN-71 Experimental Studies of the Acoustic Detection 420of Particle ShowersL.R. Sulak, T. Bowen, B. Pifer, P. Polakos,H. Braqner, VI.V. Jones, J. Learned, T. Armstrong,M. Bregman, M. Levi, J. Strait, I . Linscottand A. p\rvulescu /
MN-100 The Aco'Jstivc Detection of High Energy Neutrinos 427G.A. Askarjkn, B.A. Dolgoshein, A.M. Kalinovskyand N.W. Mokhov
MN-101 On One of the poss ib i l i t i e s of Investigationof the Characteristics of the Primary CosmicRadiation at Supexhif;h EnergiesU.V.Boisembaev an\ Yu.A.Vavilov
432
HE - HIGH ENERGY P?
HE-18
HE-20
HE-39
HE-50
HE-53
HE-55
SICS
Sect ions on Nucle iI n e l a s t i c Neutron Crosat FNALL.W. J o n e s , H.R. Gustafsd^j, M.J. Longo,T. Roberts and M. Whalley
Charged P a r t i c l e stween 300 and
Multiplicity Distributionsin Proton-Proton-Collisions2100 GeV/cI . Derado, R. Meinke, H. PreissVer and S.Uhlig
Ultrasonic Signals from Heavy Changed ParticlesW.V. Jones
Nuclear Interaction' of Energy aroundNlOOO TeVObserved by Chacaltaya Emulsion CiiambiMini—Centauro InteractionJapan-Brasil Emulsion Chamber Collaborai
The Pamir Experiment - IThe Energy Characteristics, of Gamma-Famili«with Measured Energies over 30 TeVCollaboration bf the Experiment "Pamirs'
The Pamir Experiment — IIIThe Meclianisnf of the Central Dark Spot Formation^in Gamma Families with Energies Above 500 TeVCollaborati/n of the Experiment "Pamirs"
43S
441
447
453
459
469
XIII
Spectra of Gaua Families Predicted byNuclear Interaction MedalsA. Toaaazewaki and J.A. Vrotnlak
HK-63 How DispM?ate are tb« energetical and SpatialChara.ctex\etlca of Paaiir Gamma Families,Pradietad W two Différant Modela of NuclearInteraction^A. ToaiassawaVi and J.A. Vrotnlak
7JE-78 Th* Electromagnetic Caaeada Showers inLaad AbsorberS. DaJce, H. Itot>H.Munakata, Y.IY.Yamamoto, H.Su§K.Kasahara, T.Yuda,\I«Ohta
HE-93 New Particle BrentaMina BxpariaientaM.R. Kriahnaawajty, M.6aianan, N. I to, S. Kawi
HE-98 The Nucléon Caecade in tA. Liland
HB-100 Maaauraaent of theFlux Ratio at 2900 MatRadiation Detector -R.V. Ellaworth, A.R.S. Streitmattar,and G.B. Yodh
HS-112 The Theory of tBurst SpactruBF. Aahton, DA.J. Saleh
HE-127 On PattIsobaraE.G. Bubbler
HE-128 CluaProfrçA Nuclei
HE-13p/Interactiona of kOO GeV Protons withNuclaiP.S. Young, K. Fukui and Y.V, Rao
469
, V.S. Nara-S. Miyake
taoabpere
iad Pion-Protona Transitionts
cFall, F.Siohan,•R. Vishwanath
interpretation HadronTargets
arvaresh,
Recognition FireballsVelocity
Intersadi Nucléons
CM. ZinovJ
509
514
520
xIV
HB-133 StudyNof High Energy Interactions at Co saleRays ink an Emulsion Stack Combined withIonisation CalorlaeterJ. Dubindky, L. fust, A.J. Soaogyi, S. Sugar,B. Chadraàu B. Baican, M. Haiduc, S. Neagu,T. Visky, Yu Basina, S, Brikker, H. Grigoro*,
• L. GrigorysVa, M, Kondratyeva, L. Misehenko,R. Nymmik, lA Papina, A. Podgurakaya, Lj/popa-rakova, I. Raftpport, V. Sokolov, V. Sobinyakor,Ch. Trotyakova\ L. Chlkova, V. Shaatoj^aroT,and Zh. Slio^r-iib«
523
HE-1U2 Second QuantizatiiConfinementT. Palev
with ParticlaOQuark) 529
HE-183 of 12C,fuel«! withInelastic InteractionEmulsion at 50 GaV/CV.A. Bakaev, B.P. Banni!S.D. Bagdanov, R.A. Bond!A.El-Naghy, V.G. GubinskyyH. Haiduc, M. Karabova,S. Nasyrov, D. Neagu, V/I. ô«trouao-r, N.A.1'erfilov, G.D. PestoTa/ V.A.POyushchev, J.A.Salomov, 0.3. Shabxat^va, M. Sberif, E. Silesh,
532
Bogdanov,o, G.M. ChernoT,
K.G. CrulamovfU.G.Gulamovarin, U. Mihalschao,
S . I . Solovieva, L.M./SvechnikoiJ. Szonert, K.D. ToVstov and S.
K. Skrzypczakfokal
ME-18't Search for New StEmulsionA. El-Naghy
/rt-Lived Partiel< i n
HE-185 Remarks on Spaétra of k"«.Ray and HadroiFamilies at the Pamir AltitudeJu.A. Fomin,/ J . IvempaA. PiotrowqKa and J . Vdowczyk
550
571
COMPARISON OF HIiiH ENERGY UAhMA RAYS FROh |fr| >3O°
WITH THE GALACTIC ivJiUTRAL HYDROGEN DISTRIBUTION
H.E.Ozel. H. Ogelman, T. Turner
Middle East Technical University,Ankara,
Turkey
C.E.Fichtel, R.C.Hartman, D.A.Kniffen,D..J.Thompson
NASA/Goddard Space Flight Center,Greenbelt,haryland,USA
Abstract:
High energy (E^35 KeV) gamma ray data of SAS-2 satellite hasbeen used to compare the intensity distribution of gamma rays with thatof neutral hydrogen (HI) density along the line of sic~ht, at hi~h ga-lactic latitudes (|o| >30 ) . A model has been constructed where the ob-served gamma ray intensity has been assumed to be the cum of a galacticcompetent proportional to the HI distribution plus an isotropic extra-galactic emission. The X -test of the model parameters indicate thatabout kO% of the total high latitude emission nay originate within thegalaxy.
I. Introduction
Cosmic ray-galactic diffuse matter interactions are expected tocontribute the high energy gamma ray flux at significant levels, tforexample, Schliokeiser and Thielheim (197&) calculate that the magni-tude of local galactic contribution to high lattitude gamma ray emis-sion is
+4G(>40 1-ieV) = 21 Jg> of the total intensity
(1)
G(>1CO heV) = 51 +^#. " " " "
•lith these ideas in mind, a two-component model (galactic and extra-galactic) for the observed high lattitude rramraa ray omission hr.a beendeveloped and compared with the SA S - 2 data.
II. iiethod and hodel
Ths observed intensity variation of the hi-rh ener.-jy ( y ~-jj r.e\Ogamma rays in 10° x 10° (.030 sr) equal solid single bins is presentedin Ficure 2 in galactic coordinates, ( £ , •&). Vhis isap was obtained bymaking use of the gamma ra,,. data from the SAS-2 e::perir.:ent whose detailed
.ascription is given in Derdeyn et al.(1972)- In order to avoid as muchas possible the effects of the galactic plane which is an intense gamma-ray source, only the regions with |&| >30° will be considered in theanalysis.
As the representative of the matter distribution at \u\> 30°the HI distribution surveys of Heiles (1975) were used. The galacticul map used in this analysis is given as Fig.l. This figure is dividedinto same equal solid angle bias as Fig.2 and Hi-density for each binis represented by the average value of four 5° x 5° bins forming that10° x 10° bin.
The essence of the model fitting is a \ test between the ex-pected gamma ray intensity f., and the observed intensity g.t at thesame 10° x 10° bin, summed over the M(=8l) available data bins.
In our model| the expected relative gamma ray intensity value,f., for ee.cn bin, is assumed to be a sum of two terms as
f = C + K N^ N^" (2)
where C stands for the isotropic extragalaetic component constant forall f-bins and the^second term represents the galactic component; N. ,'N?R being the HI and cosmic ray (CS) densities for that bin. Further-more, it was assumed that the CE density was proportional to HI den-sity:
Nf ~ (Hf >* (3)
This assumption has as its basis the idea that interstellar matter,cosmic rays and magnetic fields are coupled to each other forming ahydrostatic equilibrium under the galactic gravitational attraction(Parker,1966; I969). Then, we can write,
f ± = C + K(N^)1+a = C ^
The X^-test s ta t i s t ic - i s defined as
2 ±,81 (Ei-f.)2X = ZL A
X a 1 (5)i=i Aq
whore flf. = ^±^s±^ a n d si i s tile observed relative intensity, s.i;j the sensitivity factor of the i'th bin. One further condition on 1
the statistic is thatI
j?hat is, the observed and expected total intensities are equal. Thiscondition determines the constant K for a chosen set of C and b.
The most probable values of the model parameters C and b for 2
different significance levels, can be obtained in a two-dimensional Xplot in the C-b plane as Given in Fie.3. A contour of significance level otis defined in lir.e with Lampton et al.(l976):
where X*~(°O is the value of X distribution for p-degrees of freedom,p being^the number of parameters adjusted in minimizing X (2 in our case) ,and is also tabulated in Lampton et al.(l976). A rejection of the model ]is recommended only if |
XmiQ> XilP
(of=10%) (8)
In our case, N = M-l since (6) has already been adjusted. [,
III. Hesuits !t
From Fig.3. the following inferences can be made: i_ (1) The pure extragalactic model corresponds to b = 0. The value [
of X for this case is \
X2(b=0) = 112 •
which should be rejected on the basis of (8) since the rejection limit issignificantly lower:
Several combinations of C and b have fits better than the b=0 (C=1005o)case.
(2) The minimum contour corresponds to
X2 QQ
min
The 90 % confidence l imi t i s same as the ot =105* rejection l imi t !X2
g(90 %) =95There are a laxse number of Cb-combinations within thete limits. Amongthese we should further restrict ourselves to b-values of b ^ 1. The caseswith b < 1 does not seem to be physically meaningful since tWeij requirea decrease in CR density for an increase ia HI density. Such a relation-ship is contrary to (**•) and to the hydrostatic equilibrium argumentsthought to be valid in the galactic disk. This way, C is further res-tricted to a region where C>50# of the|total high lattitude emisEion.H].As a plausible speaial case for a uniform CR density independent of Ncorresponding to b = ljthe galactic contribution is:
.'4
G( >35 MeV) = (32 + Ik) % of the total
confidence level. A similar analysis fc
o (0zel,1977)
G(> 100 MeV) = (.kk + 16) % of the total
(10)
at 90 % confidence level. A similar analysis for E>100 KeV gamma, rays,leads to (0zel,1977)
(11)
at, again, 9058 confidence level. A uniform CR denBity around solarneighborhood for. |«|^30° regions of the galactic disk is a plausibleassumption since' a relatively small region of the disk (about 10 of.the volume of the disk) has to be considered. Then (10) and (11) can betaken as the magnitude of the galactic contribution to the high lattitudeY-rays. These result are also in accordance with the theoretical es-timation given in (1).
IV. Conclusions and discussion :
When these results are used to calculate the absolute level ofintegral Y-ray intensity at the energies > 35 MeV and ^>100 1-ieV, oneobtains (see Ozel, 1977):
IO>35 MeV) = (5.0 + 1.9) 10~5 i rays/cm2-s-sr
= (6.2 + 2.8) 10~6 Yrays/cm2-s-sr(12)
for the extragalactic part of the observed diifuse emission. (12) imp-l i e s a steep differential spectrum (»"£""•') for the extracalactic Y-rays.Its possible implications are discussed elsewhere (0zel,197?)>
V. References
1. Derdeyn, S.H., Ehrman, C.H., Fichtel, C ^..Kniffen, U.A.Hoss, R.1972, Nucl.Ins. and Math., £8, 337.
2. Fichtel, C.E., Hartman, B.C., Kniffen, I'.A., Thompson,D.J.jBi^G.F., Ogelman, H., (Jzel, M.E., Turner, T., 1975, Ap.J.,198. I63.
3 . Heiles, C , 1975, Ast.Ap.Supp. 20, 37-
h. Krauahaar, W.L., Garrtire, G.,1965, Sp.Sc.Rev.,4, 123,
5. Lampton, M., Margon, B., Bowyer, S., 197fa, Ap.J.,208, 177.
6. Ozel, M.E., 1977, Ph.D.Thesis, MEl'D, unpublished.
7. Parker, B.N., 1966, Ap.J., I|f5_, 811.
8. Parker, E.N., 1969, Sp.Sc.Rev., £< 651.
9. Schlickeiser, R., and Thielheim, K.D., 1976, wature, £61,,
. liX densities along the line of si^ht, in units of lu2 0
it-cm ,in palactic coordinates, for |b|>10° (Heilee,1975).Parts with broken lines are adapted from Uarmire andKraushaar (I965).
o> m -M « N _ = ^ : _ ' : _ _
— « -
I-'-:
1 • ' ' " - « <•
Relative Paulina ray intensity in falactic coordinatea for' b ' > 50 as observed by ErtS2 Th l' > -50
P y ty n falactic coordinatea for' > -5 as observed by ErtS-2. The values corresponu to -.=
V s i ^ x l 0 0 ; n i : the o b=erved number of ;j-i.-,ir,u r^ysjs. :s-nsiitivity in units of Zi'tiO s.-l stands xor regions unofissrvedby i:A5-2. Projection used in the u. f is i lcs
xo
30
50
so
90
9 lO9l32"5l"767B6i'4^18¥23929y36944B5386417Y7B89a'3828739B6'l4a5915S449BBG2'lB57a«, 111 18(30 48 71 99134175223278341412493584685798923862215385S7B773tJ952364987799 la) 17 te8 45 66 9312516320e2Sa3163Be4S353362272a8289458722ia3^bSrc»Q736BaS9<rutl9 10116 E7 42 62 B71171S21932402923514174895686S47478479SSB71t!<^3234S9Sa2751&B69 1B\1S 25 39 58 Bna9l4Z1802232713253844495195956r7765BSB956ui,ul68281398519£;44
128 >2 9 9 114 23 37 54 761821321672B725138B35441347654461669377485Sa-l.;u4U3723533fc'Ua128 2 9 9 ) 12? 34 58 70 95123156 i9223327832738B43'7498562631782777854934BT7101 iO;:-75"20 B 9 9 13 28 32 47 66 BBU41441782162573823504024575145756397B57738439159B886J136
19129 43 61 8218613416528B23B2793233704194715265836427B2764827892957U23127 40 56 76 98124153185220257298348385433482533586648695751BBBB66924
l l I7BS 37 32 78 91U51421712B32382743133543974424B3S3S5946336a47347t,G3S718\15t3 3T~3B 65 8410613II5818B2192532893263654B644749853457962466971576]
, 1B\14 32 32 45 6B 78 981211461732822332663803363734184494895295706116531. Mlie V4 2? 29 41 55 72 91111135168186215245276389342377412448485522559596^4
27 38 51 66 8310312414717119822S2542B431434637841144447BS12S«1£380lSUl S \9 i t 17V25 35 46 61 76 94H413S1581B22a723326fl2893173473774B743B469SB0531
32 43 55 70 8618'4124i45167'l9e2T42392652*913lB34G3734B143a45d'43b29 39 51 64 79 96U31331531741?62l924326729231?3423iiB39442a<w5
19\26 35 46 58 72 87184I2II40l5918a2ei2222452672983l433736l384.;ofll?\4 32 42 53 66 88 95111128146164184284224245266287309338352374
I2\l6 2X 29 38 48 63 72 86181 ll61331Sai6BI862BS2242432652B23B23223-4211 M 20>26 34 44 54~66 78 92ie6ftll3>lS3l69lB72B422224B2S8276295313
1511116!1616
IP.18
sue
IB1714 ll18 14 l l
19 15U2 10120 16 12 10
IB 13UB 12'\9 11
\2B 1617
32 26132 26 132 2732 2732 27
1 17 U 112 IB 1S\
IB 1S\319 1628 17 U
IB11 9\B 8'
li11li!
32 2732 2B32 2032 20.32-2932 2932 2932 2932 30
20 17 15\13 11IB 16 13 1219 16 14\13
)V2 20 17 15 M 12 IIi 28 21 IB 16 15\3 12i 24t 22 19 10 16 14X3
19 17 16 1420'19 17 16
83 21 20 19 17_22 20 19_ ~22~2f
30 29 28 2730 30 29 28 28 27 27 2631 31 38 38 30 79 29 29
1010
11
16182¥j
39 49 59 71 83 96110124139154178186202219235252283:6635 44 53 64 75 87 991121261481541691841992U23B24^iSl
39 48 57 67 78 B91U111412714B1531671B119520322323743 51 68 70 80 'jl 103114ii'GI3915116417719e2b3Jlh
46 54~63~?2 62 921831 ]4J25i26148'16ai721G3l9b34 40 48 56 64 73 82 92102112122133144155166177
36 42 49 57 65 73 82 9110811811912913914915331 37 43 50 57 65 73 81 89 98187115124134J.U
32 33 44 50 57 64 71_79J37_951B31 II11912838 44 53 56 63 78 76 I
32
118 22>tS 2B14\712 IV 19
282421
2133 38 43 49 55 61 67 73
9B166113B7 931UU
29 33 33 42 47 53 58 64 7B ?£ Q2 6011 13 Hi IB 21>4V28 32 36 41 46 58 55 61 6C 71 77IB 11
IB 12 l9 18 11\9 9 IB 11 1Z 1
8J9 9 9 18 11 12
31 35 39 43 48 52 57 6229 33 37 48 44 4B 53 57"
28 31 34 37 41 45 4826 28 31 34 37 41
~9 9 9 9 9 "9 10"
19 2116 17 19
IS16
18 IB 9 9 9 912 11 10 18 10 9
13 12 11 11 1015VTS-4A_13 13 12
&
9 ) 18 11 119 i IB 10 18 11B 13 18 18 IB 182 l l 11 11 U 11
1J t3~H 13 U
31 34
21-U..16 17 18
90
60
21 21 28 19 19 18 17 17 IS 16 16 15 151_J__12 12 1215 14 14 14V4"
28128 28 27 27 27 27 26 26 26 25 25 25 25 24 24
J__115 14 14 14V4"
18 10 ID 17'4 si a
1.0 1.2 2.0 2.2
two dimensional X plot in the C-b plane.Tabulated numbersare the X values in excess of 80. C is the percentage of theisotropic component in the total high lattitude emission; b isthe power of the HI density in bhe galactic component,ci.
COS-B RESULTS ON A SEARCH FOR POLSED GAMMA-RAY EMISSION FROM RADIOPULSARS
G. Kanbach4, K. Bennett6, G.F. Bignami2, G. Boella , M. Bonnardeau5,R. Bucsheri , N. D'Air.ico , W. Hermsen . J.C. Higdon , G.G. Lichti , J. .Masnou , H.A. Mayer-Haßelwander , J.A. Paul , L. Scarsi , B.N. Swanenburg ,D.G. Taylor , and R.D. Wills .
THE CARAVANE COLLABORATION
1. Cosmic Ray Working Group, Huygens Laboratory, Leiden2. Laboratório di Fisica Cosmica e Tecnologie Relative del CNR,
Université di Milano3. Laboratório di Fisica Cosmica e Tecnologie Relative del CNR,
Università di Palermo4. Max-Planck-Institut für extraterrestrische Physik, Garching bei München5. Service d'Electronique Physique, Centre d'Etudes Nucléaires de Saclay6. Space Science Department of the European Space Agency, ESTEC, Noordwijk
ABSTRACT Gamma-ray data from ESA's satellite COS-B have been used in asearch for pulsed gamma-ray emission from sources located in regions nearthe galactic plane. For this search, the radio data from a number of pul-sars were used. Due to the inadequacy of the available radio pulsar para-meters, which had to be derived by extrapolation from observations made indifferent epochs, the investigation has been based on a parameter scanaround the predicted value of P. As a result of this search PSR 1822-09has been recognised to be a. possible gamma-ray emitter.
The radiation from the already known gamma-ray pulsars PSRO531+21 andPSRO833-45 has been studied in detail. The two pulsars show very similargamma-ray light curves, both exhibiting peaks of about equal intensity se-parated by O.4 of the period. The pulsed fraction of the gamma rays ofenergy > 50 MeV is at least 78% in the case of PSRO531+21 and consistentwith 100% for PSRO833-45. In the range 50 MeV to 4 GeV the differentialenergy spectrum of PSRQ531+21 can be represented by (2.4 +0.4) x 10~ 'E~ |(2.1 + 0.3) photon cm ^ s"1 GeV , while it is difficult to reconcile the \energy spectrum of PSRO833-45 with a single power law over the same ener- »,gy range. About one third of the total emission of PSRO833-45 lies betweenthe pulses, while in the case of PSRO531+21 no such feature is evident.
1. INTRODUCTION Of the approximately 150 radio pulsars presently known,four have been reported as emitters of high-energy gamma rays (e.g. ögel-man et al., 1976; Thompson et al., 1975, 1976, 1977). Two of them, theCrab and Vela pulsars, are bright gamma-ray sources for which the pulsedgamma-ray emission can be studied in detail. The question'whether any ofthe other pulsars can be clearly identified as a source of high-energygamma-ray emission has significant consequences, namely:- at the present level of gamma-ray detection sensitivity any of thesepulsars, taking into account the rotational energy loss and distance,is only detectable if its gamma-ray emissivity is a very much largerfraction of the rotational energy loss than implied for the Crab andVela pulsars. Inevitably such a discovery would have an impact onpulsar models.
- if such pulsars exist, similar pulsars, not yet detected, could be can-didates for the observed but unidentified localized gamma-ray sourcesand their integrated contribution to the galactic emission could be sub-stantial (Higdon and Lingenfelter, 1976).
2. PSRO531 -1-21, THE CRAB PULSAR The Crab Pulsar, being known in 1975 asone of the strongest gamma-ray sources, was the target of the first COS-Bobservation period from August 17 to September 17, 1975.
The time structure of the gamma-ray emission from PSRO531+21 was derived
by folding the arrival times (corrected to the solar system barycentre)of selected gamma rays with the pulsar period given by nearly contempora-ry radio observations (Rankin, private communication). Gamma rays wereselected according to their measured energy and arrival direction, defi-ning an acceptance cone of half angle ©m centered on the pulsar.
The resulting gamma-ray light curve for PSRO531+21 is shown in figure 1,where the pulsar period of - 33 msec is divided in 66 phase bins. Alsoshown is the X-ray light curve derived from the pulsar synchronizer datain the energy range 2 - 1 2 keV. The gamma-ray curve comprises all present-ly available data with energies above 50 MeV and e = 1 0 whereas the X-ray curve includes only data collected over one orBit. "rtie light curvesare strikingly similar, showing two peaks separated by 13.5 + 1.0 ms. Thepvlse width at half height is about 1.5 ms for the first and about 3 msfor the second peak. The numbers of gamma rays in both pulses are compa-rable.
The pulsed fraction of the X-ray emission derived from this measurementis 8.5 + 0.8%, which is compatible with earlier,measurements reviewed byThomas and Fenton (1975). The pulsed fraction at gamma-ray-energies isdetermined from galactic longitude profiles over the region that eitherinclude avents occuring during the peaks of the light curve or are con-structed from the remaining part of the pulsar period. The latter pro-files show no enhancement above >j:he average flux at the position of thepulsar and 'a 2o upper limit to the continuous flux from PSRO531+21 andthe surrounding nebula can be derived. This value and the correspondingvalue for the pulsed fraction are given in table 1.
Table 1
so Ev>50MeV©m='0°1323 EVENTS
jPSR0531>2i|-
2keV<Ex<12keV659 868 EVENTS
Energy range
Pulled emission'>50MeV•200 MeV
Continuous emission, 2-n uPfH limn•50 MeV•200 MeV
Pulled traction. 2-o lower limn:-S0 MeV>200Mev
Contribution to total pulledllu> --50 MeVlint pulseinter reqionsecond pulse
PSR 0531 • 21
photon cm *s '159-OBI 10 '11.3 •0 .3 )10*
photon cm J s '1.7 « 1 0 '0 5 « 10*
78%
(SO • 911.• 15%150'91%
PSR 0633 - 45
photon cm s l 1(15.6 - 0 8 1 10*1 53-041 10'
photon cm 3l '1.6 » 10*07 « 10 '
91%89%
132 • 31 *130 • 4) \(38 • 4| %
Figure 1: Gamma-ray (a) and X-ray (b)l ight-curves of PSRO531+21integrated over a period ofone month (1975 August 17 -September 17) and 1.5 dayrespectively.
OSPULSAR PHASE
The energy spectrum of the pulsed gamma radiation from PSRO531+21 wasderived from a series of light-curves, which allow the determination ofthe number of pulsed gamma rays for various energy thresholds. Thepulsed gamma rays are defined as the events constituting the peaks in alight curve above a constant background level, which includes a smallpossible continuous flux from the pulsar, galactic and extragalacticemission and of course the instrumental background. In figure 2 this num-ber of pulsed counts is shown as a function of the angle of acceptance e .The qualitatively fitted curves in figure 2 reach an asymptotic value m
that indicates that all pulsed events from the source are included. Theresulting differential spectrum for the pulsed emission from PSRO531+21is shown in figure 3 for the energy range 50 to 40OO MeV. It can be-re-Dresented by a single power law of the form: (2.4 + 0.4) x 10 E- photon cm s GeV . It was also possible to derive spectra for thefirst and second pulse separately. They are identical within statistics.
200
so
PSR053W1 PSR 0633-45
E(>50MtV< 1 - WOO
>IO0OMM
i XOOOMtV HOo s n is o s w is
t M l F ANGLE OF IHE ACCEPTANCE CONE 6 m (OEGREES)
Figure 2: The number of pulsed gamma raysas a function of the half angleof the acceptance cone (6 )centred on PSRO531+21 for^sixenergy intervals (a) and onPSRO833-45 for eight energy in-tervals (b). Typical statisti-cal errors are indicated.
Figure 3: The differentialenergy spectrumfor the pulsedcomponent of thegamma-ray emissionfrom PSRO531+21.Statistical errorsare indicated.
3. PSRO833-45, THE VELA PULSAR
The region of the Vela supernova remnant has been specifically observed
• i;
10
twice by COS-B, once from October 20 to November 8, 1975 pointed atPSP.0833-45 and from November 8 to 28, 1975 pointed at 3UO9OO-4O (about 7°away) and a second time from July 15 to August 24, 1976 again pointed at3UO9OO-4O.The data of the first observation were analysed using the parameters ofManchester, Goss and Hamilton (1976). The light curve derived is shown infigure 4. The period of 89 ms is divided in 89 bins and gamma rays withE > 50 MeV and e = 10 havs been included. Two strong, narrow peaks cha-racterize the emission from PSRO833-45, separated by 38 + 1 ms. The widthat half maximum of the first pulse is 3 ms and of the second' 5 ms.. As inthe case of the Crab, the X-ray data from the pulsar synchronizer havebeen used to search for X-ray pulsations from Vela. No such pulsationshave been detected. An absolute comparison between the gamma-ray and ra-dio phases has not yet been possible due to unavailability of the rele-vant radio data. A significant feature of the gamma-ray light curve fromPSRO833-45 is the emission between the two pulses. The pulsed fraction ofthe radiation from PSRO833-45 was determined following the method de-scribed above and as given in table 1.
The energy spectrum of thepulsed radiation fromPSRO833-45 is presentedin figure 5. It was de-rived according to themethod already describedfrom the numbers of pulsedevents shown in figure 2.T,ie spectra for the indi-vidual components, i.a.first pulse, second pulseand interpulse emissionhave also been determined.They contribute aboutequally to the flux (seetable 1) and do not differsignificantly in spectral£ nape.
The spectrum is difficultto fit with a singlepower law over the energyrange 50 MeV to 10 GeV.Integral fluxes are givenin Table 1.
Figure 4
OS- PUL5AR PHASE
Gamma-ray light curve of PSRO833-45for the period 1975 October 20 -November 28.
4. COMPARISON OF PSRO833-45 AND PSRO53T+21: PSRO531+21 and PSRO833-45 havebeen studied extensively in a wide spectral range. The relative fluxesvary dramatically over the spectrum from radio to gamma-ray energies.Furthermore the light curves at radio and optical wavelengths are distinct-ly different. In the gamma-ray energy range however the pulse profilesshow a striking similarity. Figure 6 shows a comparison of the light curvesof the two pulsars for two tnergy intervals 50 to 200 MeV and greater than200 MeV. This graph also shc*s no indication of any energy dependence ofthe gamma-ray phase. In fact the pulses of PSRO531+21 are at the samephase from radio wavelengths to gamma-ray energies (Kniffen et al., 1974).In the case of PSRO833-45 the situation is markedly different in that theradio, optical and gamma-ray pulsations do not coincide in the phase(Thompson et ai., 1975, Wallace et al., 1977) and also show differentlight curves. The spectra measured* by COS-B above 50 MeV indicate that
11
t<r*
icr!
E IO-6
10Ej(G«VI
Figure 5: The differential energyspectrum for the pulsedcomponent of the gamma-ray emission from PSRO-833-45. Statisticalerrors are indicated.
the spectral differences, observedfor the two pulsars at lower ener-gies, extend into the gamma-rayrange. The power law fitted to theCrab gamma-r^y data is consistentwith other measurements at leastdown to 100 keV. For PSRO833-45 thegamma-ray spectrum between 50 MeVand 10 GeV is not easily fitted witha single power law. The slope of thespectrum seems to decrease belowabout 500 MeV. A tentative extrapo-lation of the gamma-ray spectrum.below 500 MeV using a power law tothe X-ray range coincides with the3o upper limits placed on the pulsedemission at 2 - 2O keV by Pravdo etal. (1976). However a further extra-polation into the optical range liesseveral orders of magnitude abovethe measurement of Wallace et al.(1977).
5. GAMMA-RAY PULSAR SEARCH: Thegamma-ray pulsar search has beenbased mainly on the radio data pi-b-lished in the summary of Taylor andManchester (1975) and an updatedlist provided by Manchester (1977,private communication). Because noneof the radio measurements was con-temporary with the COS-B observationit was necessary to extrapolate theperiod from the epoch of measurement.The absence in some cases of a valuefor the derivative P or of the pre-cise epoch of radio observation re-duces the useful sample from 149 to88. The uncertainties in the radiovalues of P and P distinguish twoclasses of pulsars:
Class (a) Those 55 pulsars for which the uncertainty of the extrapolatedvalues at the epoch of the COS-B observation is small enoughto introduce a phase shift < 0.05 of the period over one month;in this case the analysis in 20 phase bins based on a straightforward folding of the barycentric arrival times of the gamma-ray events can be made.
Class (b) Those 33 pulsars for which the analysis requires a scanning bysteps of AP and aP within the extrapolated error box.
6-^CLASS (a) PULSARS: 32 pulsars of class (a) given in table 2 were within20 of the pointing direction of any one of the observation periods usedfor the present study. A single phase analysis in 20 bins was made usingthe values of P and P extrapolated to the COS-B epoch.No source shows any indication for pulsed emission above the 2o level ofconfidence. Notice the negative result for PSR1818-O4 which has beensuggested as a gamma-ray emitter by Ogelman et al. (1976).
12
Table 2Class (a) pulsars investigated: PSR 0525+21, 0540+23, 0611+22, 1451-68,1556-44, 1557-5O, 1641-45, 1706-16, 1749-28, 1818-04, 1859+03, 1900+01,1907+00, 1907+02, 19O7+1O, 1910+20, 1911-04, 1915+13, 1917+00, 1913+19,1919+21, 1920+21, 1929+10, 1933+16, 1944+17, 1946+35, 1952+29, 2002+31,2016+28, 2020+28, 2O21+51, 2111+46.
ou
50
40
30
20
10
0120
PSR 0531+21E*:5OMeV-2OOMeV a
6m=10°Eg>200MeV c
em=8° -I
PSR 0633-4511 E*:5OMeV-2OOMeV b
" em=io«1Eg>200MeV
©m=8° d
10 15 20 25 30 0 5 10 15
PULSAR PHASE*32
20 25 30
Figure 6: Comparison of gamma-ray light curves of PSRO531+21 and PSRO833-45 in the energy ranges 5O - 200 HeV and above 200 MeV.
7. CLASS (b) PULSARS: For these pulsars less accurate radio parametersare available and the analysis procedure therefore has to be more elabo-rate. A total of 15 pulsars of this class were within 15 of a pointingdirection. Of these the 6 that have the highest specific rotational ener-gy loss E t/d were examined using a procedure of scanning the error re-gion arouna the extrapolated value of P. For each trial period a phasehistogram is constructed and the deviation from uniformity present inthis histogram is indicated by a x -value. A further description of thismethod is given by Buccheri et al., 1977. Only two pulsars show signs forthe presence of pulsed gamma-ray emission. ~PSR1742-3O exhibits significant deviations from uniformity (x = 46,19 d.o.f., 200 scanning steps). The plfese histogram however shows a com-plicated structure and further analysis is required. ,PSR1822-09 exhibits the highest level of significance found <x = 48,19 d.o.f., 100 scanning steps). The phase histogram shows two broad peaks.
8. CONCLUDING REMARKS Before drawing conclusions from the above findingsthe following remarks have to be made:
13
- The radio data are extrapolated over 1 to 5 years; period glitches areknown to happen on this time scale and therefore the actual periodcould differ from the extrapolated '-alue enough to make the pulsationundetectable.
- Small- irregular period fluctuations of the kind reported by Taylor andManchester 1976 could similarly alter the extrapolated period values.
- Neglecting a systematic P term could also invalidate the extrapolation.
Further studies of data already obtained are in progress. More recent ra-dio data would reduce the period of extrapolation or permit a backwardextrapolation to reduce the uncertainties in the pulsar parameters at thetime of gamma-ray observation. Ideally, future observations should beaccompanied by contemporaneous radio measurements.
ACKNOWLEDGEMENTS: The authors thank Drs. G.S. Downs, R.N. Manchester andJ.M. Rankin for the communication of pulsar parameters.
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Kniffen, D.A., Hartman, R.C., Thompson, D.J., Bignami, G.F., Fichtel, C.E., Turner, T., and Ogelman, H.B., 1974, Nature 251, 357.
Manchester, R.N., Goss, W.J., and Hamilton, P.A., 1976, Nature 259, 291.
Ogelman, H.B., Fichtel, C.E., Kniffen, D.A., and Thompson, D.J., 1976,Astrophys. J., 209, 584.
Pravdo, S.H., Becker, R.H., Boldt, E.A., Holt, S.S., Rothschild, R.E.,Serlemitsos, P.J., and Swank, J.H., 1976, Astrophys. J. 208, L67.
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Thomas, R.M., and Fenton, K.B., 1975, Proc. 14th ICRC, 1, 188.
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Thompson, D.J., Fichtel, C.E., Hartman, R.C., Kniffen, D.A., and Lamb,R.C., 1977, Astrophys. J., 213, 252.
Wallace, P.T., Peterson, P.A., Murdin, P.G., Danziger, I.J., Manchester,R.N., Lyne, A.G., Goss, W.M., Smith, F.G., Disney, M.J., Hartley, .K.F., Jones, D.H.P., Wellgate, G.W., 1977, Nature, 266, 692.
14
COS-B OBSERVATIONS OF LOCALISED GAMMA-RAY EMISSION
W. Hermsen , K. Bennett , G.F. Bignami , G. Boe11 a , R. iuccheri ,
J.C. Higdon , G. Kanbach , G.G. Lichtî , J.L. Masnou ,yW.A. Mayer-
Hasselwander , J.A. Paul , L. Scarsi , B.N. Swanenburjj , B.G. Taylor and
R.D. Wills .
THE CARAVANE COLLABORATION
1. Cosmic Ray Working Group, Huygens Labo/atory, Leiden
2. Laboratório di Fisica Cosmica e Tecno/ogie Relative del CNR,
Université di Milano
3. Laboratório di Fisica Cosmica e Te^nologie Relative del CNR,
Université di Palermo
k. Max-Planck-Institut für Extraterrestrische Physik, Garching bei
München
5. Service d'Electronique Physique, Centre d'Etudes Nucléaires de
Saclay
6. Space Science Department o^the European Space Agency, ESTEC,
Noordwij k.
The ESA gamma-ray satellite CÓS-B has completed a survey of the
galactic plane. The long exposure time combined with the effective
angular resolution of 2.57 (FWHM) for gamma rays above 100 MeV
permits a detailed study of the spatial distribution of the radiation.
In four observation periods a search for localised gamma-ray emission
has been performed. Eaah of the studied regions exhibits significant
fine structure superimposed on a diffuse emission along the galactic
plane. This fine stmeture is consistent with the presence of a large
number of high-enemy gamma-ray sources. A first catalogue, including
11 so far unident/fied gamma-ray sources, is presented. The latitude
distribution of ychese sources indicates a galactic nature.
1. Introduction. In/recent years it has been recognised that localised
gamma-ray sources /Contribute to the overall galactic emission. Some of these
sources have been identified with known astronomical objects, namely
PSR 0531+21, Ps/o833-'»5, »SR Whl-kt>, PSR 1818-0*1 and Cygnus X-3 (Hartman
et ?'., 1976),/although the evidence for the actual detection of gamma rays
from the latter three objects is not conclusive. In addition several
19
emission, and since the typical individual luminosity /s of the order of
-10 ' erg s , the understanding of the nature of these sources is of particu-
lar astrophysicai importance. Two inherent limitations make this difficult.
Firstly, the positional errors virtually exclude uofique identification with
a known object. Secondly, the finite angular resolution makes it impossible
to distinguish between a compact object and an emission region of angular di-
mension up to 2 degrees. This situation is not^ery different from that in
the early days of radio and X-ray astronomy.
Future steps towards a better understanding (ff the results presented here
should include:
- construction of the galactic distribution of sources using all available
COS-B data, with the best possible^corriections for selection effects, and
comparison of this distribution with tmat of other galactic populations;
- a sensitive search for radio pulsars/around the positions of the unidenti-
fied sources, since the two identified gamma-ray sources are pulsars;
- a search for time" variabi 1 ity simMar to that reported for CG 195+*» (Hart-
man et al. 1976, Masnou et al. 1977), which suggests a compact object;
- careful inspection of available/and possibly new optical, infrared and ra-
dio data to investigate the po/sible contribution of interstellar clouds
as likely candidate sources
References.Bonnardeau, M., Buccheri, R., Hermsen, W.,
i—Hasseiwander, H.A., Paul, J.A., Scarsi, L.,and Wills, R.D., 1977, Astron. 6 Astrophys.
-Bennett, K., Bignami, G.F.Kanbach, G., Lichti, G.G.,Stiglltz, R., Swanenburg,56, kf,\.- Hartmah* R.C., Fichtel ,/C.E., Kniffen, D.A., Lamb, R.C., Thompson, D.J.,Bignami, G.F., Ogelman, jk., Ozel, M., and Turner, T., 1976, Proceedings of theSymposium on Galactic Gslmma Rays, GSFC, NASA X-662-76-15A, 12.- Hermsen, W., Bennett/K., Bignami, G.F., Boella, G., Buccheri, R.,Higdon, J.C., KanbachVG., Lichti, G.G., Masnou, J.L., Mayer-Hasselwander, H.A., Paul, J.A., Scars/, L., Swanenburg, B.N., Taylor, B.G. and Wills, R.D.,1977, Proceedings \2fh ESLAB Symposium "Recent advances in gamma-rayastronomy", ESA SP-- Kniffen, D.A.,_B/gnami, G.F., Fichtel, C.E., Hartman, R.C., Bgelman, H.B.,Thompson, D.J., Oael, M.E., and Turner, T., 1975, l*»th International CosmicRay Conference, Munich J , 100.- Masnou, J.L., Bennett, K., Bignami, G.F., Buccheri, R., Caraveo, P.,D'Amico, N., He/msen, W., Kanbach, G-, Lichti, G.G., Mayer-Hassel wander, H.A.,Paul, J.A., SwaTnenburg, B.N., and Wills, R.D., 1977, Proceedings 12th ESLABSymposium "Reoent advances in gamma-ray astronomy", ESA SP-124.- Scarsi, L.,/Bennett, K., Bignami, G.F., Boella, G., Buccheri, R., Hermsen,W., Koch, L.I Mayer-Hasselwander, H.A., Paul, J.A., Pfeffermann, E., Stiglitz,R., Swanenbprg, B.N., Taylor, B.G., and Wills, R.D., 1977, Proceedings 12thESLAB Symposium "Recent advances in gamma-ray astronomy", ESA SP-124.
20
DECENT ARIEL V MEASUREMENTS ON HARD X-RAY BURSTSAND THE IMPLICATIONS FOR y-BURST ORIGIN
J . J . Quenby, M. J . Coe and A. R. Engel
Blackett Laboratory, Imperial College, London SW7 2BZ
Further Ar ie l V observations of X-ray bursts from" regionsw i t h i n 11° of the rapid burs ter , MXB1730-335 have been carr iedout in 1977 A p r i l . While events in the 2 •+• 17 keV energyband occurred at a-rate of greater than 1 in 80 seconds, only15 possible events at energies >50 keV were seen in 500minutes. These possible hard X-ray bursts were delayed, onaverage, by 43 seconds w i th respect to the s t a r t of the sof tX-ray burst but carr ied comparable amounts of energy. However,the s t a t i s t i c a l s ign i f icance of the observations was less thanfo r comparable data obtained in 1976 March.
1. Introduction
Both X-ray and y-ray bursts take place on a time scale of seconds and y-bursts contain an appreciable fraction of their total energy in the X-ray regionbelow 100 keV. However; the largest y-ray bursts have energy flux densities•vlO"1* erg cm"2 whereas X-ray bursts are in the 10~7 erg cm"2 or less region.Also X-ray bursts tend to be emitted from regions close to the galactic centrewhile the large y-ray bursts are received in a much pore isotropic manner. Hencethe possible connection between these two phenomena is uncertain.
Ariel V measurements in 1976 March (Quenljy et a.. 1976) identified sixevents from near the galactic centre which were characterised by time scales ofseconds, energy fluxes at >50 keV and in the range 2 + 7 keV of roughly equalmagnitude and delayed arrival of the high energy photons. It was suggestedthat the appearance of >50 keV photons might indicate an important connectionbetween the origin of the X- and y-burst classes of events. In an attempt toconfirm this suggestion, further observations were carried out in 1977 April.
2. Observations
Ariel V. observed in a direction centred on RA 263.3°, dec -33.3° during1977 April 19 to 27 in a data recording mode which obtained 2048 consecutivebins of i s counting rate per orb i t of the sa te l l i te . The sc int i l la tor tele-scope (ST) witli 8 cm2 area, 11° effective FWHM employed an energy channel ex-tending from 50 keV to 190 keV while the col 1imated proportional counter (CPC),effective area 35 cm^worked in either of two modes, one using an energy channelbetween 5.2 keV and 9.1 keV and the other with a channel from 1.65 keV to 16.5keV. Burst sources MXB1730-335, MXB1728-34, MXB17*»3-293 and MXB1742-297 werefn the f ie ld of view of the ST but only the f i r s t two could be seen by the CPC.The rapid burster, MXB1730-335 was clearly on since the CPC recorded burstevents at a rate of at least 1 every 80 seconds.
A search (3,712 t r ia ls) was made throughout the ST data to find a l ls ta t is t ica l ly significant increases in 8 second intervals. Data recorded overthe Atlantic, American continent and Eastern Pacific was excluded as possiblycontaminated by trapped radiation precipitation. 15 events showing a >3a
21
•icrease were found in a time period when only 5 such occurrences should ariseoy chance. .Only in two cases' did an obvious overlap arise in the time struc-tures of single CPC and ST peaks although the possibility of a complicated,multi-peak structure made it difficult to determine the true length of the lowenergy pulse.
In all cases, a significant delay between the onset of the low and highenergy pulses was allowed by the data although it was not always possible toassociate clearly the pulses in the two energy channels. The following Tablelists the mean characteristics of the events seen in 1977 April and comparesthem with our previous data obtained in 1976 March. The CPC data energyfluxes were normalised between the. two modes assuming a flat spectrum between1.65 and 16.5 keV, while the ST fluxes were derived assuming that all thephotons lay at 50 keV energy. The ST pulse width could not be determinedbetter than 8s in 1977. A difference in the time recording mode in 1976 Marchrendered it impossible to measure the delay without some ambiguity and hence arange of possible values is given.
TABLE
Date
April1977
March1976
Mean Flux, ergs cm"2
1.65 - 16.5 keV
1.9 x 1(T7
2 - 7 keV
1.0 x 10"7
50 - 190 keV
1.8 x 1CT7
3.1 x 10'7
Range of meanstatisticalsignificancefor ST
3 * *.3a
3-7 -* 6.5o
Meanwidthof CPCpulsesec
18
9
Meandelay ofSTonsetsec
43
5 - 36
3. Discussion of Results.
In both years, roughly comparable amounts of energy were seen in the highand low energy burst fluxes and signif icant delays in the high energy photonarrival seem indicated. However, the high energy events were of greater ind i -vidual s tat is t ical significance and better associated with low energy data inthe 1976 observations. Indeed, f ive our of the 15 events in 1977 must be ascri-bed to chance. We therefore regard the 1977 data as only weak additional ev i -dence for the possible extension of soft X-ray bursts into the hard X-ray/y-rayregion. Further experiments with larger area sc in t i l l a to r detectors are re-quired to explore this association. Note that the existence of small y-burstsin the 10" erg cm"2 range is in dispute as a result of a number of inconclusiveNorthern Hemisphere balloon searches.
h. Acknowledgements
•We thank Mrs. J . Burnell for use of the MSSL CPC data and the Appleton
22
Laoora tory for s a t e l l i t e control ar.j Jdt.a a c q u i s i t i o n .
Rot ore nee
i u e n b y , J . J . , C o e , M . J . , E n g e l , A . R . a n d M i l l s , J . S . , 1 9 7 6 , N a t u r e262, 471.
r.
23
Observation of a Gamma-Ray Burst at Balloon Altitude
J. Nishimura*, M. Fuji!*, T. Tawara*. S. Miyamoto*, M. Oda*,Y. Ogawara*, T. Yamagami*, M. Kajiwara**, H. Murakami**,M. Yoshimori**, M. Nakagawa*** and T. Sakurai***
* Institute of Space and Aeronautical Science, University of Tokyo** Department of Physics, Rikkyo University, Tokyo*** Department of Physics, Osaka City University, Osaka
Abstract
During the search for gamma-ray bursts with balloonflights of about 120 hrs duration, a significant increaseof X-ray counting rate was observed in three independentcounters. The event started at 10h 06™ 31s UT September23, 1975 and lasted for about 30 sec. The peak intensityis estimated to be approximately 10"6erg/cm sec and thetotal flux is 6.10~6erg/cm .
No obvious solar-terrestrial disturbances arereported during this period, and the event is concludedto be a small gamma-ray burst. From the analysis of themodulated X-ray flux observed by the rotating-cross-modulation-collimator used in this experiment, the mostlikely celestial position of the burst is determined ata = l 9 h 5Om ± ymt 6 = 45° 06' ±10'.
This is the most accurate determination of theposition of the gamma—ray burst thus far obtained.
1. Introduction •
Since the gamma-ray burst was first discovered in 1973, approximately '50 events have been observed with artificial satell i tes^'2). In addition,- hseveral bursts of smaller sizes have been found with balloon-borne "..detector-* .4,5,6) of i a r g e sensitive area.
No burst has been identified with any astronomical object due to theuncertainties in the celestial position of the bursts thus far observed.The value of precise measurements of the burst position is evident. Inorder to determine the precise position of the gamma-ray bursts which cannot be predicted to occur in advance, the detector has to be provided witha wide field of view and the capability of precise location of the source.A rotating-cross-modulation-collimator (RCMC) is a device to fulfill theseapparently conflicting requinnents and was proposed at the MunichConference^).
Search for gamma-ray bursts with long-duration balloon observation wasattempted using the RCMC. The instrument was flown from Sanriku BalloonCenter 141°49'30"E, 39°09'30"N, Japan on September 1975 for about 150 hrs ;Ytotal observation time. During this observation, we found a small burst- ,,;like event o<" a peak intensity 10~6erg/cm2 sec after the correction for the w!
24
atmospheric absorption at 10h 06m 42 s UT September 23, 1975. This eventexhibits several known features as the gamma-ray bursts and i t occurredwhen no obvious solar-terrestrial disturbances were present8'. It i s ,hence, quite unlikely that this event i s of solar or terrestrial origin.
From the analysis of the modulated X-ray flux observed with the RCMCthe burst location was determined with an accuracy of about 0.2".
2. Ins trumentationThe principle of the RCMC which possesses a wide field of view and can
determine the burst position i s described in the previous report''. Theconfiguration of the device i s i l lustrated by F ig . l .
5"<J> Nal(Tl) 4"<j> Nal(Tl)
Fig.l Design of the Burst Detector
Two modulation collimators were set in two directions perpendicular toeach other. An additional detector monitored the burst to produce the bursttime profile. Each two-grid modulation colllmator was constructed with gridsof tungsten rods of 1 mm in diameter with 1 mm spacing. The separation ofthe two grids was 5 cm, providing the transmission band-spacing of 2.29°.Scintillation counters of Nal(Tl) of 5" in diameter were placed underneaththe collimators. The monitor counter was a Nal(Tl) counter of 4" in diameter.The field of view of each counter was approximately 100" x 100° FWHM. The X-rayenergy band from 20 to'200 KeV was devided into four channels, 20-40, 40-60,60-100, 100-200 KeV, respectively.
To avoid the instrumental effects, electronic circuits, power suppliesand high voltage supplies were furnished independently for each of threedetector systems. Three identical balloon payloads were prepared.
25
3. Observations
To achieve the long duration flight, we predicted the term when thehigh altitude wind is the weakest of the year.
Three balloons were launched from Sanriku Balloon Center onSeptember 23, 24 and October 4, 1975 and they reached the ceiling altitudeof approximately 5 mb. The gondolas were rotated around the axis ofsuspension rope at a rate of 2 rpm. The observations were performed forapproximately 55 hrs, 65 hrs and 25 hrs respectively, total integrationtime being about 150 hrs. Subtracting the overlapping time of the firsttwo flights, we monitored the gamma-ray burst for approximately 120 hrs.A significant increase of the count-rate was found at about 10n06m40s UT,September 23 as shown in Fig.2.
40
40
(1)
NNjrf /y^
(2)
rt^^Vlfo^
i t i t i i i i
19:0U 19:07Sep. 23 1975
JST
Fig. 2 Time Profile of the Count-Rate
1,2) ; Observed by Detector with Modulation Collimetor
3) ; Observed by Detector without Collimetor
The event started at approximately 10h 06m 31s UT, reached the maximum at06m 42s and disappeared by 07m 00s. The signal to noise ratio of the eventobserved by the monitor counter was approximately 11 sigma. The energyspectrum of the burst as observed by the monitor counter is shown in Fig.3.The atmospheric absorption is corrected and the intensity given in. thefigure is the averaged for the period from 06m 39s to 44s.
4. Conclusion and Discussions
When the event was observed, the position of the balloon was at144° 15' 44" E, 38° 36' 36" N. The L-value of the location is 1.30.
• > f
26
10"
if
I6
ur3
10 100
photon energy KeV1000
Fig. 3 The Energy Spectrum of the Event
The event is unlikely to be of solar-terrestri&l origin by the followingreasons.
1) Magnetic latitude of the observed place was comparatively low asindicated by the small value of L.
2) The event occured more than 2 hrs after th . sunset.3) The solar-terrestial environment were qule 8) when the event wasobserved, i.e.
i) Solar activities were low during several days prior and afterSeptember 23 : The sun spot index was 0, solar X-rays werebelow the cut-off level of observation, and there were nosignificant radio features on September 23.
11) Geomagnetic disturbances have also been low for more than afew days : Kp index was 1 + or 1 from 03
h 00 m UT to 12h 00 m UTon that day.
4) The fact that the X-ray flux was modulated by the collimatorindicated that the source is not extended as expected for theterrestrial phenomena.
5) The energy spectrum extends to the high energy range. The spectralshape is similar to that of the gamma-ray burst.
It is thus concluded that the event is a small gamma-ray burst.
The position of the the spin-axis of the gondola in the projected fieldof view of the collimator on the celestial sphere was determined using Cyg X-las the reference. The off-set angle of the spin axis was 0.4°±0.1° from thedirection of the maximum transmission of the modulation collimators.
27
Following two methods of analysis were adopted in order to determinethe burst position.
1) Expected count-rate profiles for the detectors with modulationcollimator were computed for assigned source position from thecount-rate profile obtained by the monitor detector. Observed dataof detectors with the modulation collinator were compared wiht theexpected count-rate profiles, thus finding the source location whichproduces the minimum xZ~value-
2) A correlation map on the celestial-sphere was produced using theratio of the count-rates of the modulation-collimator counters andthe monitor counter.
The "off-set" of spin axis from the direction of maximum transmissionresolves the redundancy inherent to the modulation collimator in locatingthe position. The position of the burst is thus determined uniquely if oneignores the effect of the counting fluctuations. In order to reduce thiscounting fluctuations, we combined the data from the two modulation-collimatordetectors considering the 90° phase difference of two counters. In theanalysis the running average method and the maximum entropy method wereutilized. The details of analysis will be published elsewhere.
The correlation map obtained from the above analysis is shown in Fig.4.As seen in Fig.4 the most likely position of the burst source is ata=19 h 50m±lm, 6 = 45° 06'±10', approximately 10° north-north-west of CygX-1.Second position, a = 19h 36m± lm , 5 = 44°00I±10I is also probable but with lesslikelihood, 50%, compared to the former. The mirror images of the candidate
a - 19h 50" i.-.!>• • -7*.
Fig.4 Correlation Map to Locate the Burst Positi<
28
with respect to the spin axis are seen in the figure. The sign of the mirrorimage is negative, since the "off set" of the spin axis is about 1/4 of bandspacing of the modulation collimeter.
It is noted that the burst occurred when Cyg X-l was in the field ofview, which is suspected to be one of the burst sources*). However, thesignificance level of Cyg X-l being the source of this event is estimatedto be 0.1% and hence, it is unlikely that the burst was generated byCyg X-l.
It should be noted that a gamma-ray burst was located with aconsiderable precision for the first time with a single experimental device,whereas the location of the gamma-ray bursts has been thus far achieved bymeans of the method of time of flights among two or more satillites.
Acknowledgement
The authors thank to the members of Sanriku Balloon Center for theirexcellent efforts in making the long duration flights so successful. Wealso acknowledge to Prof. Y. Tanaka, M. Matsuoka and A. Nishida lor theirhelpful discussions throughout this work.
References
1) I. B. Strong, R. W. Klebesadel and D. Evans ; Ann. N. Y. Acad, Sci.,262, 145 (1975)
2) T. L. Cline, U. D. Desai ; Astrophys. and Space Sci., 42, 17 (1976)3) Y. Ogawara, M. Matsuoka, S. Miyamoto, N. Muranaka, J. Nishimura and
\i. Oda ; Astrophys. and Space Sci. 42^ 211 (1976)4) T. Cline and D. D. Desai ; Proc. 9th ESLAB Symp. ESR-SP 1065) A. Bewick, M. J. Coe, J. S. Mills, J. J. Quenby ; Nature 258, 686 (1975)6) R. Koga, G. Simnett and R. S. White ; Astr. Phys. J. L _115, 203 (1976)7) J. Nishimura ; Proc. Int. Conf. Cosmic-rays Munchen, JL2, 4091 (1975)8) Solar-Geophysical Data 20, 374A (1976)
Solar-Geophysical Data 8, 378A (1976)Solar-Geophysical Data 98-100, 314A (1976)
29
An Estimation of the Primary Proton Spectrum
Between 1012 and 1014 eV.
T. K. GaisserBartdl Research FoundationSwarchaore, Pa., 10981 USA
F. Siohan*Code 661, NASA/Goddard Space Flight Center
Greenbelt, Md., 20771 USA
G. B. Yodh+
Department of Physics and AstronomyUniversity of Maryland, College Park, Md., 20742, USA
Abstract
,11Based on measurements of unaccompanied charged hadron flux froa 10
to 10 eV at mountain altitudes, ve estimate the primary proton flux using
recently determined proton-proton total cross sections from new measurements
of the real part of the forward scattering amplitude at ISR, and Glauber theory
to calculate proton-air inelastic cross section, The derived spectrum.
agrees well with extrapolation of the direct measurements below 2 x 10 " ev
without change of slope
*NAS/NRC Resident Research Associate.tOn sabbatical leave'at Laboratory for High Energy Astrophysics, GoddardSpace Flight Center.
30
In a recent paper (Amaldi, et al., 1977) the expected behaviour of
* 2 13proton-proton total cross sections between 2 x lO* and 3 x 10 has been
deduced using dispersion relations and the measured value of the real part of
the forward scattering amplitude. The proton-proton total cross section,
o c , is found to increase and reach 55 + 2 mb at A x .10 eV. We derive,
PP ~ •
using Glauber thejM$, the proton-air inelastic cross section, °INE7 T (E),
from 2 x 10^ to 4 x 10 eV, and calculate from the measured unaccompanied
single hadron flux at mountain altitude (F. Siohan 1976 and Nam, et al. 1975)
an upper bound to the primary proton flux.
Mountain altitude experiments measure the .unaccompanied charged hadron •
vertical flux, j(E,x,A,E) in units of particles per (m ,sr,sec,CeV) where E
is the hadron energy, x the atmospheric overburden in g/cm , A the anti-r '
coincidence area in square meters and E is the minimum energy needed for
accompanying particles to register in the anticoincidence arrangement. This
flux is an upper bound to the flux of uninteracted 'or surviving protons.
Therefore we can write
i (E,x,A,E)
where X(E) is the interaction length of protons in air,
X(E) - 23,550/ a(E) g/cm2
(1)
(2)
and o is in mb. The probability that the single hadron is unaccompanied
decreases with energy of the hadron and depends also on E and A In the
2 2experiments considered here, A varies from 3.3 m to 9 m and E between
15 MeV and 2 MeV. Above A x 10 eV, single unaccompanied hadrons are unlikely
to be progeny of primary particles heavier than protons (MacKeown 1970).
Furthermore, the flux of charges hadrons contains pions, kaons and secondary proton*.
Of these; kaons can be shown to be negligible and an estimate of plons and
secondary protons can be made by measuring the pion to proton ratio and the
.,'•',
31
neutral to charge ratio (J. MacFall 1976). The ratio of number of secondary
protons to neutrons must be equal to or greater than unity. Denoting charged
pions by * , neutrons by n, uninteracted protons by p and the measured charged
flux by c, one obtains
p <_ c -it - n (3)
and
jp(E,x-O)<. e X ( E ) pr(E,x) (4)
In this paper, the upper bound is calculated using formulas (3) and (4) below
12 12
10 eV, from (3) and (4) with only n correction up to 8 x 10 eV, and using
formula (1) above 8 x 10 cV. Above 5 x 10 eV calculations (Caisser and
Yodh 1973) on accompaniment to be expected Indicate that the measured flux
should be within 40Z of the true residual proton flux.
To calculate <JT%I_, from a and slope parameter b, one must
1NLL pp
realize that interactions of protons with air nuclei leading to excitation
of the nucleus without pion production (quasi-elastic scattering) and diffrac- \
tive excitation of target nucleons do not give rise to detectable accompani-
ment. Also, in addition to elastic screening, inelastic screening corrections
must be made. Denoting quasi-elastic, diffractive excitation and inelastic
screening cross sections by o , ff and &0, , respectively, we can
qe o incx
write (Gaisser et al. 1974, Gaisser et al. 1975)
„ P-Alr P-Air _ F-Air • .„ „ „ ,,»
°INEL " ° ToT " ° EL " AffIKEL " °qe " °D (5)
We have carried out these calculations using a root mean square effective
radius for air of 2.60 fermis and a gaussian wave function for nuclear
density, the results of which are given in* Table I (cross section In tub,
b In (GeV/c)"2 ; E In GeV).
32
TABLE I
zoo
500
L000
5000
LO4
2xlO4
LO5
i P P1 ToT
39
40
42
47
50
53
57
b P P
11.54
11.84
12.43
13.91
14.8
15.7
17.2
ABS
°P
320
324
335
356
370
382
398
AoINEL
7.7
9 .9
11.5
12.2
12.6
13.8
V26.4
t |
11
t l
• 1
t l
11
°D
14.3
I I
II
f t
I I
I I
I I
P-Air°INEL
271
275
285
303
317
329
343
The theoretical technique to obtain inelastic hadron-nudeus cross sec-
tions outlined here has been used to calculate cross sections which can be
compared with various accelerator measurements with different projectiles
from 20 to 200 GeV (Yodh 1976). Theory and experiment are in agreement within
+ 32 . Our estimate of the theoretical uncertainty in proton-air cross sec-
tions is less than + 7 mb or about 3S. A three percent error in ° propagates
to a 25Z uncertainty in calculated flux.
The vertical integral fluxes of unaccompanied charged hadrons at 730 g/cm
12(and residual protons below 3 x 10 eV) and derived primary fluxes are given
in Table II. The resulting primary spectrum is shown in figure 1 and compared
with an extrapolation of the directly measured spectrum, (Ryan et al. 1972). Also
given in the figure is the EAS measurement at 10 eV.
As remarked earlier, these fluxes should be quite close to the actual
primary proton flux above 4 x 10 eV. Thei spectrum shows no steepening as
observed by PROTON experiments (Akimov et al. 1970).
We would like to acknowledge discussions with V. K. Balasubrahmanyan,
R. W. Ellsworth, J. Ormes and R. E. Srreitmatter. This work was supported by
N3F Granf.PHY76-14853. One of us (G. B. Yodh) would like to thank Dr. F. B.
McDonald for his hospitality during his sabbatical leave.
3J
33
Table II
2 2Integral Flux in p/m sr sec at 730 g/cm
E(GeV)
225
500
1020
2223
3001
4001
6000
8000
15,700
26,500
40,000
J(E,x)
(0.35+.01)xl0"3
(0.46+.01)xl0~4
(,91+,04)xl0~5
(3.95+.46)xl0~6
(1.55+.28)xl0~6
(1.02+.19)xl0"6
(3.54+1,l)xlO"7
(1.18+.62)xlO~7
(l.l+.O4)xlO~7
(.04+.02)xlO~6
(,016+.011)xlO~6
X(E-1.71E)
85,9
83.6
80.9
77.9
76.7
75.4
73.9
72.5
69.7
67.5
65.6
jp(>E,O)
1,72+.43
.29+.07
.076+.019
.046+.012
.0211+.005
.016.004
(6.9O+2.8)xlO~3
(2.78+1.6)xlO~3
(3.89+.9)xlO~3
(1.99+.9)xlO~3
(1.09+.7)xl0"3
Comments
II
II
••
It
tt
It
no corr.
tt
rt
Reference
Siohan 76
11
Of
II
tl
tl
II
•1
Nam et al.75
II
II
34
References
Akiaov, V.V. et al., 1970, Acta. Phys., Suppl. No. 1., 2]_, 517.
Amaldi, U., et al., 1977, Fhys. Lett. 66B, 390.
Gaisser, T. K., Yodh, G. B., 1973, 13th Int. Cosmic Ray Conference, Denver, 3, 2140.
Gaisser, t. K., Nobel, C. J. and Yodh, G. B., 1974, Paper submitted to the XVII
Int. Conference on High Energy. Physics, London, to be published.
Gaisser, T. K., et al. 1975, 14th Int. Conference on Cosmic Rays, Munich, ]_, 2161.
MacFall, J. R., 1976, Doctoral Thesis, University of Maryland, U. of Md. Report
No. PP-76232.
MacKeovn, P., 1970, Proceedings of the VI Interamerican Seminar on Cosmic Rays,
LaPaz, Bolivia, Vol. Ill, page 684.
Nam. R. et al., 1975, 14th Int. Cosmic Kay Conference, Munich, ]_, 2258.
Ryan, M. J. et al., 1972, Phys. Rev. Lett. 2£, 985.
Siohan, F., 1976, PtuD. Thesis, University of Maryland, U. of Md. Report
No. PP-77611.
Yodh, G. B., 1976, Invited talk, International Colloquium on Multiparticle
Reactions, Tutzing, page 461.
,r
• SIOHAN 7r/c,n/c CORRo SIOHAN n/c CORRa Aseikin et ol NO CORR
*== Ryan et al— - Extrapolation of Ryan ef a',
a EAS
u
Ryanetal 8060 E.-1.66
100
_r i l i i l l ' « i i • n I ' i '
36
Figure Caption: Calculated Integral flux of primary protons between 100
and 100,000 GeV. The points below 1000 GeV shoulo be a close approximation
to the true primary proton flux and they are seen to be ir good agreement
with direct neasurements. The points upto 8000 GeV have beqn obtained
Including a correction for secondary protons of 0.67 based qn neutral to
charge ratio only. The higher energy points have not been corrected for
possible contamination due Co secondary protons and therefore are upper limits.
66*90031537
On the High En *_.: Proton Spectrum Measurements
R. W. Ellsworth, A. Ito , J. MacFall , F. SiphanR. E. Streitmatter, S. C. Tonwar*, P. R. Vishvanath,and G. B. Yodh?.
Department of Physics and AstronomyUniversity of Maryland \
College Park, Md. USA, 20742 \
and \
V. K. BalasubrahoanyanGoddard Space Flight Center
Laboratory for High Energy AstrophysicsGreenbelt, Md., USA, 20771
t Mow at State University of New York at Stony Brook, Long Island, N. Y.* NAS/NRC Resident Research Associate at Goddard Space Flight Center,
Greenbelt, Md.# Now at Tata Institute of Fundamental Research, Bombay, India.€ On sabbatical leave at Goddard Space Flight Center, Greenbelt, Md.** Now at Pfizer Corp., Columbia, Md.
38
Abstract
The steepening of the proton spectrum beyond 1000 GeV and the
rise in inelastic cross sections between 20 and 600 GeV observed by the
PR0T0N-1-2-3 sa te l l i t e experiments nay be explained by systematic effects
of energy dependent albedo (bacUscatter) from the calorimeter.
Resume
L'accroissement avec l'ene.rgie de 1'albedo du au calorinetre peut
expliquer 1'augmentation de la pente du spectre primaire de protons au-dela
de 1000 GeV et la croissance des sections efficaces inelastiques entre
20 et 600 GeV observes lors des experiences en sate, l i t e PROTON 1, 2 et 3.
39
I. Introduction:
CoBmic ray particles constitute the only sample of matter from
outside the solar system available to us for direct studies. Study ot
the composition and energy spectra of cosmic ray particles provide
important data with which one may test theories of astrophysics^ processes
such as stellar evolution, nucleo-synthesis (Schraua and Arnett, 1973),i
Interstellar processes (Shapiro and Sllberberg 1970), as veil as theories
of acceleration and propagation of cosmic rays (Scott and Chevalier, 1975,
Rasmuasen and Peters, 1975).
The most abundant component of cosmic rays up to 2000 GeV Is pro-
tons (Akimov et al. 1969, Grigorov et al. 1971, Ryan et al. 1972 and Schmidt
et al. 1969). The question of the origin of these protons has been a per-
plexing one: Do they arise in acceleration processes of supernova ejecta
mixed with interstellar hydrogen at the interface of supernova remnants and
intersteller medium (Scott and Chevalier, 1975), or do high energy protone
arise as secondary products in nuclear collisions of heavier nuclei In
interstellar medium in a galaxy closed to escape of particles (Rasauisen and
Peters 1975 and Peters and Westergaard 1976)T To understand these problems, *
knowledge of the proton spectrum beyond 2000 GcV is of importance.
The only measurement of the proton energy spectrum above 2000 GeV
comes from the lonization calorimeter experiments doue on the PROTON 1, 2
and 3 satellites (Akimov et al. 1969a, 1969b). These measurements gave
two unexpected results: (1) a steepening of the proton spectrum at * 1000
GeV with an apparent change of slope by 0.7 unit and (2) a twenty percent
increase in inelastic cross sections of protons on carbon and polyethylene
nuclei between 20 and 600 GeV.
40
The observation of a steepening of the proton spectrum at BO low
an energy has given rise to many speculations about the Interpretation
of extensive air shower measurements (Gaisser et al. 1973. McCusker 1975,
Udovcyzk 1973). The Increase of twenty percent In cross sections has led
to speculation about the possible existence of deuterons in cosmic rays
(Grlgorov et al. 1975). Therefore, It is important to examine the
experimental technique for possible energy dependent systematic effects.
Back scattered particles from Interactions In the calorimeter could
give rise to an energy dependent bias which can cause steepening of the
observed proton spectrum. The PROTON experimenters did consider backacatter,
but came to the conclusion that It was not significant. Recent experiments
done by the University of Maryland group at Sacramento Ridge Cosmic Ray Lab
(SRCRL), Sunspot, New Mexico (elevation 2900 m) (Ellsworth et al. 1975a ;
MacFall 1976; Slohan 1976), have shown that the magnitude of the backscatter,
which is indeed quite large, has a logarithmic variation with the energy of
the Incident hadron. Using this Information from thi Maryland calorimeter,
we have made attempts to correct the PROTON spectrut for systematic bias. .
We show that effects of energy dependent albedo can jive rise to steepening
of the proton spectrum at high energies.
In section II we describe the experimental apparatus used In the
PROTON experiments. In section III we describe the University of Maryland
experimental setup to study the albedo from the calorimeter and experi-
mental results obtained on the magnitude and energy variation of albedo.
The effects this albedo could have on the proton spectrum and cross section
measurements of the PROTON experiments is estimated in se'ction IV. Finally,
a summary discussion of these results Is given in section V.
41
II. Experimental Apparatus of the PROTOH Series.
The calorimeter In the PROTON experiments (Grigorov et al. 1967a),
Akiraov et al. 1969 a and b) (Fig. 1) had a depth of three Interaction
lengths. A scintillator N was placed above the calorimeter with 2.5 cm of lead
immediately above it. A block of carbon (34 gm/crn ) was used to separate
this scintillator froa a stack of two proportional chambers, called Zy
The trigger required a minimum energy deposition in the calorimeter, E .,
a pulse in the proportional chambers Z., and a pulse in scintillator N.
To select protons, the pulse heights of both proportional chambers Z. were
required to be less than 2.7 V , where V is the nost probable pulse
height for sea level muons. In order to decrease the probability of albedo
particles from the calorimeter affecting Z. pulse heights, the carbon block
was in place for most of the experiment. The proton spectrum data was taken
in this configuration in which all events interacting either in the carbon
block or in the calorimeter were included. It was argued that this con-
figuration eliminates backscatter problems (Grigorov et al. 1971).
III. Study of Albedo from Calorimeters:
(i) Apparatus of University of Maryland Experiment.
The SRCRL calorimeter (Ellsworth et al. 1975b; MacFall 1976; Sioh&n
1976) had a total depth of 8 interaction lengths of iron and an area of
about 4 m . The hadronic cascade is sampled by seven layers of liquid
scintillators. The experimental array had the following componenta (see
figure 2).
* The first published spectra from the PROTON experiments (Grigorov et al. 1967b)were taken with a trigger Z^N^Eci, where 'N^' is the requirement that
the pulse height in scintillator N be in a window 0.4 to 1.7 times themost probable sea level rouon pulse height. Later publications (Aklmovet al. 1969a) present the combined spectra ZJNJE j + z i N 2 E i "^ere 'H2*
is the requirement that the pulse height in N be > 1.7 times the mostprobable muon pulse height.
42
2 2a) A scintilla tor Tl, of thickness 1.25 gm/cm and area 3.3 m placed just
above the calorimeter.
b) A transition radiation detector CTRD) consisting of a stack of 24
proportional chambers placed above the beam spark chamber described
below. (The proportional chamber* (PC), which were used to differ-
2entlate between protons and plons, had an area of lm and active depth
of 5 cms and were filled with Argon-Methane mixture (90Z Ar and 10Z«
CH.)-at a pressure.of 0.73 atm.).
c) A set of" 4 wide gap chambers: A beam chamber, SCB, placed above the
counter Tl and underneath the TRD; three chambers, SCI, SC2 and SC3
placed below IX, 3X and 6X of iron in the calorimeter.
Special features which made this'instrument suitable for the study
of backscattered albedo were: (1) the trigger was oc the total detected
signal from the calorimeter and did not depend on the pulse height of
detectors placed directly above the calorimeter Iron (Tl and PCs), (2) the
spark chambers embedded in the calorimeter made it possible to select single/
hadronic Jets, (3) these Jets could be correlated by reconstruction with th«
Incident track In the beam spark chamber, (4) for ea< h event the pulse
heights of Tl and the PCs were recorded and (S) these detectors were com-
pletely enclosed in aluminum boxes which shielded them from spark chamber
noise.. Therefore, It was possible to study the pulse height distribution
of these detectors as a function of energy of the hadron and of the depth
of the point of*first Interaction.
The response of the Tl counter was measured in terms of pulse height
deposited by a union with energy greater than 800 HeV. For the same mions,
V the most probable pulse height from the PCs In the TRD was determined
to be 5.6 keV.
43
The exposure factor ac 2900 m altitude enabled us to cover an energy
range of 100 to 2000 GeV for the study of backseatter.
(ii) Rasults OK Albedo from the SRCKL Experiment.
While the main purpose of the experiment was a study of cosmic fay
fluxes at mountain altitude, the magnitude and energy dependence of the
backseatter albedo from the calorimeter was also measured. The events which
interacted in the first X (interaction length) and beyond the first X were
labelled as "Jfel" and "Fe2" events respectively. The proportional chambers
used for this study were the lowest {Si - #1) and the middle (#8 --#13)
chambers in the TRD stack. Table 1. shows t ; average signals as a function
of energy and depth for the scintlllator Tl. The table also lists signals
of FC1 (0.66m above the calorimeter iron) and the average of PCs 8-13
(approximately 2.75 meters above the calorimeter iron). The Individual
hadrons for which the averages have been presented in Table 1 were required
to have traversed the detector being studied i.e., they were "hits". A
similar study, not presented here, was done for "misses" also.
The most important point to note Is the Increase of the average
signals in Tl and PCI for events whic*: iaceracted in the 1st A. In these
"Fel" events, signals show a logarithmic increase with energy. Figs. 3 and
A also show the pulse height distributions in Tl and PCI at energies of
130 GeV and 1300 GeV. It can be seen that the pulse height tail increaseo
with energy in both the scintlllator and the proportional chamber.
The magnitude and energy dependence of this backscatte- becomes
smaller with an increase In the distance and the amount of matter between
the point of first interaction and the detector, as illustrated by the
following points: 1) When the interaction takes .place deeper In the calo-
rimeter (Fe2 events), the average signal in Tl Is auch smaller than when
44
the interaction Is in the highest layer of the calorimeter. 2) When
the depth of Interaction in the calorimeter is fixed (Fel), Table 1
Indicates that the average signal in PCI (near the calorimeter) is larger
and Increases more rapidly with incident hadron energy than that of the
high PCs 8-13. These two results can be understood as due to the ranging
out and geometrical divergence of the backscatter particles.
The albedo from a calorimeter will, in general, be made up of (1)
heavy charged particles, (ii) neutrons, (ill) photons and (lv) electrons.
In the proportional chambers of the TRD, an additional energy dependent
contribution due to transition radiation will exist for those incident
particles whose Lorentz factor is above TR threshold.
Scintillation counter Tl and proportional chamber PCI will both
record charged backsc&tter with high efficiency. Neutrons contribute to
the Tl pulse height with greater efficiency, while photons contribute to
the PC pulse height with greater efficiency,
(iii) Effect of Albedo on the Measured Proton Spectrum
The magnitude of the albedo observed in the SRCRL experiment Implies
that the pulse heights in the proportional chambers, Z., of the PROTON
experiment were significantly increased by albedo from interactions In both
the carbon block and the calorimeter. Since the fraction of events with
pulse heights greater than 2.7 V also increases with energy, the per-
centage of events rejected as nonproton events increases with energy.
To estimate the effects of albedo on an apparatus similar to that
of the proton experiments, we examined the signal distributions for a
subset of data; i.e. for those hadrons which passed through both PCI and
its projection downward on the horizontal plane at the depth of spark
chamber SCI. Any differences between these data and those of PROTON experi-
ments are due only to the following differences in the apparatus: (a)
45
There is 7 gm/cm of absorber between PCI and top of the SRCRL calorimeter
due to which some aibedo nay range out (b) PCI la located 0.66 m above Che
calorimeter and hence has a smaller gometrical acceptance than proportional
chambers Z in the PROTON experiments (c) The upper calorimeter layer is
iron and not carbon. While the presence of carbon may decrease the albedo
effect, the total number of Interactions which increase with energy and
contribute to an increasing albedo is not expected to be very different
from the number in a pure iron calorimeter.
Geometrical divergence of the albedo permits subtraction* of the TR
contribution in PCI by using pulses from higher chambers which subtend a
small angle to the point of cascade origin. Let f(E) be the fraction of
events with signals in a particular counter greater than 2.7 V . By a
mp
study of pulse height distributions at several energies, the magnitude and
variation of this fraction with energy was obtained for T. and the lower
and the nlddle proportional chambers. Both Fel and Fe2 events were used for
this analysis. The increase due to transition radiation, as given by the
middle clambers (PC. its 8 - 10), was subtracted from the observed fractions;
for PCI. The resulting fractions reflscc the increase of backscatter alone
with energy. The values of f for T_ and PCI have been listed in Table 2
and plotted in Fig. 5.
When f(E) is the fraction of protons rejected at energy E, the true
differential flux J at that energy is related to the observed differential
flux J as J - J /(1-f (E)). We have taken J from the fitted PROTON 1-2-3o t o o
integral spectrum reported by Akimov (Akimov, et al. 1969b). Using the
fractions f(E) for Tl and PCI, corrected intergral spectra were obtained and
are plotted in Fig. 6 along with the PROTON 1-2-3 spectrum.
* Being 0.66 m above the Fel layer, PCI itself will give f values which arean underestimate of those from the PROTON experiment counter Zy. While adownward extrapolation could be made to hypothetical chambers on thecalorimeter, a lack of knowledge about the energy and angular distributionof the backscatter makes Interpretations of such extrapolations difficult.
46
The important point to note is that the steepening in the corrected
•pectra is less than in the observed spectra*. Since the PROTON experiments
had two proportional chambers immediately above the calorimeter to veto
larger signals, the corrected spectra are approximations to the true
spectrum. The correction derived from the response of the scintillator Tl
has the limitation that neutron backscatter will count more efficiently In
the scintillator than in the proportional chamber Z,. Since PCI was
located farther above the calorimeter than Z. In th« PROTON experiments,
. the flux corrected from the response of PCI will be smaller than the true
flux.
V. Effect of Albedo on Cross Sections
In the sane series of experiments, inelastic cross sections of protons
on carbon were measured using a transmission technique. A trigger ^N.E "as
used to measure J , the flux of protons without the absorber and J with the
absorber between the scintillator and the proportional chamber. The pulse
heights in Z- and N. were required to be less than 2.7 V ™ and 1.7 V,,-,,
1 orespectively. The Inelastic cross section was calculated using o - T- in — ,
k Jxwhere k is a constant dependent on the absorber thickness and properties.
An increase of 20X in cross section was seen in the energy range 20 to 600 GeV.
While this rise has not been seen in accelerator measurements with different
projectiles (protons, plons, and neutrons) on nuclear targets, (Busza et al.,
1975, Murthy et al., 1975, Baker et al., 1975), this apparent increase can
also be attributed to albedo related effects.
This increase (y20X) in the cross section arices from a small (V1-0Z)
increase in the ratio J /J . In Aie SRCKL data the fraction of events,o x
which give a pulse height in PCI for hadrons whose trajectories miBsed PCI
increases from about 9Z at 100 GeV, to about 25Z at 1300 CeV. Similarly,
47
in the PROTON experiments backscatter from hadrons whose trajectories alas Z,
and N but deposit enough energy in the calorimeter, can give rise to Z.N.E
triggers and contribute to a spurious increase in J . This effect on J Is
much smaller since the absorber attenuates the backscatter giving less than
tinimura signals in 2 . . Thus, this systematic effect due to albedo also explains
the apparent increase in the cross sections. With limited stat ist ics , data
taken with direction detector DD in the trigger show no statistically signif-
icant increase in cross section (Grigorov et al 1970). The Cerenkov counter
DD does not detect slow aoving backscatter.
Discussion
We have seen that both unexpected observations from the PROTON experi-
ments-steepening of the proton spectrum and Increase of cross sections- can
arise as consequences of energy dependent albedo from the calorimeter. While
we have given estimates of corrections to the observed proton spectrua, we note
that i t i s difficult to obtain the true spectrum due to the differences between
the two experimental setups. There exists; however, a clear need for extending
the proton spectrum measurements beyond 2000 GeV with experiments noti
susceptible to backscatter.
One may further ask if the albedo effects would have interfered with
the measurements of t^" He spectrum reported in the same series of experiments.
Backscatter effects can modify the He spectrum. However, the magnitude of the
effect might be smaller than that for protons, because of the large window
allowed for Z, pulse height in the cr-aode (2.7 V <V_ <8V ) . As far as one
i. mp z, cap
can understand the triggering for the or-mode, it appears that the Cerenkov
counter signal was required to be in coincidence with those of Z^ and the
calorimeter, the Cerenkov detector is Insensitive to low velocity backscatter
and therefore a pulse height requirement on it would not remove the high energy
a particles. Thus the ar-spectrum may be an undistorted result. The exposure
factor for the a spectrum 16 not large enough to reach energies of
the order of 5000 GeV/nucleon, hence there was no significant
48
overlap with the bend region for the proton spectrum. .
One additional observation is in order regarding the all particle
spectrum. The albedo effects discussed in this paper should have no effect
on the flux or the slope of all particle spectrum. Indeed, the measurements
of the satellite experiment (Aklmov et al. 1969a) and those of GSFC exper-
iment (Ryan et al. 1972) are in agreement where they overlap.
Since the rise in cross sections can be attributed to albedo effects,
it is not necessary to Invoke a large fraction of deuterons in the primary
cosmic ray beam to account for this increase, as discussed recently (Grigorov
and Maroontova 1975). A small fraction of deuterons is not ruled out
(Apparao 1973).
Finally, we make a few remarks as to the origin and 'nature of albedo
particles.
While we have established the magnitude apd energy dependence of the
albedo, a more difficult task is to determine the nature of these particles.
Their logarithmic dependence on energy suggests that they arise from inter-
actions of secondary and tertiary hadrons in the cascade. Since the number
of these secondaries increases logarithmically with energy, the number of
their interactions also has the same dependence on energy. Every one of
these interactions, apart from producing fast particles, gives rise to a
small number of slow particles, both protons and neutrons. The charged slow
particles, known as heavy prongs In emulsion techniques, are isotropic In
the lab system. While the number of these heavy prongs per interaction itself
is Independent of energy, their total number'increases with incident hadron
energy. While the slowest (the "black" tracks) of the slow particles get
absorbed soon, the faster ones (the "gray" ;tracks) with a typical energy of
160 MeV are likely to reach the top of the calorimeter. An analytical
49 -;'>t^|f •''"''
calculation (Siohan et al. 1977) was done assuming an isotropic production
of these particles. It was found that the number of these particles reaching
the top cf the calorimeter did indeed increase with energy. Apart from
these charged particles and neutrons, the backscatter also contains photons
from the electromagnetic cascade. A proporclonal chamber placed immediately
on top of the calorimeter can ba studied to obtain a better estimate of the
photon flux.
• '-si'-
^ . 50
References
Akimov, V. V., Grlgorov, N. L., Mamontova, N. A., Nestrov, V. E.,
Prokhln, V. L., Rapoport, I. D. and Savenko, I. A. 1969b, Proc.
of Int. Ccnf. on Cosmic Rays, Budapest, Acta Physic* Hungarlcae, Suppl.
j29, Vol. 2, 211.
Akimov, V. V., Grigorov, N. L., Nesterov, V. E., Rapoport, I. D.,
Savenko, I. A., Skuriden, G. A. and Tirenkov, A. F., 1969a, Proc.
of the Int. Conf. on Cosmic Raya, Budapest, Acta Physica Hungarlcae,
Suppl. 29, Vol. 1, 517.
Apparao, M- V. K., 1973, Proc^of 13th Int. Conf. on Cosaic Rays,
Denver, Vol. 1, 126.
Baker, W., 1975, private communication, preliminary results on pion-
nucleus and proton-nucleus inelastic cross section*
Busza, 1975, Phys. Rev. Letters 34, 836.
Cheshire, D. L., Huggett, R. W.,'Jones, W. V., Schmidt, W. K. H., Sinon, M.
and Kurz, R. J. 1975, Proc. of 14th Int. Cosmic Ray Conf., Munich
Vol. 2. 3244.
Crannell, H., Crannell, C. J., Whiteside, H., Ormes, J. F. and Ryan, H. J.,
1973, Phys. Rev. D7, 73Ô.
Ellsworth, R. W., Goodman, J., Ito, A., MacFall, J., Siohan, F.,
Streitmatter, R. E., Tonwar, S. C , Yodh, G. B., 1975a, Proceedings
of the Calorimeter Workshop, Fermi National Ace. Lab., page 201.
Ellsworth, R. W., Goodman, J. A., Ito, A. S., MacFall, J. R-, Siohan, F.,
Streitoatter, R. E., Tonwar, S. C. and Yodh, G. B., 1975b, Proc. of
14th Int. Cosmic Ray Conf., Munich, Vol. 7, 2528.I
Gaisser, T. K., Maurer, R. H., Noble, C. J., 1973, Proc. of 13th Int.
Conf- on Cosmic Rays, Denver» Vol. £, 2652.
51
Grigorov, N. L., KakhLdxe, G. P., Nesterov, V. E., Rapoport, Z. D.,
Savcnko, I. A., Smiraov, A. V., Titenkov, A. F., Shishkov, P. P.,
Kosmicheskie Issledovanija, 5.» 383, 1967a.
Grlgomv, N. L.. Nesterov, V. R., Rapoport, I. D., Savenko, I. A.,
Skuridin, G. A., Ticenkov , A. F., Kosnlcheskie Issledovanija, JÏ, 39St 1967b.
Grigorov, N. L., Nesterov, V. E., Rapoport, I. D., Savenko, I.'A., and
Skuridin, G. A., 1970, Soviet Journal of Nuclear Physics, 11, ASS.
Grigorov, N. L., Manontova, N. A., Rapoport, I. D., Savenko, I. A., Akiaov,
V. V. and Nescerov, V. E., 1971, Proceedings of 12th International Conference
on Co3nic Rays, Vol. 1, 1752.
Grigorov, N. L<-, Gubin, Tu. V., Rapoport, I. D., Savenko, I. A., Yakovlev, B. M.,
1971, Froc. 12th International Cosmic Ray Conference, Vol. S, 1746.
Grigorov, N. L. and Mamontova, N. A., 1975, Froc. of 14th Int. Conic Ray
Conf., Munich, Vol. 1, 2303.
MacFall, J. R., 1976, Ph.D. Thesis, University of Maryland, Report Ho. PF76232
(Unpublished).
McCusker, C. B., 1975, Physics. Reports.
Murthy, P. V. R.f 1975, Nucl. Physics, S92, 209.
Peters, B., and Uestergaard, N. J., 1976, Danish Space Research Institute, Preprint.
Rasmussen, I. L., Peters, B., 1975, Nature, 258, 412.
Ryan, M. J., Ormes, J. F. and Balaeubrahmanyan, V. K., 1972, Phys. Rev. Letters,
L8, 985.
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52
TABLE I. Average signals of Detectors
Energy(Gev*
1305007001300
Fel
3.89+.5.27+.
T]
4212
5.98+.177.10+.10
LFe2
1111
.34+.05
.81+.10
.95+.10•92+.07
PCIFel
1112
34+.14.84+.10.87+.11V.23+.16
Av. PCs 8-13Fe 1
1.09+.091.47+.071.51+.091.67+.12
TABLE II. Variation of f with energy
Energy (Gev) ,
1305007001300 .
f(Tl)
0.29+.040.49+.020.52+.030.56+.04
ftPU)
0.16+.040.23+.040.24+.040.27+.05
t ir !••
53
Figure Captions
Figure 1: SEZ-14 instrument flown in PROTON 1-2-3 experiments.
Figure 2: A vertical cross section of the University of Maryland
cosmic ray calorimeter showing the locations of proportional
chambers and counter Tl which were used in studying backseatter.
Figure 3: Pulse height distributions of counter Tl for single unaccompanied
hadrons of average energy 130 and 1300 Gev, interacting in
2the first- 120 g/cm of iron. The abcissae are in terns of
minimum particles.
Figure 4: Pulse height distributions of proportional chamber 1 (PCI)
for single unaccompanied hadrons of average energy 130 and
1300 Gev, The abcissae are in Kev deposited.
Figure 5: f(E) vs incident hadron energy.
Figure 6: Integral energy spectrum of protons with and without
correction for backseatter.
Acknowledgements
We would like to thank Dr. J. F, OtSSifor useful discussion and Dr.
W. V. Jones for Monte Carlo simulation. The work was supported In part
by National Science Foundation Mo. Phy. 76-14853 and by the' University
of Maryland Computer Science Center.
CARBONBLOCK — ^ .(34g/cm2)
PM-I
CARBON P M " ^ -
IRON C"-v_LEAD PM-K
•—
*F=" F"
^Mmmmm
r\t^mmmmma
V/////////////
'/////////////AV////////////Avy//////,'/////Y/////////7//A'/////////////Ay//////////////
-DD(CERENKOV)
- Z , (PROP CH.)
-N,(SC CTR)
PM-I
>v PM-m
/
SCHEMATIC DIAGRAM OFSEZ-14 INSTRUMENT
FIGL'RE 1
55
PC24
SCB
O
o
o
(fi
00
Xo(Z
TlY/Z77//////////Z77//7A+--
SCI
[S7_X7777/,'
Si 3)
V///////////////////A
in: JL SI2|
Y/Y///77////////777/VAJL SIT) lm
Y/ ///JL SlOl
SC3
JL
L2J JL
IRON SCINTILLATORS(SI TO S!4)
FIGURE 2
50
40
c
3XI
| 20
10
00
1
4
Tl130 GeV
Fe I Events
en
8 12Tl Pulse Height (particles)
16
FIGURE 3
57
10-
LJ
e3
FLPCI
1300 GeVFe I Events
Jl
20 40 60 80KeV Deposited
FIGURE 4
1.0
0.9
0.8
0.7
- 0.6UJ
^ 0.5
0.4
0.3
0.2
0.1 t
\0'. . . I
I0 3
Energy (GeV)
Tl
U100
I03
16"
£ 8(/> CO
= "jo5
c £I "o in
•5 f
167
~ T - . . . . • !
— Fit to observedspectrum inproton 1-2-3 exps.
— Spectrum after correctionusing PCI, (lower limit)
•— Spectrum after correctionusing T l , (upper limit)
10'
CO
I I I I I
Energy (GeV)
FIGURE 6
60
COSMIC HAY ABUrOAWCES FROM NITROGEN TO ZIN3 ,CELLULOSE NITRATE PLASTIC DETECTOE
EIC A
G.S.Kainth, V.S.Bhatia anl Suman Pan l th i
Physics Department, Panjab Univers i ty , Chani^garh-160014,India.
A s tack of Cellulose Ni t ra te sheets' , ejxposed over For t Churchi l lhas been used to ob t a in , with good: r e s o l u t i o n , the cosmic ray-charge d i s t r i b u t i o n from Idtrogeil t o z inc.After chemical e t ch ing ,a t o u t 2900 conical p i t s b e l o n g ! ^ to 1137 stopping cosmic r a ynuc le i have been analysed. Inmroved procedures of measurementsar t analysis yield a charge resolution of 0.2 charge units fornuclei upto Sulphur and 0.3 ./units of charge for heavier elements.The present experiment, therefore, shows that Cellulose Nitratedetectors can be used successfully for the study of cosmic raynuclei with charges as high as 30. Charge distribution of nucleiwith Z - 7-30 is presented. The rat io of the number of even Znuclei to that of odd 2 nuclei comes out to be 3.1. The rat ioHn/Fe i s determined a/0.23+ 0.09.
1. Introduction
An' accurate measurement yof the charge distribution of primary c osmicray me le i i s important for establishing the origin and propagation of theseniclei. In view of t h i s , a large number of investigations regarding thecharge composition have beenrconducted in recent years. In particular, atlow energies, the charge composition has been studied by various investigatorsusing different types of detectors such as nuclear emulsions, Cerenkov counters,scintillation counter telescopes and ionization chambers.'Plastic detectorshave also been used extensively for th i s purpose. Lexan polycarbonate detectorshave been mostly used./Only a few investigations have been carried out usingcellulose nitrate {CM as a particle detector (Enge e t a l . , 1973a, 1973b;Beaujean and Enge, 1571, 1972; Pukui, 1972). However, these investigationshave been confined to nuclei of Z^lO only. Benton (1968) had tried CNdetectors for stud/ing cosmic ray niclei of charges upto about 30 but hisresolution was not satisfactory. The present experiment was done vath a viewto evolve suitable procedures for obtaining good charge resolution in CNdetectors for cyosmic ray nuclei of charges as high as 3 r >
2. The Experiment
For/this experiment, we used a stack consisting of eight nuclearenulsion .pellicles placed on top of 163 Daicel CN sheets of size 14.5 cm x18.1 cm lie 0.03 cm. The stack was exposed to cosmic rays for 12 hours on July15,196a/at 2.9 mbar over Fort Churchill. Several pieces cut from one of theCN shafets ware exposed to a beam of 10.2 MeV/n c1^ iom from the HILAC,Berkeley, California. These ions were used for calibration of CN sheets.
The CN sheets were chemically etched, in batches of 14 sheets, in a5 N KaOH solution containing 0.03* Kodak Wetting agent. For each batchetching was carried out for 4 hours, ecploying vigorous mechanical s t i r r -
/Ing, at a constant temperature of 40 i 0.05°C. For each batch,a freshly
11
MEASUREMENTS OF THE ISOTOPIC COMPOSITION OF
COSMIC-RAY NUCLEI WITH Z=10-14
G. A. Simpson, J . C. Kish, J . A. Lezniak and W. R. Wehber
Physics DepartmentUniversity of New Hampshire
Durham, N. H. 03824
We repor t here measurements of the i so topic composition of cosiaic-ray nuc l e i with Z=10-14 using a Cerenkov x t o t a l energy technique.These measurements- are for an energy in t e rva l from 40-120 MeV/nucwide at a typ ica l energy "\»500 MeV/nuc a t the top of the atmosphere.The mass reso lu t ion a var ies between 0.4 and 0.5 AMU in this chargerange. A t o t a l ^450 events are analyzed for t h e i r i so topic compo-s i t i o n . These s tudies ind ica te tha t the i so top ic composition ofthese elements a t the source must be very s i m i l a r to the knownsola r abundances.
Introduct ion. In t h i s paper we wish to report measurements concerned with theiso top ic composition of cosmic-ray n u c l e i with Z=10-14. The main in te res t ofi so top ic composition s tud ies of these charges i s to t ry to determine the com-posi t ion of the source nuc le i , p a r t i c u l a r l y Ne, Mg and S i , and to compare theobservations with the known so la r system abundances and with theories of nu-c leosynthes is . Some previous measurements ex i s t of the mean mass of cosmic-ray Ne, Mg and S i , b u t , as i s common in a new f i e l d , there are differences inr e s u l t s possibly r e l a t e d to the techniques of mass determinat ion. Maehl e.t at.(1975), using a Cerenkov-range method of isotope a n a l y s i s , have reported thepresence of a neut ron- r ich component of Ne with an observed mean mass of 20.8±0.1 AMU. This value requires tha t the cosmic-ray source contains more neu-t ron- r i ch Ne than i s observed in solar-system mate r ia l . Measurements of themean mass of these nuc l e i have also been made using the geomagnetic cut-offtechnique (Pe te r s , 1975). At 1.2 GeV/nuc Dwyer and Meyer (1977) find a meanmass of 20.43±0.10 AMU for Ne. This measurement i s cons i s t en t with a sourceabundance of Ne isotopes s imi lar to t h a t found in the s o l a r system. I t i s notc lear whether the d i f f e ren t conclusions reached in the d i f f e r en t types of ex-periments are r e l a t e d to the methods used—or to the fact t ha t the cut-offdata refers to a higher energy. A l i m i t a t i o n of a l l of t h i s e a r l i e r work i sthat only the mean mass of the ind iv idua l charges i s measured—no substant iveinformation is ava i l ab le on the abundance of isotopes of a given charge. Inthe resu l t s we repor t in this paper, the i so topic r e so lu t ion i s good enough sotha t meainngful data on the i so topic d i s t r i b u t i o n of Ne, Mg and Si nucle i can >be obtained. ;:.:
The Experiment. The same instrument i s used in these s t ud i e s as was used to .j."jobtain the mass distribution of Z=20-26 nuclei reported in a companion paper ';>.-at this conference (Simpson zt oJL., 1977). We refer the reader to the above B£paper for a drawing of the instrument and detai ls of the data analysis and :''iinclude in this paper only specific new deta i l s as they r e l a t e to the analysis ?f:of Z=10-14 nuclei . The data on which th is analysis i s based was obtained on ythree balloon f l igh ts in the summer of 1974. The to ta l col lect ion factor was <i8450 cm2-ster-sec and the average atmospheric depth was 2.8 g/cm2. -h
73
lsotopic analysis is achievedin this experiment by combiningmeasurements of:
1) the particle charge from the
3— x E and -3— * C counterdx dxcomb inat ions,
2) the particle velocity fromthe UVT Lucite Ceienkovcounter C, and
3) the kinetic energy as mea-sured in the thick scintil-lators El and E2 which bringthe particle to rest.
Q 1. Uaii KeAolwtion and ma&iAe.pcuicrfU.on dZagticum in the. Ce.ie.nkovand totat-e.neA.gy couiiteJU* &0H. Neand S-L nucZeJi.Although all particles that
stop in the total-energy countersand are above the Cerenkov threshold can be used in the C x E mode of analysis,the actual mass resolution is a strong function of energy which is maximizedover a fairly narrow band of energies. We illustrate this effect for Ne andSI nuclei in our telescope in Figure 1. This figure shows the expected massseparation in percent/AMU as a function of energy in both the C dimension andthe total E dimension, as predicted by a detailed calculation of each detec-tor's response. Also shown are the actual resolutions of the Cerenkov andtotal-energy counters.
This figure shows that: 1) The resolution in the El and E2 dimension issufficient to resolve adjacent isotopes in the Z=10-14 charge range. Theability to resolve these isotopes depends only weakly on charge or energy.2) In the C dimension the 1 a mass separation is greater than the 1 a resolu-tion over a band of energy ranging from ^60 MeV/nuc wide for He to 130 MeV/nucwide for Si. This optimum band of resolution corresponds to particles stop-ping in the E2 counter. For this reason we have utilized only E2 stoppingdata in this study. Because the E2 counter was more difficult to compensatethan El, the resolution of this counter was not as good as El, and in thiscase provided the limits on the mass resolution obtained. From the data inFigure 1 we estimate a mass resolution a = 0.4-0.6 AMU for charges withZ=10-14 provided the energy band of maximum resolution is chosen.
Aspects of the Data Analysis and Calibration. The rejection of nuclear inter-actions in the telescope is of great importance in this technique since theparticles are brought to rest and typically ^1/2 of them interact. In addi-tion the light output In the plastic scintillators and Cerenkov counter mustbe known accurately as a function of Z and 5 so that the location of the masslines may be put on any two-dimensional matrix of events. These proceduresare discussed in a separate paper on experimental techniques given at thisconference (Webber tit at., 1977) .
The Experimental Data. Prior to the mass analysis, it is first necessary to
classify events according to charge. A two-dimensional charge analysis tech-
nique (^ vs. E and -j— vs. C) is used, the results of which are shown for the
Z=9-16 range in Figure 2. Next a matrix o£ the Cerenkov versus total energyoutput is made for each charge for particles stopping in E2. This is thebasic matrix used for mass analysis, and an example for Mg nuclei is shown inFigure 3. The location of the mass lines on this matrix is based on the re-sponse functions derived from the fiducial data points.
79
We now construct a series of masshistograms by summing events in C-E2space perpendicular to the inferred massl ines for each charge. This data, forcharges with Z= 10-14 i s shown inTigure4.
The most effective way we havefound for presenting the data showingboth the charge and mass resolutionssimultaneously i s in the form of a Z-Aplot , which i s effectively a chart ofthenucl ides. On this plot each eventi s represented by a point at the chargeand mass assigned to i t with the chargeand'mass shown to the nearest 0.1 Z and0.2 AMU respectively. This plot for theZ=10-14 nuclei i s shown in Figure 5.
The mass histograms in Figure 4have been f i t by assuming Gaussian formsfor the individual isotope peaks by alinear least-squares f i t (with Poissonerrors) using the i s o -tope abundances as f i t t ing parameters. '
In this procedure the resolutiono of the isotope peaks i s varied, andthe location of the centroid of the massdistribution i s allowed to vary by ±0.2AMU from that predicted from the calibra-tion data. An appropriate number of i s o -topes is considered to be present foreach charge along with a "background."The "best" mass distributions for eachcharge are then taken to be those whichproduce a minimum x2- I n a H cases ex-cept Ne the absolute minimum x2 wasfound when the centering was within the .
. +0.2 AMU limits . A l i s t of parametersused in this f i t t ing procedure i s givenin Table I. From this table we see thatthe best a increases slowly with chargefrom 0.40 to 0.55 AMU. The goodness off i t to the distributions as evidenced bythe minimum x2 varies considerably fromcharge to charge. For Mg i t i s verygood, for Na, Al and Si acceptable, andfor Ne less good. The presence of "back-ground" events as determined by the curvef i t t ing program i s also a measure of thegoodness of f i t . The percentage- of"background" events generally followsquite closely the behavior of the mini-mum x2-
dE/di«CCdorgtVt*.
I •:K> 12 14 IB
d E / d « « E Clwrg« v to lue—••
Two-DimensionalCharge Assignment
9FI
•>. a'Ne
..No
,.Si
- 16
Ftgute 2. Ttoo-dimejt&lonal chaAQZ1=9-16 nuaLeA..
Cvmlov Choml Hxrtm-
1974 New Hampshire
Mognesium Obserwtiore
II Sl/SJ2) i
3. Ce.n.wkov vi. totaL-mtoiix ion. Mg nude*.
80
B 20 22 « 26 26 JO 32 M 36Atomic Moss —
2 _.
10
II
12
13
4
, I
Sodium J j - i „_
" Magiwfium ~
i •
Alu
Silii
iwmm
.on
-u-
IJ(jv
r
Mass HistogramaE2 Analysis
TK1 EM l
1
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I E M
•
19.74New Hampshire
Isotope Data
Mass—•-
Ftgu/ie 4. Mai-4 tf^^og/taJM: \-AjgfV\x. 5. Z-A p£ot2=10-14 nucZbi. 2=9-16 nucZ&L.
The mass distributions obtained for the minimum x f° r each charge aregiven in Table I I . These mass distributions are also given in percent of thetotal charge present. In the case of Ne we show the mass distribution ob-tained for the minimum x2 within the +0.2 AMU centering limits. The absoluteminimum x2 f ° r this charge is obtained with the centering displaced by ±0.45AMU. While we believe that this error is outside of that permitted by thecalibration data, we show in brackets in Table II the number of Ne isotopeevents predicted in this case.
The errors quoted are the total statistical errors for the best set ofparameters as determined in each case by the curve fitting program. Changingthe resolution and the centering of the isotope distributions within the lim-its imposed changes the number of events, but in. a l l cases,even for the ex-treme Ne situation, this change is less than the s tat is t ical uncertainties.
Table I
Parameters Used in I s o t o p i c Composition Calculat ion
harge
Ne*Ne
Na
Mg
Al
Si
Best a(AMU)
0.400.40
0.45
0.45
0.50
0.55
Best Centering
+0.20+0.48
-O.20
+0.11
-0.15
+0.15
AMUAMU
AMU -
AMU
AMU
AMU
Background(% of t o t a l events)
1613
18
.2
\6 •
7
Min. x2
27.320.6
10.55
13.31
19.18
Degrees ofFreedom
99
4
15
9
12
81
T.-ililn I IIsotopic Abundance:. <••. ;!=]0-14 Nuclei and
A Comparison t'iiti Predictions
At 3 g/cm* Propagation (Solar)Isotope ( of Events \ of Charge Atra. Depth 1 - 6 g/cm2 Source
" N e 33 (39) 63 .5114.3 68.9 70.6 89.210 (6) 19.2115.4 11.4 10.2 < 0 .1
9 (7) 1720
2871
.3115.
.6410.
.6126.
.4123.
814
58
1920
693
.7
.51
.2
.8
19.20.
100
146.
1020
ion
,B.22
-615
22.7140.14 22.94 23.66 23.0023Hf. 9 5.4 14.5 0.4 -2 ' 'ME 97 57.6 ±9.2 69.1 69.8 78.6"H E 36 2J.4 ±6.0 15.1 14.8 10.126Hg 26 IS.4 ±6.3 ]5J> 15^4 11.3
24.4510.05 24.50 24.45 24.33
• 26A1 7 20.5114.1 12.4 (2.2) 11.3 (0)27A1 27 79.5122.3 87.ft (97.8) 88.7 100
26.7910.09 26.88 26.89 27.002 7Si 15 14.4112.2 0.3z 8 Si 70 67.3119.5 84.4 85.8 92.2J 9 Si 19 JB.4113.5 B.3 7.9 4.73"Si 0 . Q t 6.6 7JJ 6^3 3.1
28.0610.OB 28.22 28.20 28.11
Comparison of Data with Predicted Abundances. We proceed in this comparisonby first considering only the relative isotopic abundance of each charge sepa-rately. As we have shown in the paper by Simpson e-t a£-> 1977, the instru-mental nuclear interaction corrections for isotopes of the same charge aresmall—only neutron stripping reactions can affect these fractions consider-ably, and our calculations show that these effects are much smaller than theerrors on the data. The isotopic abundances also refer to slightly differentenergy intervals and interval widths, but these effects are again small com-. pared with the statistical error. The data in Table II can therefore be" takento be the isotopic abundance measured at the atmospheric depth of 3 g/cm2 atan energy OO MeV/nuc. . .
The extrapolation of the cosmic-ray source abundance, to that expe.cted atan atmospheric depth of 3 g/cm2 follows well-established procedures. We con-sider an initial source isotopic distribution, comparable to that observed for 'solar material (Cameron, 1973). The model used for cosmic-ray transport inthe galaxy is the "leaky box" model (Cowsik, 1965) which leads to an exponen-tial distribution, of lifetimes or material path lengths in the interstellarmedium. Charge composition data have established that the mean path length is*v<6 g/cm2 of hydrogen for energies <1 GeV/nuc. We integrate stepwise the cos-mic-ray transport equation including fragmentation, energy loss and radio-nuclide decay at each step. Proton-nucleus Cross sections bjised on experi-mental data are used where possible—otherwise the scmi-empiric3l formula of.Silberberg and Tsao (19.73) is used. To obtain the partial cross sections forthe atmosphere we multiply these by the target factors presented by LindstromeX at., 1975. For total reaction cross sections we use the formula of Meyer-'tt at., 1975.
The isotopic fractions calculated at 600 MeV/nuc are shown at the bound-,ary of the heliosphere after propagation through 6 g/cm2 of interstellar hy- 'drogen in column 5 of Table II. Solarr modulation effects will cause slightchanges in these ratios due to the different charge-to-mass ratios of the iso-topes (not significant in this case) and will also contribute to an averageinterplanetary energy loss "H00 MeV/nuc. The further propagation through «v3
82
g/em2 o£_ atmosphere is shown in column 4. We believe that a meaningful com>-parison can be made between our data and these predicted isotope fractions at3 g/cm2. By following the growth of the various secondary isotopes at eachstep of the propagation (e.g., columns 4 and 5), one can visualize the effectsof taking a different source distribution.
Th« following represents a charge-by-charge summary of our results:1) Ne contains a primary isotope 2DNe but also shows the presence of
heavier isotopes with fractions consistent with those predicted for a solarsource. The mean mass of Ne is 20.64+0.14 AMU.
2) Na shows a marginal evidence for the presence of 22Na. This wouldonly be a very, small constituent of cosmic rays, and this measurement reallyreflects the limited stat is t ics for this charge. The mean mass of Na is 22.71±0.14 AMU.
3) The isotopic composition we observe for Mg is the most well-definedof al l charges. The distribution is in very good agreement with a solar,source distribution of material. The mean mass of Mg is 24.45±O-.O5 AMU.
4) Al is dominated by the isotope 27A1 with 2°A1 present in only a mar-ginally significant abundance. The combination of limited statistics and res-olution do not allow us to make a statement regarding the decay of 26A1. Themean mass of Al is 26.79±0.09 AMU.
5) Si is dominated by the isotope 28Si. A small amount of 27Si and29Si are .observed, but 27Si is unstable and would not be expected in the cos-mic-ray beam,and the presence of both of these odd isotopes is probably againsimply a result of our resolution, which for Si is now greater than that ne-cessary to resolve adjacent isotopes. Some 29Si and 30Si should be presentin the cosmic-ray beam—we see no evidence of 30S'i, but the s tat is t ical errorsare such that this result is not inconsistent with a solar source abundance.The mean mass of Si is 28.06±0.08 AMU.
Our overall result is that the isotopic composition of Ne, Mg and Si areconsistent with a solar-system composition for the cosmic-ray source—whetherindividual isotopes are considered or in terms of the expected mean masses.Although our data is limited in both s tat is t ical accuracy and resolution, i trepresents the f i rs t significant attempt to study individually the isotopiccomposition of .these nuclei. I t clearly demonstrates the value of being ableto individually resolve isotopes. Further improvements in resolution -are nowneeded to examine in more detail the isotopic composition of these nuclei atthe cosmic—ray sources and to further understand the composition of nucleisuch as Al, which include comparable source and fragmentation components.
Acknowledgments: This work was supported by NASA under grant NGR-30-002-052and by NSF under grant NSF GP 39475.
R e f e r e n c e s
Cameron, A. G. W. , 1973,- Space S c i e n c e R e v i e w s , J ^ , 1 2 1 .Cows I k , R . , P a l , Yasli , Tandon, S . N . , and Verma, R. P . , 1 9 6 5 , P h y s . R e v . , 1 5 8 ,
1 2 3 8 .IKfyer, R . , and K e y e r , P . , 1 9 7 7 , P h y s . Rev. L e t t e r s ( In p r e s s ) .LIndstrom, P . J . , Greener , D. E . , Heckman, U. I I . , Cork, B.<, and B u s e r , F. S . ,
1 9 7 5 , P r e p r i n t , C . B . I , . , 3 6 5 0 .Maehl , R . C . , F i s c h e r , A. J . , H o g e n , F . A . , ond Ormes, J . F . , 1 9 7 5 , Ap. J . ,
2 0 2 , L119 . IMeyer, J. P . , Casse, M., and Hescergaard, N . , 1975, Proc. 13th I n t . Cosmic Ray
Conf., 12_» 4144.Peters , B. , 1974, Hue. InsL. & Methods, Ul_, 205.Sllbcrbcrg, R. , and Tsao, C. H. , 1973, Ap. J. Suppl . , 25_, 315.Simpson, G. A . , Ktsh, J . , Lcznlalc, J . A . , and Webber, W. R. , 1977, paper OG-94
t h i s conference.Webber, W. R. , Simpson, C. A. , Lczniak, J. A. , and Klsli, J. C . , 1977, paper
-. 1-7 t h i s conference.
89
Transport of Cosmic Rays in Supernova
Remnants
G.E. Moffill (Max-Planck-Institut fur Kernphysik,.69Heidelberg, FRG) & M. Scholer (Max-Planck-Institutfilr Extraterrestrische Physik, 8046 Garching b. MUnchen,FRG)
I. Introduction
There is a large body of evidence in favour of eithersupernovae or pulsars being responsible for the produc-tion of cosmic rays (e.g. composition - Hainebach et al.f1976; gamma-ray observations - Stecker et al.r 1975;Kodaira, 1974; Seiradakis, 1976"; and energetics - Kuls-rud et al.f 1972). On the other hand, the big problemwith discrete but very powerful sources, which occur ata slow rate (one every 10 to 50 years), is the cosmicray dispersal from the source (Kulsrud and Pearce,' 1969;Wentzel, 1971 a, b) into a sufficiently large region ofinterstellar space without appreciable energy loss.
In this paper we address ourselves to two problems in aneffort to try to understand whether maybe the dispersalproblem can be reconciled with the favourable evidence,and we shall discuss:
1) general transport properties of energetic ions andelectrons in a supernova remnant (SNR) model - using aplausible SNR topology (Sedov, 1959) and an advanced mi-croscopic scattering theory (Morfill et al., 1976).
2) energy gains and losses of particles injected into aSNR from a central source (pulsar) up to the time peri-od when they escape from the SNR.
2. The Model
From a time period*^200 years (after SN explosion) to afew x 104 years the topology of a typical SNR may beapproximated adequately by the Sedov (1959) blast wavesolution (Kahn, 1975; Chevalier, 1974). Any cosmic rayproduced by a central pulsar during that time must passthrough this remnant if it is to escape into interstel-lar space. Thus the transport properties in the SNR maywell affect the energy spectra and composition of the•cosmic rays - one of the main reasons why we are interes-
90
ted in using a model which is as realistic as possible.Of course, the cosmic ray pressure from the, pulsar maymodify the topology of the inner part of the SNR, and wewill discuss this later.
For the shock speed, the post shock gas speed and theplasma density we use the similarity solution of Sedov(1959) given in parametric form by Kahn (1975). Weassume that the initial SN explosion, with its huge re-lease of electromagnetic radiation, has ionised the sur-rounding interstellar medium fully and has excited waveson all wavelength scales. We assume further that allwave modes, except for Alfven waves, damp away quicklyand that - in keeping with our experiences in the so-lar system - the total wave energy density does not ex-ceed the energy density of the background field. The fre-quency distribution of the waves is chosen to be repre-sented by a Kolmogorov type power spectrum (see eg. Leeand Jokipii, 1976), with a correlation length given bythe scale size of observed irregularities using radiopolarisation data (Downs and Thompson, 1972, Scott andChevalier, 1975). For the strength of the background mag-netic field and its spatial variation we assume isotropiccompression and the frozen-in field condition, whichgives the relative (spatial) field strength variation.The absolute field strength is kept as a variable para-meter, since field enhancements in the early phase (be-fore the Sedov solution is applicable) can occur (Kahn,1975) and observations seem to support enhancements of afactor 100 to 300 (Cowie, 1975) over thi normal inter-stellar field, although this may vary from case to case.
The region of application of this model, if the centralregion is distorted by cosmic ray emission from a pulsar(which emits a relativistic "wind") is determined asfollows: Outside the pulsar magnetosphere the emitted re-lativistic particles (Ostriker and Gunn, 1969; Havnes,1971) are the energetically most important constituent,and expand freely into a near vacuum (a bubble "blown"into the SNR by the initial energetic particle emissionfrom the pulsar)"carrying magnetic field with then in amanner similar to the solar wind. Although the free ex-pansion reduces the random part of the particle energy,the particles nevertheless retain nearly all their ori-ginal energy in the directed outward flow. The two im-portant questions, which have to be answered (and whichare closely linked) are: What happens at t;he interactionboundary with the SNR plasma? and: Where is this bound'arylocated? Clearly, if pulsars are to be the dominant sour-ces of cosmic rays and if acceleration in the SNR can be
91
ruled out, most of the energetic particles must get outof their "bubble" and escape without too much energy lossinto the SNR. This means that "escape", ie. transportacross the interaction boundary, must in the majority ofcases occur as soon as a cosmic ray reaches this bounda-ry, since otherwise it would randomise its directed flowenergy and quickly become adiabatically deceleratedwhilst doing work against the SNR gas.
'i
We have estimated that random curvature and gradientdrifts (which may even be caused by' selfgenerated waves- velocity space instabilities generated by the small re- \fleeted fraction of cosmic rays) form efficient processes !for transporting energetic particles rapidly across tan- \gential discontinuities. Field line merging, if it takes *place, will make the interaction boundary even more "lea-ky" to energetic particles.
In such a situation, the region of influence of the pul-sar is bounded approximately by a sphere of radius r onthe surface of which the cosmic ray pressure (due to allthe cosmic rays emitted at time t - | after the SN explo-sion) equals the energy density of the &NR backgroundplasma - if it had not been distorted. It turns out thatour transport calculations (single particle motion in aSedov-type SNR) should be applicable as long as = £, 0.4,where R is the radius of the SNR. shock front. s
Clearly, a continuous slow injection of cosmic rays froma pulsar which is,gradually spinning down (over a period f-of /v 104 years) eises the dispersal problem mentionedearlier considerably, as long as the cosmic ray trans-port in the SNR allows particle escape.
3. Wave-particle interaction in SNR's
In order to determine the transport coefficients in theSNR, both in co-ordinate space and momentum space, wehave to find a reliable microscopic theory of particleinteraction with the background medium. We have alreadyshown that our model, as described in section 2, isapplicable for = Jt 0.4, ie. in over 90 % of the SNR,and that the energetic particles emitted by the pulsarenter this region essentially without modification asregards their source properties. Thus it is very impor-tant to use a realistic and, if possible, experimentallyverified microscopic theory of energetic (test) particleinteraction with a turbulent magneto-active plasma. Themost comprehensive theory, which is suitable for the case
92
under study (wave-particle interaction with Alfven wavesin a turbulent medium where turbulence exists on allwavelength scales), has been described by Morfill et al.,1976. This incorporates, in addition to the standardquasilinear theory (Jokipii, 1966, 1971, Hasselmann andWibberenz, 1968, V61k et al., 1974) and its nonlinearcorrection (Jones et al., 1973, V51k, 1975) also an ave-rage over medium scale nonresonant irrecularities in themagnetic field. For our particular application we use asimplified expresion (Morfill, 1975) for the diffusioncoefficient in momentum space, which is applicable whenwe assume (quite reasonably) that the wave vector dis-tribution of the (resonant) Alfven waves is isotropic inthe frame of reference moving with the plasma. The re-sulting medium scale averaged spatial diffusion coeffi-cient < / ^ is then assumed to be isotropic (Calculationsonly yield the coefficient parallel to the homogenousbackground field J^ , and the isotropy assumption for<X>implies that turbulence is so large, even on long andmedium wavelength scales, that the field is not orderedand can be regarded as almost stochastic).
The assumption of wave-vector isotropy implies that par-ticles in the SNR not only loose energy by adiabatic de-celeration and synchrotron losses, but may also gainenergy by second order Fermi acceleration. With our mo-del it was possible to calculate the time scales
J. m J
for the above processes, and"the determination of all \these transport coefficients allows, in principle at i:least, a determination, of the evolution of the cosmic ;ray distribution function f (r, p_, t) in the SNR. How-ever, it is a very difficult task, to obtain a (numeri-cal) solution of the full Fokker-Planck equation, incor-porating sources, losses and spatial as well as energydiffusion, and we have instead solved the energy equation
-L <££ L _ JL +±E <A* ~ r ^ trsy • t>
where for protons//^jcan be ignored. This yieldsfor given injection time to after the SN explosion andinjection energy Bo • In order to find the energy of theparticle when it leaves the SNR, we utilise the factthat our calculations show that the r-dependence ofis small, and that the transport of the particles incoordinate space is mainly diffusive (ie. ignore convec-tion in the expanding SNR). We then have
where E (E o , t o , t ' ) i s g iven by the£ s o l u t i o n of the
93
energy equation. For given Eo, to we can thus determinethe time of escape from the SNR, t, and the energy E(Eo# tOf t) which the particle has when it escapes.
4. Results
Figs. 1 to 4 sftow a.few examples (of many) of the resultsobtained from our model, which — and this point has tobe stressed'- has not been taylored to mathematical con-venience, but^instead has incorporated in it only thosephysical considerations which we have regarded as ir.ostreasonable, based on astronomical and near Earth measure-ments .
io-5
10"'
10"5
llf*
151
•
FERMI REGIME
ADIABATICREGIME
i j , , - S.0Q0 y
/
/
_
DIFFUSIVE :
- — ^ REGIME \
/ -
/
10™R [v]
Fig. 1: Regions of dominant "energytransport for protons in the SNRmodel described in the text plottedover a range of magnetic field strength(Bo) and particle Rigidity (R).
94
10'10' ID*
Fig, 2; Same asFig. 1 _exceptfor electrons.
Leaving the absolute value of the background magneticfield as a variable parameter (as was mentioned earlier)we have plotted in Figs. 1 and 2 different regimes inBo~R (rigidity) space for protons and electrons, respec-tively. The boundaries between the regimes (drawn herefor a SN age of 5000 years) are given by equality oftime constants (where 'tkrff s ^ /<>£> ) . As can beseen, low rigidity and high field strength (and thushigh wave activity) favours Fermi acceleration, mediumrigidity and low field strength yields adiabatic- dece-leration as the most important transport in energy space,and at high rigidities particles diffuse too fast foradiabatic deceleration to be appreciable. For electrons,high field strength and high rigidity yields an additio-nal regime dominated by synchrotron losses.
Fig. 3 shows the solution of the energy equation. Curvesof E (EQ, to, fc) have been drawn for different Eo, allparticles injected into the SNR at to = 100 years. Ascan be seen, adiabatic deceleration is important in theyoung SNR (age less than a few x 10^ years), to be re-placed by Fermi acceleration when the SNR is older. After"" 105 years we assume that the SNR has broken up ar. 'dispersed so much that.the cosmic rays can escape freelyinto interstellar space - in fact the SNR is then vir-tually indistinguishable from interstellar space.
95
Fig. 3
Time [ y 1
Fig. 4Fig. 4 shows the solution of the last equation, ie. thedetermination of the trapping time of cosmic rays in theSNR. As can be seen, the trapping time is strongly depen-dent on B o for energies below a few x 104 MeV. This isdue to the fact that Fermi acceleration becomes impor-tant earlier in the evolution of the SNR if B o is larger,and this allows more energy gain by the lower energy (Eo)particles and thus a faster escape. At very high energiesthe curve in Fig. 4 should go over into the rectlineartravel time &s /c , however no attempt has been madeto incorporate this limit here.
s *
5. Discussion
We have attempted here, to give as "physical" a descrip-tion of energetic particle transport in SNR1s as possible.In so doing we have shown that pulsars as cosmic raysources may well be feasible if they emit particles overa few x 1O^ years, especially since the trapping time inthe SNR can be large for particles with initial energyE o g few x. 1O4 MeV. Our model also shows that secondorder Fermi acceleration is not negligible in SNR's.
96
In order to evaluate our model fully, and produce thelink from the source (pulsar?) to the product (cosmicrays?) we would need to calculate the distribution func-tion, averaged over the "life time" of the SNR, somethingwhich so far we have not yet done. In addition, theeffect of varying EQ must be investigated more closely,since the measured cosmic rays probably represent par-ticles coming from a whole ensemble of sources. Infor-mation on the spectral form of cosmic rays at low energymight well yield important clues about the cosmic ray .sources, if our calculations describe the transport pro- \cesses in the source regions reasonably well. *
There is one far• or v'-ich so far we have not considered \(because it relates to particle acceleration outside the |3NR) and that is Fermi^acceleration by repeated reflec-tions at the SN shock. 'The fact that such processes dooccur (in interplanetary space) has been demonstrated byScholer and Morfill (197 5) and there is no reason tosuppose that an additional modification of the sourcespectrum due to this effect can be ruled out here. Brief-ly the process works as follows: Cosmic rays arescattered by waves in the interstellar medium until theyare overtaken by the shock. Magnetostatic reflectioncoupled with the resulting energy gain (Fermi accelera-tion) can give an appreciable effect, provided that eachcosmic ray particle can stay near the shock long enoughto be reflected many times. In interplanetary space- Scho-ler and Morfill (1975) considered "upstream" scattering 5.to be parasitic (ie. feeding off existing waves), where- ias in the case considered here, the waves would probably I.;have to be generated by the cosmic rays themselves. Thisthey could do in the early phase of the SN, when par-ticle fluxes are higher, and the very instability whichhinders dispersion ir.ay then be responsible for allowingparticles to take energy from the strong early SN shock.
REFERENCES:
Kahn, F.D., Proceedings of 14th Cos.Say Conf., Miinchen,3566, 1975Kulsrud, R.M. and Pearce, Ap. J. 156. 445, 1969Kulsrud, R.M., Ostriker, J.P. and Gunn, J.E., Phys.Rev.Lett. 28, 636., 1972Lee, L.C. and Jokipii, J.R., Ap. J. 206, 735, 1976Cowie, L.L., Mon.Not.R. astr. Soc. 173, 429, 1975I-Zainebach, K.L., Norman. F.. R- and schramm, D.M., ftp.j.103, 245, 1976Stecker, F.W., Solomon, .P.M., Scoville, N.Z. amd Ryr.er..
97
C E . , Ap.J. 201, 90, 1975Kodaira, K., Publ. Astr. SOG. Japan 26, 255, 1974Seiradakis, J., Proceedings of Int.Symp. on Structureand content of the Galaxy and Galactic Gamma Rays, GSFCx-662-76-154, 299 1976Wentzel, D. , Ap.J. 163, 503, 1971aWentzel, D. , Ap.J. 170, 53, 1971bMorfill, G.E., J. Geophys. Res. 80, 1783, 1975Morfill, G.E., Volk, H.J. and Lee, M.A., J. Geophys.Res.81, 5841, 1976Sedov, L.I., Similarity and Dimensional Methods in Me-chanics (Chapter 4) Cleaver Hume Press, London, 1959Chevalier, R.A., Ap.J. 188, 501, 1974Scotc, J.S. and Chevalier, R.A.,, Ap.J. 197, L5, 1975Downs, G.S. and Thompson, A.R., A.J. 77, 120, 1972lavnes, 0., Astron-and Astrdphys. 13, 52, 1971Ostriker, J:P. and Gunn, J.E., Ap.J. 157, 1395, 1969Jokipii, J.R., Ap.J. 146,. 480, 1966Jokipii, J.R., Rev. Geophys. Space Phys. 9, 27, 1971Hasselmann, K., and VJibberenz, G., Z. Geophys. 34, 353,1968Volk, H.J., Morfill, G.E., Alpers, W., and Lee, M.A.,Astrophys. Space Sei. 26, 403, 1974Volk, H.J., Rev. Geophys. Space Phys. 13, 547, 1975Jones, F.C., Kaiser, T.B. and Birmingham, T.J., Phys.Rev.Lett. 31, 485, 1973.Scholar, M., and Morfill, G.E., Solar Phys. 45, 227, 1975
98
44CROSS SECTIONS FOR SPALLATION PRODUCTION OF Ti : APPLICATION TO
DETERMINING COSMIC RAY ACCELERATION TIME
G.'M". Raisbeck and F. Yiou
Laboratoire Ren£ Bernas du C.S.N.S.M., 91406 ORSAY, France.
t' 44Experimental cross sections for spallation production of Tiin targets of Fe and Ni have been measured with protons of 0.6to 25 GeV and alpha particles of 0.6 to 4.6 GeV. Propagationcalculations using these and electron attachment cross sectionsdeduced from recent measurements are presented. The resultsare discussed in connection with the suggested use of thisnuclide for determining the time between cosmic ray nucleo-synthesis and acceleration.
44Shapiro and Silberberg (1) have suggested that the isotope " Ti could be
used as a probe of the time between nucleosynthesis of cosmic rays and theiracceleration. This suggestion follows from the idea of CassS (2) and CassS andSoutoul (3) regarding the similar use of other pure electron capture isotopes,such as -*°Ni, °Ni and "co. The general principle of this idea is that cosmicray isotopes which are synthesized as pure electron capture progenitors, willonly decay if they have spent a time longer than their normal half-lives at re-latively low energies where they are not fully stripped. The advantage of'44Tiis that its half-life (47 years) extends considerably the range of- delay timesthat can be examined. For example, as discussed by Hainebach et al."r(4), this isjust the order of delay that one might expect between a supernova" explosion andsome models of cosmic ray acceleration. Nevertheless., there are several difficul-ties with the possible use of 44Ti, and it is these aspects that we wish toexamine quantitatively here.
44First, in addition to the " primary " Ti (which is presumed to be the
progenitor of 44Ca) there will be a substantial quantity of secondary 44Tiproduced by spallation during propagation. On the basis of semi-empirical crosssections, Shapiro and Silberberg have estimated this spallation 44Ti as aboutequal to the " primary " 44Ti, assuming the latter has not decayed. Since thereare uncertainties associated with such semi-empirical predictions, which occa-sionally may be in error as much as a factor of two, it is clear that an ex-perimental determination of the principal production cross sections is essentialin order that reliable corrections can be made for this secondary 44Ti. To thisend, we have determined the production cross sections for 44Ti from Fe and Niwith 0.6, 1.0, 2.0, 3.0 and 23 GeV protons, and 0.6, 1.2, 2.8 and 4.6 GeV alphaparticles. The measurements were made by direct y counting of the irradiatedtargets with a calibrated Ge(Li) detector, as described in detail elsewhere' (5).The only difference between the present work and that described is that,because of the long half-life and small cross section of 44Ti, it was necessaryto wait (a minimum of 6 months) until most of the shorter lived activities haddecayed away, before the 44Ti could be reliably counted. The 44Ti itself decaysby pure electron capture, accompanied by 2 very low energy y rays (68 and 78keV). However, these are in an energy region where Compton effects are verysevere, and where efficiency calibration of a Ge(Li) detector is rather dif-ficult. We have therefore chosen to use the 1.157 MeV y ray from the 44Scdaughter nuclide, which has a half-life of 3.9 hours, and therefore quicklycomes into radioactive equilibrium with the Ti. Count rates were very low(less than 1 cpm) and even after the extended " cooling " period backgroundeffects important, so that long counting times (several days) were necessary toreduce the counting errors to acceptable levels.
99
Preliminary results (some of the data are still being analyzed) for theproton cross sections in Fe are given in Table I, along with predictionscalculated- from the semi-empirical formula* of ref. (6). At high energies thedifferences are of the order of 30 %, which is rather typical in this regionof the periodic table.
Using the experimental cross sections for Fe, we have carried out propa-gation calculations either setting all other 44Ti production cross sections tozero, or by letting them have the values based on the Silberberg-Tsao predic-tions. In this way we estimate that Pe contributes about 45 ft of the total *^production in the energy region above *\« 500 MeV. Amongst the other reactions,by far the most important, especial-ly at lower energies, are expected to befrom 4^Ti and 4^Ti. Thus a more accurate estimate of the secondary productionwill require measurements of 4 4Ti in these targets, plus cross sections for the^ T i and ^ T i themselves from Fe. For the moment, however, we proceed on thebasis of the above estimates.
A second important drawback of Ti is that, unlike Ni or Co, Tidoes not represent an appreciable fraction of the total cosmic ray yield of thecorresponding element. Thus, an iaotopic determination of the cosmic ray Tiis absolutely necessary before its potential as a " chronometer " can berealized. Unfortunately, at the energies where present techniques for isotopicseparation seem most promising (< 500 MeV/n), it is necessary to consideranother effect - the possibility of electron capture isotopes picking up elec-trons and decaying during propagation (7). Thus we have also included thiseffect in our propagation calculations. The electron pickjp and loss crosssections were calculated in the manner indicated previous.!./ (8). The essentialcorrectness of this approach has been recently confirmed experimentally, asdiscussed in another paper at this conference (OG-132).
44The final results are shown in Fig. 1, where we show the ratio Ti/Fe,
both with and without decay of " primary " 44Ti at the source (and making thesame assumption as Shapiro and Silberberg - i.e., that this source abundanceis given by the " universal " 44Ca/Fe ratio = 1.46 x 10~3 (9) ). An example ofa " typical " modulation effect is also indicated in Fig. 1.
44The first thing that is evident is the very small quantity of Ti (about
100 tines smaller than expected for non-decayed *°Be ! ) . Also since the amountof calculated 4 4Ti at low energies (< 500 MeV/n) is dependent on a number ofmodel dependent factors (such as the assumed density of the propagation mediumand the amount of solar modulation), it is clear that only at higher energiescan it be unambiguously used as a probe of acceleration time. It is thus likelythat such a use will have to await considerable improvements in cosmic raydetection techniques. It is also evident that the conclusions that can bedrawn depending on whether a " primary " component of 4 4Ti is observed or notare not of equal weight. The absence of 44Ti could indicate its decay at thesource or_ simply that less 44Ti was formed in this way than suggested by the" universal " 4 4Ca abundance. Positive observation of an excess 44Ti comparedto that calculated for spallation would, on the other hand, appear to be fairlysolid evidence for a relatively short (< 47 years) delay between synthesisand acceleration.
Finally, there is perhaps one small encouraging point that should bementioned. Since 45<ri is unstable, it is not necessary to have ] mass unitresolution in order to separate 4 4Ti from the remaining Ti isotopes. As has
100
7been observed for some time with Be, such an advantage can be considerable.
References
1 - H.H. Shapiro and R. Silberberg, 14 Int. Cosmic Say Conf., Munich (1975),vol. 2, p. 538.
2 - H. CassS, J.3th at. Cosmic Ray Conf., Denver (1973), vol. 1, p. 546.3 - M. Casse and A. Soutoul, Ap.J. Lett. 20£, L 75 (1975).4 - K.L. Hainebach, E.-B. Noraan and D.N. Schraatt, Ap.J. 2O3_, 245 (1976).5 - G.M. Raisbeck and F. Yiou, Phys. Rev. C UJ, 915 (1975).6 - R. Silberbefg and C.H^Taao, Ap.J. Suppl. 25_, 31S (1973).7 - G.M. Raisbeck, -G. Comstock, C. Perron and P. Yiou, 14th Int. Cosmic Ray
-• Corif., Munich. {1975), vol. 2, p. 560.8 - G.M. Raisbeck^. proceedings of the 2 n d High Energy Heavy Ion Summer Study,
Lawrence Berkeley'Laboratory, Berkeley, Calif., July (1974).9 - A.G.W. Cameron, Space Sci. Rev. 5_, 121 (1973).10 - I.H. Urch and L.J. Gleeson, Astrophys and Space Sci. \T_, 426 (1972).
4 4 TABLE 1Cross sections for Ti production in- targets of Fe bombarded with high energy
protons
E (GeV)
0.6
1.0
2.0
3.0
23
0 44Ti exp(mb)
0.96 + .17
1.15 + .18
0.78 + .13
0.75 + .12
0.73 + .09
a 44Ti calc(mb)
.92
1.07
1.00
.98
.98
Calc/exp.
.96
.93
1.28
1.31
1.34
101
44 Ti/Fe
0.004
0.003
0.002
0.001
OG.142
At « 47 yr.
200 600 1000 1400Energy (MeV)
FIGURE 1
44 44Calculated Ti/Fe ratio in cosmic rays with " primary " Ti decayed(At » 47 yr.) or not decayed (At « 47 yr.). Dashed lines are an exampleof the possible effect of solar modulation aa calculated with the parametersof Urch and Gleeson (10) for 1970.
102
SOME THOUGHTS ON THE MUSALA ANISOTROFY;
PITCH ANGLE DISTRIBUTION OR WHAT ELSE?
J. Kota and A.J. Somogyi
Central Research Institute of Physics, Budapest, Hungary
Based on the results obtained in the Musaia exper-
iment and in other anisotropy measurements, an attempt
is made to explore the three-dimensional structure of11 14
cosmic ray anisotropy in the 10 -10 eV range.
/i/ It is investigated whether observations can be
reconciled with a pitch angle distribution.
/ii/ Assuming that the principal axes of the tensor
anisotropy are known, the vector and tensor anisotropies
are separated.
Diseussed are the theoretical implications of the
results obtained and possible origins of the second
harmonic.
1. Introduction. In the recent years sevt ral measuremante
have found evidence for galactic cosmic ray anisotropy in the
10 -10 eV energy region. Among these th.: Musaia /Gombosi et
al 1975, 1977/ and Mt. Norik^ra /Nagashima et al, 1977/ ex-
periments show the presence of a second harmonic of the daily
variation, too. The most important implication of this is that
the three-dimensional atiisotropy cannot be described as a
simple drift but it should have a more complex structure. To
determine the three-dimensional anisotropy a set of measure-
ments would be needed at various geographical latitudes.
Further uncertainty arises from the difference of energies
in the Musaia, Poatina /Fenton and Penton, 1976/ and London
/Davies et al, 1977/ measurements. Although we have no reason
•to expect drastic changes, one should keep in mind that the
anisotropy is not necessarily constant through two orders
of magnitude of energy.
•In this work we try to draw some conclusion concerning the
three-dimensional anisotropy based on the limited experimental
evidences available.
103
2. Pitch angle distribution? Cosmic ray particles of ener-
gies below 10 eV are strongly tied to the few j* gauss galac-
tic magnetic field. They may perform several turns before be-
ing scattered thus it seems plausi"ble that a pitch angle dis-
tribution around the direction of the local magnetic field
should be resulted. Indeed, the Imperial College group /Davies
et al, 1977/ has found that, after making correction for the
apex motion of the solar system w.r.t. the local stars /b =25,
i, =44°/,their data are in good agreement with a pitch angle
distribution around the direction b =i>5°, I =75°.
In the case of a pitch angle distribution, the observed
sidereal variation should obviously be symmetric with respeot
to the R.A. of the pitch axis. Hence it immediately follows
that
/i/ all harmonics of the sidereal variation should have
extremum /maximum or minimum/ at "the R.A. value of the pitch
axis.
The restriction /i/ has the following consequences:
/ii/ At the maximum of the first harmonic all the other
harmonics of the sidereal variation have extremum.
/iii/ The phases of the first and second harmonics should
either coincide or differ with 6 hours.
/iv/ At different geographical latitudes the phases should
either coincide or be opposite for each harmonic.
Inspection of the phases of the first /2.5 11.0 hr after
apex correction/ and second /5.0 +0.8 hr/ harmonics obtained
at Musala shows inconsistency with th.e condition /iii/. The
results seem to be stringent enough so that the possibility
of a pitch angle distribution, although not entirely excluded,
can be considered as rather improbable.
Hagashima et al /1977/ has discussed the pitch angle model
in detail and pointed out that a good agreement with the pre-
diction of the pitch angle model can be achieved by applying
apex correction with respect to the interstellar gas /4.4 hr
instead of IT.9 hr/.
104
It should also be noted that the absence of significant
third and higher harmonics at the Musala exp&riment would not
necessarily involve that the whole angular distribution can
be described with first and second order terms only. Figure 1
shows the pitch angles /y / and w values //* =cosy / seen by
the Musala apparatus as a function of the declination of the
pitch axis. The Musala results mean that the distribution can
well be approximated with first and second order terms of M
in the region covered.
t _ _WO*
costX%*
\
\ \ y
i
i
\\
\N
s s.
\
y
-90* 90s -1SINf
Figure 1. Pitch angles If/ and cos^ values seen by
the Musala apparatus as a function of the declination
of the pitch axis /<T/. .A =42° represents the decli-
nation of Musala station.
3. Separation of Vector and tensor anisotropies. It has been
pointed out by Somogyi /1976/ that all components of the vec-
tor and tensor anisotropies /except for the vector component
parallel to the earth's axis/ can be determined even from one'
measurement under the following assumptions:
/i/ The anisotropy consists of vector and tensor artisotro-pies only.
/ii/ The principal axes of the tensor anisotropy point
along known directions.
• . To illustrate this method and its implications we shall
consider two plausible cases. In the first case we assume that
principal axes point along; the direction of the Spiral Arm
and toward the galactic North Pole. In the second case the
principal directions point toward the Galactic Centre and
toward the North Pole. The third of the principal axes is
perpendicular to the two others in both cases. The results
of calculations are summarized in Table 1.
p
b
0
0
90
. Axes11 I11
° 340°0 70°o
Case
Tensor com-
ponents
0.261+
-0.110 +
-0.151i
/I/
0
0
0
{%)
.103
.081
.069
Table
P.b 1 1
0°0°90°
1
Axes
I11
0°90°-
Tensor com-
ponents
0.204 1
-0.187 i
-0.017 1
Case / 2 /
10
i 0
t 0
{%)
.078
.114
.075
Inspection of Table 1 shows how sensitive the results are for
choosing different directions of the principal axes. In both
cases there is a two-way maximum from the direction of about
the Galactic Centre. In the first case there is a two-way mi-
nimum from the directions of the Galactic Poles which disap-
pears in the second case. It is interesting to note that the
equatorial components of the drift vector calculated in this
way /0.1981 0.108 %, 17.7±1.1 hr in the first case and.
0.228 10.117 %, 21.0 10.9 hr in the second case/ point along
directions strongly different from those estimated on the ba-
sis of the first harmonic only. The first case may be con-
sistent with a net flux of cosmic rays from the direction of
the Galactic Centre.
Most probably one 'of the principal axes of the tensor an-
isotropy should point along the local magnetic field. It may
be argued that the magnetic field direction need not be in
the Galactic Plane but higher galactic latitudes are equally
probable. At present, in the absence of information on the
local structure of galactic magnetic field, the calculations
presented in this section remain tentative. Nevertheless, it
is well demonstrated that the direction of the net cosmic ray
'•&•
106
flux should not be identified with that of the first harmonic
of sidereal daily variation;
4. Theoretical implications, origin of higher harmonics. In
a few gauss -galactic magnetic field the gyx-oradius of par-
ticles observed at Musala /*-6.10 ^eV/ is in tlie_ range of
0.01-0.1 pc which, most probable, is much less than the scat-
tering mean free path-. Thus the propagation of these particles
can be treated as pitch angle diffusion along the magnetic
field lines.
The Musala results raise the following questions:
/i/ What may cause deviation from pitch angle distribution?
What .is the structure of this deviation?
/'ii/ What kind of pitch angle distribution is expected
from the pitch angle diffusion? How can higher harmonics be.
produced?
4-.1. Deviation from pitch angle distribution, BxVy diffusion.
It is well known from diffusion theory that density gradient
in direction perpendicular to the magnetic field induces cos-
mic ray streaming perpendicular to both the magnetic field and
density gradient. The magnitude of the vertor-type anisotropy
arising in this way is of the order of
where R stands for the gyroradius, L is the cViaracteristic
length of the confining-voliime /half thickness of the disc or
radius of the spiral arm/ or, in the case when the contribu-
tion of a nearby source is dominant, it represents the dis-•
tance from this source.-The factor P /P<l/ takes into account
that the anisotropy reduces if the sun happens to be at a
central position with respect to the sources and the confining
volume. Similarly, two-way density gradients may produce ten-
sor-type anisotropy of the order of
^ 2 J * (R/L) 2
Taking L * lOOpc as a reasonable value, we conclude t'hat there
107
may appear a detectable vector-bype anisotropy perpendicular
to the magnetic field but the appearance of higher harmonics
cannot be explained in this way. In other words, we expect
the galactic angular distribution to :•• a \ • . .. angle distri
bution with a possible additional perpendicular drift super-
imposed.
4.2. Pitch angle diffusion, higher harmonics. Particle pro-
pagation is governed by the diffusion equation
__ ^ ^f =i_3_ D 3fa t 7 " a t " ~2 ^t 3yM £ 3 * /•/• 3*<
where f () is the distribution function, v is the particle
velocity, D.... stands for the diffusion coefficient. 3/31
represents derivation along the magnetic field line. The last
term of the left hand side of Eq.l accounts for adiabatic
focusing in the presence of diverging magnetic field lines.
The diffusion equation /I/ has been studied by Earl /1975/ in
detail. Prom his work it can be seen that, in general, the an-
isotropy cannot be described with an anisotropy vector only.
The anisotropy is vector-type only in the most simplified case,
namely if scattering is isotropic /D «: 1-u / and the field
lines are not diverging. Here we consider some simple classes.
/i/ Constant magnetic field strength. In the absence of
adiabatic focusing, the steady-state, near isotropic solution
of /I/- approximately is . A
where f stands for the omnidirectional density averaged over
pitch angles. Inspection of relation /2/ shows that f is an
odd function Qf p thus the three-dimensional aniso.tropy has
no second but third harmonic. This, of course, may appear as
secon . .»*rmonic in daily intensity variation.
/:;, V-.otropic scattering, weakly diverging field lines.
The field is meant to be diverging weakly if >-91nB/at < 1,
~X being the mean free path. In this case an expansion can be
108
made in terms ,0/ Legendre polynomials yielding /Kota, 1975/
f = f0 + yufn + CM2- *Vfo + ...
with
f 1 w — «X- rr-r- and
It can be shown that f,, fp, ... form a sequence of decreas-
ing values thus higher harmonics should decrease in amplitude. ?
/iii/ Strongly diverging field lines. If the scale in which |
the magnetic field strength changes considerably is much less *
than the mean free path /i.e. >• (31nB/3t) 2> 1/ then particle
propagation becomes adiabatic. The value of f( «) will depend
on the adiabatic invariant (!-*• )/B only. In this case, f is
an even function ofyu and again second harmonic can be gene-
rated.
The real physical case may not belong to any of these pure,
simplified classes but adiabatic focusing and anisotropic
. scattering may act simultaneously. The considerations pre-
sented above show, however, that higher harmonics may arise
in a natural way from pitch angle diffusion.
References;
Davies,S.T. et al 1977, This Conference, 4_, 105.
Earl,- J.A. 1975, Conf. Papers, 14th ICRC, Munich, 5, 1733
Fenton, A.G. and Fenton, K.B. 1976, Proc. 2nd Cosmic Ray
Symp. in Japan, Tokyo, 313.
Gombosi, T. et al 1975, Conf. Papers, 14th ICRC, Munich, 2, 586.
1977, This Conference, Paper OG-154
Kota, J. 1975, J. Phys. A, 8, No.8, 1349.
Somogyi, A.J..1976, Proc. 2nd Cosmic Ray Symp. in Japan,
Tokyo, 142.
Nagashima, K. et al 1977, This Conference, 2_, 154.
109
FURTHER EVIDENCES OP THE ANISOTROPY
OBSERVED AT MUSALA STATION
T. Gombosi, J. Kota, A.J. Somogyi, A. Varga
Central Research Institute of Physics, Budapest, Hungary
B. Betev, L. Katsarski, S. Kavlakov, I. Khirov
Institute of Nuclear Research and Nuclear Energy
Sofia, Bulgaria
Recent developments of the Musala anisotropy experi-
ment are presented. A high-resolution analysis carried
out at period lengths adjacent to one sidereal day
shows rapidly diminishing amplitudes and significance
levels on both sides of the period length of. one side-
real day. This confirmes that the observed intensity
variati(
origin.
variation of *vr6.10 eV cosmic rays is of galactic
At the Munich Conference the Budapest-Sofia groups reported
on detecting a galactic anisotropy of /v6.10 eV cosmic rays
/Gombosi et al, 1975a, 1975b/. We recall that three-hourly
counting rates of the Musala small extensive air shower appa-
ratus collected during the four years of observation were ana-
lysed by applying multiple Fourier and simultaneous regression
analysis. Taken into account were the first and second har-
monics of sidereal, solar and antisidereal daily variations,
meteorological effects and linear trends in the counting re-
sponse. Both the solar and antisidereal waves remained below
or at about noise level while the following first and second
harmonics of sidereal variation were found:
amplitude (%) phase (hr)
1st 0.075 ±0.021 1.7 ±1.1
2nd 0.055 ±0.021 5.0t0.8
At this stage some remarks should be mad-e concerning the
110
errors given. It is noted that the present errors are {IF
times less than those quoted in Munich /Gombosi et al 1975b/.
What we gave there was the square root of the variance of the
amplitude square, what we give here is the square -root of the
variance of a single Fourier coefficient. Both-values have
been calculated on the basis of the residual empirical fluc-
tuation of the measured data, i.e. not on the basis of an
assumed Poissonian distribution. We changed to the latter
value, i.e. the error of a single Fourier-coefficient, since
this is generally used to indicate the error of the amplitude
/Chapman^ Bartels,1946/. As to the significance of the re-
sults, 1-p, where p denotes'the probability of observing an
amplitude higher than what was observed if the genuine ampli-
tude is zero, this has to be calculated on the basis of the
observed amplitude square, which obeys a chi-square distri- .
bution. The significance of the results are the same as re-
ported on earlier /Gombosi et al, 1975b/, i.e. 99.94 per cent
on the basis of the first and second harmonics together,
whilst 1-p is 99.82 and 96.55 per cent for the first and the
second harmonics alone, respectively.
It should be noted that the usually quoted estimate of 'the
amplitude, A=|fc" +s" , where cT and s~ are the estimated values
of the coefficients of the cosine and sine terms respectively,
is not unbiased, i.e. <A> 4 A, with A denoting the true2
value of the amplitude. The unbiased estimate of A is— Q p p ^»- m
A = "c +s -2tr , where 0"1 is the /estimated value of the/ va-
riance of "c and i" /Kota, Somogyi 1969/. The VA2 ampli-
tudes, in the case of the Musala measurement, are 0.067 per
cent and 0.046 per cent for the first and the second harmon-
ics, respectively. The significance levels are, of course,
the same as quoted above.
The Musala results get further confirmation by the remark-
ably similar results of the independent measurement carried
out at Mt. Norikura /Sakakibara et al, 1975, 1976/.
Since the Munich Conference we have found no reason to re-
vise our results. Nevertheless, to confirm that, the. .observed
111
variation is sidereal, an additional analysis has been carried
out at period lengths adjacent to one sidereal day. What we
did was repeating our former analysis /Gombosi et al, 1975b/ •
with the difference, however, that the sidereal frequency was
tuned off. Then we swept with this off-tune frequency around
the proper sidereal frequency. Of course -, the antisidereal
frequency was also changed retaining U)sid+u>agid= 2 a J
s o i< .
The resulting amplitudes of the first and second harmonics ac
well as the significance levels for the existence of genuine
variation /first and second harmonics together/ are listed in
Table 1 and shown in Figures 1 and 2 as function of period
length /T ., denoting the length of one sidereal day/.
Amplitude \%) Significance
Period length 1st 2nd level {%)
Tgid-2min 0.006 0.016 4.5
Tsid-lmin 0.017 0.026 30.7
Tsid-0.5min 0' 0 1 6 °- 0 5 8 ^ 'Z
T ., 0.073 0.055 • 99-94sid
Tgid+0.5min 0.062 0.015 95.6T .,+lmin 0.015 0.016 11.4sidT .,+2min 0.044 0.040 90.6sid
Table 1
None of the solar and 'antisidereal' waves has turned out to
be significant above noise leval.
In addition to the amplitudes, also indicated in Figure 1
are the 50 and 95 per cent significance levels of the exist-
ence of non-zero amplitudes for the first and the second har-
monics alone. Inspection of Figures 1 and 2 shows well pro-
nounced peaks at tlie proper length of sidereal day for both
the first and second harmonics as well as for significance
levels. The width of 0.5min corresponds to about the limit
of resolution of period lengths which can be achieved at
four years of total length of observation.
112
.AMPLITUDECM
aoi -
— F I R S T HARMONIC
SECOND HARMONIC
SIGNIFICANCELEVEL
.l Amplitudes of 1st and 2nd harmonics vs. period length
939
99
90
SIGNIFICANCELEVEL(V.)
1-SIGNFICANCELEVEL
icri
1 SOLAR T
DAY
Fig.2 Significance levels vs. period lengthI
113
We consider our results presented here as an evidence of
genuine galactic anisotropy an also as a strong indication
that the sidereal daily variation of cosmic ray intensity
has a-second harmonic, too.
References:
Chapman, S. and Bartels, J. 1946, Geomagnetism, Oxford,
Clarendon Press, p563.
Gombosi, T. et al 1975a, Nature, 255, 687.
1975b, Conference Papers, 14th ICRC, Munich, 2_, 586.
Kota, J. and Somogyi, A.J. 1969, Acta Phys. Hung., 27., 523.
Sakakibara, S. et al 1975, Conference Papers,
14th ICRC, Munich, 4, 1503.
1976, Proc. 2nd Cosmic Ray Symp. in Japan, Tokyo,p3l6,
114
Sidereal Anisotropy of Cosmic
* / ** ***R. M. Jacklyn, A. G. Fenton , K. Nagarshxma, S. Mori
Antarctic Division, Department of Science, Melbourne, Australia
* Physics Department, University of Tasmania,
Hobart, Tasmania 700iyAustralia
** Cosmic Ray Research Laboratory, Farculty of Science,
Nagoya University, Nafgoya, Japan
***Department of Physics, Shinshu University, Matsumoto, Japan
Abstract
Using the underground muon data of conjugate sta-
tions in the northern afa& southern hemisphere, it is demon-
strated that the obse/ved anti-sidereal diurnal variation
persisted for many wars, showing north-south asymmetry,
the phase being about 0 and 12 in the northern and
sbuthern hemisph/re, respectively. It is noted that this
asymmetry is quftte similar to the asymmetry of the sidereal
diurnal variation pointed out by one of the authors (R.M.
Jacklyn). ysing the anti-sidereal diurnal variation, some
correction^ of the solar modulation effect to the observed
sidereal/diurnal variation are made, based on the theory
derived'by one of us (K. Nagashima), which is quite differ-
ent from the Farley-Storey method. It is demonstrated that
the/corrected sidereal diurnal variation becomes very small,
indicating that the observed sidereal diurnal variation is
Largely produced by solar modulation.
! 131
Acknowledgements.
,.- I would like to thank Dr. A.S. Webster foy many useful comments anddiscussions. The Royal Commission for the Exhibition of 1351 is thankedfor support.
References.
Andrei;, B.H. (1969), M.N.R.A.S. 143., 17.
Bridle, A.H. (1967), M.N.R.A.S. 136,
Caswell, J.L. (1976), M.N.R.A.S. 177, )601.
Ilovaisky, S.A. and Lequeux, J. (197/), Astron. Astrophys. 20, 347.
Roger, R.S. (1969), Ap. J. ]j>5, 831
Strong, A.W. (1977), M.N.R.A.S. flln press).
Webster, A.S. (1975), M.N.R.A.S< 171, 243.
132
THE ACCELERATION OF COSMIC RAYS BY SHOCK WAVES
W.I. Axford, E. Leer* and G. Skadron**
Max-Planck-Institut fUr AeronomleD-3411 Katlenburg-Lindau 3Federal Republic of Germany
* Present address: the Auroral Observatory, N- 001 Tromstf, Norway** Present address: Dept. of Physics and Physical Science, Drake University,
Oes Moines, Iowa 50311, USA
The acceleration of cosmic rays in flows involving shocks and other com-pressional waves is considered in terms of one-dimensional, steady flews andthe diffusion approximation. The results suggest that very substantial energyconversion can occur.
The possibility of cosmic ray acceleration by tihock waves has been con-sidered by many authors during the last twenty years on the basis of variousassumptions concerning the exact nature of the acceleration mechanism (1-19).In this paper, we examine the question further on tlie assumption that thecosmic rays are constrained to move diffusively with respect to the backgroundmedium and find that the acceleration is very efficient. Indeed, for strongtransitions, a substantial fraction of the kinetic energy of the gas flow canbe converted into cosmic ray energy. We emphasize hwever, that the assump-tions made are not strictly valid In many circumstaices and our results shouldtherefore not be accepted as being generally correc: in detail.
Let us consider first the situation in which cosmic rays interact witha shock front without affecting the background flow. This is of course not aself-consistent approach, but provided the cosmic ray pressure is small com-pared with the gas pressure the results are relevant in many circumstances.In the frame of the shock wave (situated at x - 0 and facing in the negativex-direction) the scattering medium is assumed to have a flow speed Vi inx < 0 and V2 in x > 0, with V\ and V2 constants and Vx > V2 > 0. The relevantequations describing the behaviour of the cosmic rays in steady conditionsignoring such effects as energy losses and second order Fermi accelerationare
as 4' 3x3T(otTU)
and -*(.-ifc «->)-.£(1)
(2)
where U(x,T) is the particle density, S(x,T) the particle current, K(X,T) thecoefficient for diffusion normal to the shock front, T is the particle kine-tic energy,, a - (T + 2T0 )/(T + To ) where JI0 is the particle rest energy andC - 1 - (t/3U)3(aTU)/3T is the Compton-getting factor (15, 16). We will as-
133
sume that a may be considered a constant. Similarly, we assume that K - Ki(T)in x < 0 and R " K2OO in x > 0, although this restriction 1 B not necessary.
If a magnetic field is present, the diffusion coefficient is anisotropic,the shock will in general be oblique and the presence of an electric fieldmust also be taken into account. This situation can easily be dealt with bytransforming to a frame of reference in vhich the electric field vanishes butthe shock remains stationary so that the problem to be* solved is'not signifi-cantly different from that posed here. Note however, that if 6 is the anglebetween the magnetic field and the shock normal, the speed of the scatteringmedium in the new frame of reference is Vj sec 8 and the diffusion equationswe have used are invalid if this is not small compared with the particle' speedin the same frame.
It was shown by Gleeson and Axford (20) that the "jump" conditions at ashock front are simply that II and S should be continuous. Hence if we takeas boundary conditions U •*• Ui(T), S •+ C1V1U1 as x + -» and 9U/8x + 0 asx •> +», then it can be shown that U « U2<T) and S - Cz(T) V2D2CO in x > 0-where
(I) U2(T) - (XV1/(X+l)V2)(Uo/T0)H(T-To)(T0/T)X+1, X - 3V2/aCVi-V2) > 0 , (3)
if Ui(T) " U<jfi(T - T o ) , with H(?) and 6(5) being the step and delta functionsrespectively, and
(II) U2(T) = U,(T)/[1 - (V, - V2)C1/VJ] (4)
if Ui(T) - UoCT/Tor^ and hence Cr = 1 + (a/3)(u - 1). It is assumed that noparticles other than those defined by U1(T) are accelerated. The variation ofU(x,T) in x < 0 just before the shock front is exponentially increasing andthe thickness of the region of increase is OCVJ/K^) as might be expected. Notethat there is a characteristic spectral index (X + 1) associated with case (I)which is such that » > (X + 1) > 3/2. Furthermore, in case (II) the .form of thespectrum is preserved through the shock but the density ratio U2(T)/Ui(T) -•• °>as Cx •+ Vi/(Vi - V2) i 4/3. The solution for any given spectrum U^T) can easi-ly be obtained from (I).
The important conclusion to be drawn from these results.is that shockfronts can be very efficient in accelerating cosmic rays and that the intensi-ty increases achievable by this means can be very much enhanced over those onewould expect from purely adiabatic compression, viz. U2(T) «= U^ (T) (-V1/V2)for the case of a power law spectrum (obtained formally from (1) and (2) withK « 0). It is the presence of diffusion (i.e. K ^ 0) which permits the enhance-ment relative to adiabatic compression, since it becomes possible for partic-les to be accelerated additionally by a first order Fermi process involvingthe mutually approaching scattering media ahead of and behind the shock front(2, 10, 13-15).
It should be noted that the simple calculations we have carried out re-fer only to a strictly one-dimensional situation and that they do not indi-cate how shocks can lead to the acceleration of cosmic rays in a general way.To understand this one must Include more information concerning the overallflow patternt including the expanding region which usually exists behindthree-dimensional shock waves. However it is not difficult to see how shockacceleration and subsequent deceleration in the expanding region in the
134;
.Vicinity of'the contact discontinuity can lead to the formation of thedouble-spike events observed to be associated with forward-reverse shockspairs In the Interplanetary medium at large heliocentric distances (21-24).In this case, the particles (which are most effectively accelerated in theouter solar system) can diffuse towards the inner solar system near the earthalong Interplanetary magnetic field lines on both sides of the shocks. We sug-gest that this might also be the acceleration process responsible for the"anomalous" component of galactic cosmic rays which appear to have their ori-gin as quite low energy interstellar ions captured by the solar wind (24, 25).
If the cosmic ray pressure p c - (1/3)/JJ TUdT is not everywhere negligibly•mall compared with the gas pressure p, as may well be the case according to-the results obtained above, then it is necessary to take Into account theeffect of the cosmic rays on the background flow. Thus, for steady, one-dimen-sional flaw, In addition to equations (1) and (2) we must solve the followingequationss *
<pv) • (5)
"§ dp dPc" df "dT" (6)
pVIx f - V dx (7)
where p is the gaa density and y the ratio of specific heats for the gasalone (26). These equations can be integrated directly to yield
PV
+ pc + p
,V,
v2 - p* + pcl + p,ycl
,y,
(8)
(9)
pp (10)
where the subscript j denotes conditions at x • -».
> In order to solve equations (1) and (2) with V now variable and relatedto p c through equations (8), (9) and (10), it is convenient to make use ofthe Mach number M - /(pv /YP) as dependent variable and assume thatK(X,T) - K(X) independent of T. Accordingly, we find that
(.1)
and thst M satisfies the first order differential equation
(12)
135
where we use as independent variable £, *• Vijdx/K(x).
The solutions of equation (12) depend in a rather complicated manner onthe initial values of the Mach number Mj and the ratio of the cosmic ray andgas pressures' and it is not possible to describe them in full in this paper.It is perhaps sufficient to restrict our attention to the case of a relative-ly strong transition (Mi2 « 100) for which the results corresponding to vari-ous, values of Pci/pi are shown in Figure 1. Note that for all values ofPcl/Pi> t h e f l o w remains supersonic (M2 > 1) unless a shock wave is inserted,which produces a uniform subsonic flow with M and pc constant. If Pci/pi issma.ll, a smooth transition to subsonic flow can occur in. cases where Mj issomewhat smaller (Mi2 £10). Such supersonic-subsonic transitions are howeverpossible only if the downstream boundary conditions (i.e. x •*• <») can be cor-rectly matched and this will usually be the case only by chance. Normally ashock front is required to match given subsonic downstream conditions.
Figure 1.
Variation of the Mach number withdistance for various values ofpci/pj and with Mi
2 «• 100. Notethat the flow never becomes sub-sonic with this value of Mjz.
20 25
The most interesting aspect of these solutions is that the cosmic raypressure can undergo very large changes, as shown in Figure 2. In fact it is
P/P,
Figure 2.
The variatior ,L pc/pj, p/pj andM 2 with distance for the caseMi? - 100 and pcl/Pl - 1 and 0,1.A shock can be inserted at anypoint since K2 >1 everywhere.
136
possible for a large fraction of the kinetic energy of the gas in a highlysupersonic flow to be converted to cosmic ray energy, the mechanism beinga combination of adiabatic compression and the first-order Fermi accelerationdiscussed previously. It can be shown that if FK, FT and Fc are the kinetic,thermal and cosmic ray energy fluxes respectively, then for large values ofMi , the kinetic energy flux decreases by a factor a /(6 + a) « 0.06 (a = 2),0.02 (a = 1) and the thermal energy flux increases by a factor [(6 + a)fa]y~l
ra 2(a =2), 3. (a = 1) with Y = 5/3. Thus only a small fraction of the kineticenergy is converted to thermal energy of the gas, and the major part is con-verted into cosmic ray energy, as shown in Figure 3. We conclude on the basisof these admittedly over-simplified calculations that shock acceleration ofcosmic rays can be a very efficient process. Indeed it seems possible that alarge fraction of the kinetic energy of, for example, a supernova explosion,can be converted into galactic cosmic ray energy, not all of which is givenup again as a result of the adiabatic cooling associated with the expansionof the envelope. We expect shock acceleration to be important also in connec-tion with the acceleration of energetic solar particles, energetic storm par-ticle events, "Interplanetary" acceleration associated with stream-stream in-teraction regions and the termination of the solar wind (27-30). It is reason-able to suppose that qualitatively similar results would be obtained for morerealistic situations In which K is not independent of energy and the scatter-ing mean free path does not have the unlikely property of decreasing with in-creasing cosmic ray energy.
100
3_lU_
Oor
10 -
L - "
Fc :
S
v •
^ ^ F ''
Figure 3.
The variation of the kinetic (FK),thermal (F'p) and cosmic ray (Fc)energy flu<es with distance forthe case Mi2 = 100. Note that mostof the kinetic energy is given tothe cosmic rays in this case if noshock occurs.
10 IS
REFERENCES
1. Glnzberg, V. and S.I. Syrovatskyi: The Origin of Cosmic Rays, (New York:Macmillan Co.), 1964.
2. Schatzmann, E.: Ann. d'Astrophysique 137, 135, 1963.3. Parker, E.N.: Phys. Rev. J09_, 1328, 1958.4. Parker, E.N.: Interplanetary Dynamical Processes, (New York: Intersclence
Publishers), 1963.5. Hoyle, F.: .M.N.R.A.S. J2p_, 338, 1960. -*6. Axford, W.lT and 6.C. Reid: J. Geophys. Res. 67, 1692, 1962; 68, 1793, 1963.7. Wentzel, D.G.: Astrophys. 3. J37_, 135, 1963.8. Wentzel, D.G.: Astrophys. J. 140, 1013, 1964.
137
9. Hudson, P.D.: M.N.R.A.S. \3±, 23, 1965.10. Jokipii, J.R. : Astrophys. J. J43_, 961, 1966.11. Sonnerup, B.U.O.: J. Geophys. Res. 74_, 1301, 1969.12. Ogilvie, K.W. and J.F. Arens: J. Geophys. Res. 76, 13, 1971.13. Fisk, L.A.: J. Geophys. Res.: 7£, 1662, 1971.14. Van Allen, J..A. and N.F. Ness: J. Geophys. Res. 72.. 935, 1967.15. Scholer, M. and G. Morfill: Solar Phys. 45_, 227, 1975.16. Quenby, J.A. and S. Webb: 13th Internat. Cosmic Ray Conf. £, 1343, 1973.17. Chen, G. and T.P. Armstrong: 14th Internat. Cosmic Ray Conf. 5_, 1814,
1975.18. Alekseyev, i.i. and A.P. Kropotkin: Georaag. Aeron. JHD, 755, 1970.19. Sarris, E.T. and J.A. Van. Allen: J. Geophys. Res. 79_, 4157, 1974.20. Gleeson, L.J. and W.I. Axford: Astrophys. J. J49_, 6115, 1967.21. Barnes, G.W. and J.A. Simpson: Astrophys. J. 210, L91, 1976.22. Pesses, M.E., J.A. Van Allen and C.K. Goertz: J. Geophys. Res., in press,
1977.23. Leer, E., G. Skadron and W.I. Axford: EOS 5_7, 780, 1976.24. Fisk, L.A., B. Koslovsky and R. Ramaty: Astrophys. J. 190, L35, 1974.25. Klecker, B., D. Hovestadt, G. Gloeckler and C.Y. Fan: Astrophys. J. 212,
29G, 1977.26. Jokipii, J.R. and E.N. Parker: Planet. Space Sei. JL5, 1375, 1967.27. Axford, W.I.28. Axford, W.I.29. Wallis, M.K.
The Solar Wind, NASA SP-308, 609, 1972.Proc. I.S.T P. Symp., Boulder, Colorado ^» 270, 1976.Astrophys. Space Sei. 20, 3, 1973.
30. Jokipii, J.R. and L.C. Lee: Solar Wind 3, 224, 1974.
66MQ0522138
ON THE ORIGIN AND PROPAGATION OP ULTRA HIGH ENERGY COSMIC RAY;'
-£, Kiraly
Central Research Institute for Physics, Budapest, Hungary
A discussion is given of some consequences of extraga-lactic and Galactic models of cosmic ray origin. Expectedpatterns of intensity peaks are described and their con-nection with source distribution and propagation is dis-cussed. An observable, time dependence of the anisotropyis found to be unlikely.
1. Introduction
Experimental and theoretical 'developments go hand in hand.
While it is quite obvious how experimental findings can affect
the credibility of theories, 'experimental facts' are also
affected, by theories. An experimental finding of marginal sta-
tistical significance is often dismissed i_" it has no sound
theory to support it.
Now it is to some extent a matter of taste whether a
certair experimental evidence is convincing enough. Sceptics
/like myself/ are hard to convince until tie experimental evi-
dence is very strong indeed or until the findings arrange them-
selves into a nice pattern suggesting a- plausible and more or
less unique physical interpretation.Up to the time of writing
/i.e. before reading the contributions to this conference/
I failed to find such a convincing patterrjjin the very high
energy anisotropy measurements. The issue is, however, important
enough to justify some speculation about the possible patterns
of anisotropies for a few scenarios of origin and propagation.
2. Extragalactic origin
a/ Models with small angular deflections
The magnitude and structure of iritergalactic magnetic
fields is largely unknown, but it might well happen that they
are so weak that cosmic rays with E?10 eV can reach us with
deflections comparable to the experimental uncertainty on
arrival directions /for.E«10 "eV, however, deflections ori- t
ginating in the Galaxy should be large enough to destroy in-
dividual intensity peaks/. A search for .correlations of arrival
139
directions with plausible source candidates was carried out
in Durham /Kiraly et al., 1975/ with negative results. The
energy requirements^ the sources were also found hard to
satisfy. It is, however, quite possible that the sources at
extreme energies are mostly exotic objects /like white holes
or systems of moving black holes/ and have not been found yet
by astronomical observations.
Suppose that particles are arriving to us from a set of
unidentified standard sources from a certain volume of space
beyond which black-body cutoff is effective /this volume should
decrease with increasing energy/. The pattern of expected
anisotropy then depends strongly on the number of standard
sources /N/ in that volume. Assuming that the spatial distri-
bution of sources is random and the inverse square law is valid
for the intensities, the probability distribution of the ratio
of the intensity arriving in the k-th largest peak to the total
can be worked out for any given N. The most.probable value for
the 'most inte-isive peak.to total*
ratio is given in Pig.l as a func- too'A ^
tion of N. /The most intensive
peak is expected to be even more
intensive relative to the total
if some o£ the sources are in-
side our Supercluster/.
Thus the detection of some
individual peaks should not be
unexpected if bhe bulk of the .
ultra high energy radiation comes
from a reasonable number of sour-
ces and the Galactic and inter-
galactic magnetic fields are not
too strong. Fig.l
Another interesting point is whether there should be any
characteristic pattern of the energies and arrival directions
within a single peak. Peaks are expected to be more pronounced
at higher energies /smaller deflections and smaller total
number of sources/, thus the share of high energy particle:.;
la*.
10*. -
100 Wo N
140
should "be higher in peaks than elsewhere. If the deflecting
fields are regular enough, then the deflections should regularly
increase with decreasing energy, thus the highest energies
should he observed close to each other /and to the source
direction/.and the energies should decrease in a definite di-
rection. In the other extreme case most of the deflection is
caused "by small-scale random magnetic; fields, and the most
energetic particles are-expected to "be at the centre of the
peak, surrounded by increasinly soft components. A crude cal-
culation based on the propagation model of Kiraly et al. /1975/
suggests that the separation between the two patterns can be
characterized by the quantity
*l = .015 BDE"J fZ,where B is the r.m.s. magnetic field injmits of 10 - gauss,
D is.the distance to the source in Mpc, E, Q is the energy in-l q -1-"
units of 10 JeV and n is the number of 'independent field cells'
between so' rce and observer /i.e. D/n -Jt is a sort of corre-
lation length/. For *l«.A +-he first, for <p> A the second pattern
applies. The two patterns can also mix due to irregular extra-
galactic and regular Galactic fields,
b/ Models with large angular deflections
If the angular deflections outside our Galaxy are large,
then the hopes for the direct identification of individual
extragalactic sources are slight. Itowever, the niurt.er of sources
contributing to the local flux should then be smaller,- and it
is quite possible that the Supercluster /and mainly the Virgo
cluster/ dominates the scene. Astronomical observations giving
support to such an idea are quite possible in the not too
distant future. A search was made for large-scale correlations
with relevant directions of the Supercluster /Kiraly and White
1975/ and the result was again negative. It is rather hard to
invent a field configuration which . on the one hand does not
lead to observable large-scale anisotropies associated with
Vixgo and on the other is not a strongly confining field in
the Supercluster^including our Galaxy, since in that case the
spectrum should strongly decrease above a few times 10 eVbecause of the black-body cutoff.
141
5. Galactic origin
Both the attractive features and the difficulties of
Galactic models were discussed by Rillas and Oulridge /1975/
and there is little to be added. Rad.io astronomy appears to
favour halo fields at present and if they are really strong
and extended -enough then an explanation in terms of Fe nuclei
as primaries might be satisfactory. Numerical calculations
on the fields compatible with simple Galactic dynamo models
have been done by M. White /1977/, but in these simplified
models halo fields turned out to be too weak. A Galactic wind
driven either by hot Phase III gas or by cosmic rays might
help in carrying field outwards and in creating strong enough
halo fields.
One peculiarity of the anisotropy expected for Galac i ic
origin is that both peaks /intensity enhancements/ and holes
/intensify deficiencies/ might appear, while the flux arriving
with small deflections from extragalactic sources should con-
tain only peaks on a smooth background.
4. Time and energy dependence
The time scale of changes in magnetic field structures
which are capable, of deflecting ultra high energy particles
should be at least 10 years /the field should be homogenous
on scales of 1 Kpc and the convective velocities should defi-
nitely not surpass a few hundred km/sec/« Thus any change in
the pattern of anisotropies should come from the change in
sourcer. /e.g. from supernova explosions/, but even then the
energy dependence of the time delay would irake it very unlikely
to te observed in a matter of decades. One should remember
that some of the most energetic particlecs observed arrived
from near the Galactic poles and their time delays - if Galac-
tic - should be huge. These conclusions disagree with those
of Linsley /1975/f who based his arguments on discrepancies
among experiments alone.
The trajectories of particles should change much faster
with energy than v:| ":i time and a strongly energy-dependen1
142
anisotropy appears at first sight possible, mainly if the
anisotropy is connected with easy escape e;nd not with source
directions. Further model calculations would be needed on
these questions.
•j. Conclusions
The anisotropy of ultra high energy cosmic rays on the
level reported in the last Conference appears to be still
somewhat in doubt. Both the Galactic and the extragalactic
models have attractions and problems, and at present it is
impossible to cheese between them. Until further data arrive,
it is worthwhile to work or. a broad front in order to have a
clearer picture of the cmsequences of several plausible models
of propagation and origin on the pattern of anisotropy.
REFERENCES
Hillas, A.M. and Oulridge, M., Proc. Munich Conference 12.
4160-65 /1975/ . • — •
Kiraly, P. and White, M., J.Phys.A: Mat.&en. 8. 1336-48 /1975/
Kiraly, P. et al., J. Phys. A: Mat.Gen. 8. 2ol8-32 /1975/ j
Linsley, J., Proc. Munich Conference 2. 598-603 /1975/
White, M., Ph.D. thesis, University of Durham /1972/
149
SECONDARY POSITRONS AND ELECTRONS IN THE COSMIC RADIATIONG. D. Badhwar and S. A. Stephens*
NASA Johnson Space CenterHouston, Texas 77058 USA
A new and Improved calculation of the secondary productionand equilibrium spectrum of e* in the Galaxy in the energyrange of 1 MeV to 100 GeV has been performed. This hasbeen done by obtaining an analytic representation of theaccelerator data which describes accurately the Invariantcross-section of IF* and K* from threshold energy to about1500 GeV. This calculation takes Into account the correctangular distribution of electrons In the decay of muons andthe effect of nuclei-nuclei collisions. The contributionsof beta decay e and knock-on e~ have been Included. Acomparison of the present calculations with earliercalculations and experiment is presented.
1. Introduction. The nuclear Interaction of cosmic ray nuclei with inter-stellar matter gives rise to secondary e* through the decay of produced ir*and K*. Hence, the production spectrum of secondary e± in the Galaxy can, inprinciple, be calculated with reliability from a knowledge of particle produc-tion at accelerator energies and the energy spectrum of cosmic ray nuclei Ininterstellar space. Many such attempts have been made 1n the past. However,except 1n the works of Badhwar et al.1, and Orth and Buffington2, other workersdid not utilize all of the measured p1on cross-sections 1n the laboratory thusmaking it necessary for them to resort to models. Even in the above twocalculations, the representation of the analytic cross-section of Carey et al.3
was used. It Is known that the above representation^ not valid for p, £ m .Moreover, Orth and Buffington2 assumed that TT+ and IT" have the same representa-tion. This 1s not supported by data. There Is thus a need for an Improvedcalculation. We believe, the present work represents such an attempt.
2. Representation of the IT* and K* Invariant Cross-Section. In computing thedifferential production cross-section it is convenient to express them in anInvariant form. It has the obvious merit that it simultaneously expresses theenergy and angular distributions. In Figure 1, we have plotted the experimentaldata1*'5 on E ( p~) for v+ at fixed value of p, as a function of x =
[xf-i2 + T (Pi2 + m w2)3 for incident proton energies of 6.6, 12, 24, 200 GeV,f (P^ + mir
and the combined data of 1100 and 1500 GeV. Here x?i is the ratio of theparallel component of the cm. momentum to the maximum transferable momentum,and /s is the total energy 1n the c m . system. The lines through the datapoints are calculated using the expression
f A (1 + M ) r ,{zf exp [- B Pl/<1+ &)] . (1A>
0 < Z <. (1 - *fand (q - C/O+^/s)1* and C » CQ + C]p1 + C2p
2)
•NASA-NRC Sr. Postdoctoral Resident Research Associate on leave from TataInstitute of Fundamental Research, Bombay, India.
150
&-f [(1 - 4f3-k
exp[- (IB)
where Z - (1 - 3K) - [1 - (1 + f-f^ * (p^p*) and k - 3. The other constantsare given in Table 1. At energies below 6.6 GeV, data on invariant crosssections is not available. Using the above expression, we have calculateddo/dp* and this is shown along with the data6»'»8 in Figure 2. The agreement
Table 1Parameters for the Representation of Invariant Cross Section
Particle+
ir
K+
K"
A
mb/GeV2/c3
153
127
8.85
. 9.3
B
5.55
5.30
4.05
3.8
C
(GeV/c)"1 '
2.5
8.3 •
Co
5.3667
7.0334
C l(GeV/c)-2
-3.5
-4.5
C2(GeV/c)-2
0.8334
1.667
is good. We also find that the same expression applies to ir" and K~ also. Theconstants are given in Table 1, except that k=5. We also find that the totalcross section for ir and IT" is also in excellent agr^ment with the data. Thuswe have an analytical representation of IT* and K4 when is valid up to 1500 GeVincident proton energy.
In an earlier work9, we have shown that the invariant cross section in p-nucleuscollision is given by
where and Xp^ are the corresponding mean free paths, f is the fraction, of
neutrons in the target nucleus and n, a constant, is = 0.195 + 0:05.
We have already shown9 that using the above representation, the sea level muonmomentum spectrum and the charge ratio can be completely explained in the 1 to5000 GeV/c range. We are thus confident that the production cross section forboth ir1 and K4 can be accurately calculated as 4 = 2iris the angle of emission. dE
c(E -r£-)
a P p. d9, where G
3. Production Spectra of Pions and Kaons. The production of pions or kaonsper g cm--4 of hydrogen is given by
... E ^ < E V J (EP} dEP (2)
where J(E ) is the input proton spectrum. Using the available experimental data,we find that the proton spectrum during the period of solar minimum in the neigh-borhood of the Earth can be represented by three power law spectra in totalenergy and are given as: 2.0 x 10'»ED"
z'75 for Ep > 70 GeV, 6.92 x lQ3Ep~
2-5
ror 3 GeV < Ep < 70 GeV and 2.81 x 10-Ep"1-68 for 1 < Ep < 3 GeV, the/luxbeing expressed in particles (m2sr.sec. GeV)"1-. Using the parametersderived by Burger1°, we have demodulatedthe above spectra to obtain the protonspectrum in the interstellar space.Using the interstellar proton spectrumand equation (2), we first compute thet^ and Kr production spectrum in spaceand find that above about 15 GeV, theproduction spectra are power law withan index of 2.75.
4. Production Spectra of e±. Electronsarise from the decay of pions and kaons.The kinematics of the decay scheme hasbeen discussed by a number of authors.Orth and Buffington2 were the first topoint out that the energy distributionfunction used in all previous calcula-tions was not correct. In our calcula-tion we have used the energy distribu-tion function *(E, Ey) due to Zatsepinand Kuz'min11 which was derived fromthe V-A theory of weak interactions andis given by
*(E, Eu) = 32
dE[3(l-e2)-2(3+02)(E/Ey)](E/Ey) g- for
0 <_ (E/Eu) £ (l-B)/2
Eu) - f x
& i
{£[1+ jfep {4(E/Eu)-3(1+3)(E/Eu)2}]{£for
<_ (E/Eu) <.
where s is the velocity of muon ofenergy Eu and E is the energy ofelectrons from the decay of the muon.We note that the expression derived byOrth and Buffington2 is valid only for6 = 1.
In order to obtain the productionspectrum of e± in interstellar space,we have to take into account thechemical composition of cosmic rays
I
Fig. 1 - A plot of the TT invariantcross-section versus 1-5; at fixed p-jvalues. The lines are the calculationsusing Equation (1).
5 3 I . 100
-
-
WY
\.n G«V
r\\ /
//
; sc«v
v--
VICO
CMS
f-ig. 2 - A plot of da/dp* versus p*for proton energies of 1.71, 2.5 and3 GeV. The histograms are theobserved data and curves arecalculated using equation (1).
152
and of the interstellar gas. We haveassumed the interstellar gas to be75% hydrogen and 25% helium by mass.The cosmic ray composition varies asa function of energy; the variation,however, is not strong enough tochange the n/p+n significantly in theenergy range of Interest here. Wehave used an n/p+n = .105 and haveevaluated the effects of theseneutrons using equation (1C). Orthand Buffington2 have shown that theratio of e= production by all cosmicray nuclei to just those produced inp-p collisions 1s 1.34 ± 0+09 forInterstellar space. The e~ produc-tion spectrum is shown in Figure 3by curves, marked A, B, C, D.Curve A (I and II) and Curve C (Iand II) are for e+ from TT+ and K+
decay respectively, whereas Curve Band D are for e~ from v" and K"respectively. Here I and II referto the input cosmic ray spectrum of(I) J(EP) - 2 x 10* En"
2-" forE p > 1 GeV and (II) for thedemodulated proton spectrum. Wenote that the maximum difference influx resulting from the two spectra1s about 20% at ^ 35 MeV decreasingto -. 10% at 1 GeV and 0% beyond 10GeV. We also note that the e* pro-duction spectrum above about 10 GeV1s a power law with an index of 2.75and the kaons contribute about 10%of the electrons.
In the energy region below about 10MeV, knock-on electrons are thedominant source of secondary nega-trons. Using the demodulated spectraand the method of Daniel andStephens12, we have calculated the pro-duction spectrum of knock-on e" which1s shown by Curve F in Figure 3.It was+po1nted out by Ramaty et al.
13,that e arising from the decay ofradioactive nuclei produced in theInteraction of cosmic ray nuclei withInterstellar gas would contributesignificantly to the e productionbelow about 5 MeV. Following hisapproach, but using the demodulatedspectrum, we have calculated thiscontribution and It 1s shown 1n
Fig. 3 - A plot of e± production spectrumin interstellar space that includes effectsdue to cosmic ray and interstellarcomposition.
5 . 0
. - Ml
l .Q
ID"'i . . j
/
<• H
/»
'!
•o-i1 I I I ,
10" 10
• , , ' " 1
-
_/-3
3.0
g 2.1)
l.D
\
/
7^. > . . u l
— I — f ••
B—^
N
- •
Fig. 4A&B-Comparision of the e /e" andQ(E)xE0 with Daniel and Stephens (B),Ramaty (C), Perola et al. (D), Orth etal. (E). In Fig. 5B Curve (B) is of*Badhwar et al.
153
Figure 3 by Curve E. There is one additional source that contributes equallyto e + and e~. It is Lhe decay of K°, whose contribution has been obtained byscaling from K~ contributions. The total production spectrum, Q(E), ofsecondary e+ and e" can be obtained by simply adding up the various cuntribu-tions of e+ end e" respectively.
5. Comparison With Other Calculation. Instead of comparing the productionspectrum ofe" obtained above with those obtained in earlier calculations, itis more useful and more sensitive to compare the ratio e+/e" and the productQ(E) x E s where e is the spectral index of the primary spectrum used by therespective authors. This is because the ratio e+/e" and Q(E) x Ee are notsensitive to the form of the input spectrum used. Figure 4 shows the resultsof various calculations. The solid lines refer to e* from IT'S and K's andthe dashed lines include knock-on electrons and e + from radioactive decay. Itis clear that there are significant differences between the present calculationsand those of others14'15. In particular, note that e /e" at energies I 5 GeVis not 1.27 as is generally assumed2ll2liu. We also note the e+ spectra ofRamaty14 is very steep compared to the present calculations. The differencesbetween the present calculation and those of. Orth and Buffington2 in the 1.5GeV range are due to their use of the CK.P model for pi on production.
6. The Equilibrium Electron Energy Spectrum. Having obtained improvedproduction spectra of e* in the Galaxy which was the main goal of this calcula-tion, we proceed to obtain the equilibrium spectra which depends on the modelof propagation. The simplest model, which is also consistent with the existingdata on the chemical composition, is the leakage lifetime model. In such amodel, the electron energy spectrum, N(E), can be obtained from the continuityequation
H * Q(E) -fg- [- (I + aE + BE2) N] - = 0
where x is the catastrophic leakage lifetime, I is the ionization loss, term,aE is the continuous energy loss due to bremmstrahlung (a = 9.15xlO"6Nn, whereNf.j is the interstellar gas density) and BE2 ir, loss due to synchroton andinverse comptor, scattering, e is numerically equal to (3.79xlO~18 H2 + 1.02xlO"16p) Gel/"2 sec"1, where H is the magnetic field in pG and p is the totalphoton energy density oJ .7 eV cm"3. The leakage time, T , has not been deter-mined with jny degree of certainty. It has generally been taken to be 3.3 x106 years, though recent observations suggest that it could be higher by asmuch as a factor of ten. Figure 5 presents our calculation. Note that forenergies £ 1 GeV, the flux is just proportional to the amount of mattertraversed. We have also plotted the data of Stone et al. 1 6, for e~ in the1 MeV to 3 MeV region and see that the source of these electrons can beunderstood as knock-on e".
In Figure 6, we have plotted the d' energy spectrum for 5 g cm"2 above 1 GeVfor T = 3.3 x 106 years (Curve A", T = 3.3 x 107 (Curve C) and t(E)=3.3 x 107
(E / E ) u (Curve D). Here Eo = 3 GeV and v -- 0.5 are values which fit theobserved energy variation of B/C+O ratio well. The data points are taken fromBuffington et all7 and Fanselow et all8. We see that the results are consistentwith about 5 g cm"2 of matter traversed at about 3-20 GeV (Curve B, modulated).
7. Conclusions. We have developed an elegant representation of the IT1 and K1
invariant cross section that describes the observed data from ^ I GeV to /
! b>\
^1500 GeV and which has been inde-pendently shown to provide an adequateexplanation of the vertical sea-levelmuon momentum spectrum and chargeratio u+/u". in the 1 to 5000 GeV/c.Using this representation, we haveaccurately calculated the productionspectrum of e* in the 1 MeV to 150 GeVrange. It is shown that the presente + data in 3-20 GeV is consistent "with5 g cm"2 of hydrogen traversed bycosmic rays.
References1. G. D. Badhv/ar et al., Astrophys.
& Spa. Sci., 37.. 285 (1975).2. C. Orth and A. Buffington, Ap.- J.,
206, 312 (1976).3. Carey et al., Phys. Rev. Letts.,
33., 327 & 330 (1974).4. H. Boggild and T. Ferbel, Annv.
Rev. Nucl." Sci., 24, 1 (1974).5. T. Ferbel, in Proc. of the SLAC
Summer Institute on ParticlePhys., U. of Rochester, ReportNo. UR-500 (1974)(unpublished).
6. W. B. Fowler et al., Phys. Rev.,103, 1479 (1956).
7. T. W. Morris et al., Phys. Rev.,103, 1472 (1956).
8. W. J. Fickinger et al., Phys.Rev., 125_, 2082 (1962).
9. G. D. Badhwar et al., Phys. Rev.PIS, 820 (1977).
10. J. J. Burger, Ap. J., 166. 651(1971).
11. G. T. Zatespin and V. A. Kuz'min,JETP U, 1294 (1962).
12. R. R. Daniel and S. A. Stephens,Rev. Geophys. & Spa. Phys., 12,233 (1974). ~
13. R. Ramaty et al., J. Geophys.Re s., 75_, 1141 (1970).
14. R. Ramaty, in High Energy Particles& Quanta in Astrophys., p.122 (1974)
15. G. Perola et al., Nuovo Cimento,52B, 455 (1967).
16. E. C. Stone et al., Cal Tech,Preprint (1976).
17. Buffington et al., Ap. J., 199,669 (1975).
18. J. L. Faneslow et al., Ap. J.,202, 265 (1975).
Fig. 5 - A [lot of e* equilibriumspectrum. The data points in the 1-3MeV region are the e" Cal Tech measure-ments.
10*
I * > iNSaOW •» al- • E JPBNGTON tt ai
10°POSITRON ENBK2Y (G.V)
Fig. 6 - A plot of E 2- 7 5 x N(E) forpositrons. A, C, D are unmodulatedand Curve B is the modulated spectrafor various leakage lifetimes.
THE PROTON AND HELIUM RIGIDITY SPECTRA FROM TO TO 100 GV
G. D. Badhwar, R. R. Daniel**, T. Cleghorn, R. L. Golden,J. L. Lacy, S. A. Stephens*, 0. E. Zipse**
NASA Johnson Space CenterHouston, Texas 77058 USA
A magnet spectrometer flown from Palestine, Texas, inSeptember 1976 and May 1976 under ^6 g cm"2 hasproduced measurements on 7x105 protons and 5x101* heliumnuclei of rigidity greater than -v4 GV. In the interval9-100 GV, the proton and helium nuclei can be wellrepresented by a power law in rigidity, J(R)=AR~Y, withan index, y, of 2,78±0.0j and 2.80+0.0B respectively.From analysis of the a/p ratio, which has the virtue ofremoving common instrumental biases, one finds that(YM - y ) is 0.02+0.02 and this ratio has the numerical
value of O.15O±.O02 at the top of the detector. We havealso placed an upper limit of 10% on the 2H/p at %35 GeV/n .
1. Introduction. Proton and helium nuclei are the two dominant cosmic raycomponents. It is therefore of basic importance to study their spectral shapeand relative abundance. Though numerous experiments have been performed in thepast to study these components, there are, perhaps, only six1"6 in which directmeasurements significantly greater than 10 GV have been made. In these experi-ments, Anand et al.1 and Badhwar et al.2 used the variation of geomagneticcut-off with zenith angle, Webber et al.3 employed a gas Cerenkov counter andthe geomagnetic cut-off, Verma et al.1* used a permanent magnet with an emulsionstack, Ryan et al.5 used an ionization calorimeter and Smith et al.6 used asuperconducting magnet spectrometer. There is, however, considerable disagree-ment among the spectral indices determined by the various experiments. In thetwo experiments of Ryan et al.5 and Smith et al.e with the highest statisticalaccuracy, the spectral indices of helium nuclei above %20 GV are respectively2.77±0.05 and 2.47±0.03. The measurements of Verma et al.4 and Anand et al. *are in agreement with a steeper index of 2.7 - 2.8. As for the protoncomponent, it seems from the measurements made so far5 that in the rigidityrange of 10-50 GV the spectrum is somewhat flatter than that of 2.75 nowgenerally accepted for rigidities between 50 and 1000 GV5. In the presentpaper, we describe an experiment with a superconducting magnet spectrometer todetermine the spectral shapes of protons and helium nuclei in the rigidityinterval of 10-100 GV.
Z. Experimental Details. The magnet spectrometer which is described in detailelsewhere7 is shown in Figure 1. It consists of: (i) a gas Cerenkov counter,G, having a threshold, T C = 4 0 ; (ii) scintillators SI and S2 each of 0.625 cm thickPilot Y; (iii) a stack of multiwire proportional chambers, MWPC, with a spatialresolution in the cathode coordinate of %200um8, and (iv) scintillators PI-P7 eachof 0.625 cm thick Pilot y and e?.ch separated by £1.2 radiation lengths of leadforming a shallow shower counter of %7 radiation length. The signals from SI, sr,Pl-P/ and G are all pulse height analyzed. The magnet was operated at a curren'of 120 amps producing a magnetic field of £40KGauss at the center of the coil.
*NASA-NRC Sr. Postdoctoral Resident Research Associate on leave from TataInstitute of Fundamental Research, Bombay, India.**NASA-NRC Postdoctoral Resident Research Associate.
156
Only events satisfying the trigger SIPI P7 were accepted for analysis.This mode has a useful geometry factorof % 315 cm2sr. Events were selectedby requiring that (a) they representa single particle traversal throughall MWPC, (b) the particles have adownward direction of motion asdetermined by the time of flightbetween SI and PI. (c) the chargedetermined by SI, 52 and PI 1sconsistent with Z=l or Z=2.
The MWPC chamber alignment is madeusing a multiparameter minimizingroutine to obtain best straight linesto tracks of a larg« number of sea-level muons which trigger the gasCerenkov counter when the magnet isoff. We define magnetic deflection,D, as the inverse of a particle'srigidity: Since D is proportional tothe measured spatial deflection, itis an appropriate parameter for usewith magnetic spectrometers. Thedeflection distribution for themagnet-off muons gives the errordistribution due to position measure-ment and Coulomb scattering errors.It is important to note that becausethe /Bxdl_ varies by a factor of tenin the spectrometer, the error func-tion is not a Gaussian. Ideally, onewould like to obtain this error func-tion in flight with the magnet off;however, due to prematuretermination in both flights, thiswas not possible. In order to checkthat the ground lave! error functionis applicable to the flight data, wedetermined the deflection distributionof helium nuclei which triggered thegas Cerenkov (cut-off rigidity -v80 GV).By folding (i) the experimentallydetermined gas counter efficiency asa function of momentum of sea-levelmuons, (i1) the error function deter-mined using sea-level muons and (iii)assuming that the helium nuclei have apower law rigidity spectrum R"2-8
above 80 GV, we computed the expecteddeflection distribution of these highrigidity helium nuclei. A comparisonof the expected and observed distri-bution is given in Figure 2 for the
0
Figure 1 - Magnet Spectrometerdetector array.
Magnetic deflection (GV
Figure 2 - Calibration data,.May 1976flight.
157
Hay 1976 flight. The offset betweenthe two distributions is -0.001 ±0.002.In the September 1975 flight, thisoffset was 0.008±0.003.
3. Results3.1 The "Proton Component. Thedeflection distribution for Z=levents is shown in Figure 3 for theMay 1976 flight. The deflectiondistribution in the interval 0.11 to0.01 GV"1 has been fitted to a powerlaw in deflection of the formG(D) = ADY"2. In the fittingprocess, the experimentally deter-mined error function and offsetwere convoluted with the power law.The best fit power law has an indexof 2.74±0.05 (September 75) and2.83+0.04 (May 76). The fits have ax2 of less than 0.9 per degree offreedom. The errors here include theerror in determining the flight off-set. Since the two flights give thesame spectral index within errors theresult can be combined to yield aspectral index of 2.78+0.03. Thisspectral index is steeper-than theindex of 2.63±0.08 obtained bySmith et a!.6 but agrees with theindex of 2.75+0.03 obtained by Ryanet al.5 in the 50-1000 GV range.
Figure 5 gives a comparison of theabsolute flux x R* 2-" for the May1976 flight with the data of Smithet a!.6 and Ryan-et-al.5 There aresystematic uncertainties 1n theselection efficiency, dead time andgeometry factor; these systematicerrors are no greater than 15%.Figure 5 clearly shows that our resultis in better agreement with that ofRyan et al.5 than with Smith et al.6
The resulting absolute differentialrigidity spectrum is J(R) = (1.91±.28) 10" x R-2-78+0.0* (mz sej: s r
GV)" 1 for rigidities above 9 GV. Wefind the integral flux above 10 GV is178+27 (m2 sec sr GV)" 1. This can becompared with the value of 203±40(m2 sec sr GV)"1 by Ryan et al.5,203+10 (m2 sec sr GV)" 1 by VonRosenvinge et al 1 and of 140±14 (m2sec sr GV)"1 by Smith et al.6
Figure 3 - Observed deflectiondistribution of Z=l particles fromthe May 1976 flight.
Figure 4 - Observed deflection distri-bution of Z=2 particles from theMay 1976 flight.
Mill i i i i
a tA AA
Mill
20 h
18
16
14
10
i- 9
iJ L L
101
• Anancl, et al
A Badhwar, et al
• Ryan, et al
A Smith, et a'
• This work
TTT
I I I I I I I
Iff
Rigidity iCVi
Figure 5 - Particle fluxes vs rigidity. Note the 1=2 data of Ryan et al.5
have not been shown in detail. Their data falls in the band illustrated inthe upper figure.
159
3.2 Helium Nuclei. The deflection distribution of Z=2 events is shown inFigure 4. The solid curve is the fitted spectrum with an index of 2.82±.O4(where the error includes the error on the offset). In September 1975, we findthat Y=2.78±0.05. The combined result gives r=2.80±0.03. The absolutedifferential spectrum is given by J(R)=(3.43±0.5)103 x R-2.8o±o.O3 (m2 sec srGV)" 1. Figure 5 shows the comparision of various measurements. Note thisgenera] good agreement between all of the measurements. Table I is a comparisonof the integral flux above 8.3 GV and the spectral index obtained by variousgroups.
Table I
Y
RigidityRangein GVIntegralflux>8.3 (m2
sr sec)"1
Anandet al.1
2.74+.15
12-40
40+2
Badhwaret al.2
2.54+.08
8-26
41+1
Ryanet al.5
2.77+.05
20-800
Smithet al.6
2.47+.03
8.3-100
38.6+2
Vermaet al.1*
2.8±.15
22-150
Present
•3- ^ H
9.0-100
We also note the integral flux of Von Rosenvinge et al.3 of 40+1 (m2 sr sec GV)"1
is also in agreement with these observations. We also find that the heliumspectral index of 2.82 can be continued down to 6.25 GV if a solar modulationcorresponding to a deceleration of « = .3 GeV/n for May 1976 is assumed. Thisfit has a x2 of 0.7 per degree of freedom. Note that the x2 for the fit ofSmith et al.6 was 1.4 per degree of freedom.
3.3 The Ratio a/p. The difference in the proton and helium spectra can be moreeasily displayed by plotting the a/p ratio as a function of deflection (seeFigure 6). There is no evidence of a change in this ratio between 6.25 GeV and100 GV. The least square fit yields an index of -.01+.01 and 0.036±0.02 in theMay 76 and September 75 flightsrespectively. We note that display-ing this effect in terms of a ratiohas the virtue of removing allinstrumental biases which are commonto both Z=l and Z=2 particles. Weconclude that the difference of
- Yp = 0.02±0.02 and thus withinthe experimental uncertainty the twocomponents have identical slopes.
3.4 The Ratio 2H/p. The fraction ofZ=l particles witn rigidity between50-80 GV agrees well with the frac-tion predicted from sea-level ntuonmeasurements assuming all Z=lparticles are protons. Since 2H inthis rigidity interval would lowerthe fraction of G triggers, we havededuced an upper limit of 10% on 2H/pat an energy per nucleon of -v35 GeV/n.
Figure 6 - Helium/proton fluxratio as a function of deflection
160
Events with / B.dl >_ 4 from the September 75 flight corresponding to a maximumdetectable momentum of K 200 GV were used. We hope to add the May 76 data soon.This limit is well below that required by Adair9 to explain the u /u" ratio.
4.. Conclusion. We have determined the rigidity spectra.of protons andhelium nuclei in 9 GV to 100 GV range and found them to be the same with anindex of <\,2.78. We have also placed an upper limit on 2H/p of 10% at 35 GeV/n.
References1. K. C. Anand, R. R. Daniel, S. A. Stephens, B. Bhowmik, C. S. Krishna,
P. K. Aditya and P, K. Purl, Canadian J. of Physics 46, 5652, 1968.2. G. D. Badhwar, M. F. Kaplon and D. A. Valentine, J. tiibphys. Res. 76,
4224, 1976.3. T. T. Von Rosenvinge, W. R. Webber and J. F. Ormes, Astrophys. and Spa.
Sc1. 5,, 342, 1969 and 3., 4, 1969.4. R. P. verma, T. N. Rengarajan, S. N. Tandon, S. V. Damle and Yash Pal,
Nature 240, 135, 1972.5. ft. J. Ryan, J. F. Ormes and V. K. Balasubrahmanyan, Phys. Rev. Letts. 28,
985, 1972. ""•6. L. H. Smith, A. Buffington, G. F. Smoot, L. W. Alvarez and W. A. Wahlig,
Astrophysical J. 180, 987, 1973.7. R. L. Golden, G. DT~Badhwar, J. Lacy and 0. E. Zipse, Nucl. Inst. and
Methods, 1977.8. Chambers Ml, M3, M4, M5 were used during the September 75 flight and all
chambers M1-M8 were used during the May76 flight.9. R. K. Adair, Phys. Rev. Letts. 33_» 1 1 5» 1974-
191
105
2
1 .
.5
. 2
.1
"GTI
•
- < ELECTIONS_ "X.. 1970 •
\\
•Ni i
105
2
i•
.5
• 2
m _I_
10 100 1000 /10 100 1000
KINETIC ENERGY [Mev] / KINETIC JBNERGY
Pig.l.t Magnitude of modifying /effects« /a/ increasing effectof spectral shape /dashed line/ and /b/ decreasing effect ofconvection /dotted line/. Pull line shows the resulting ratioof cosmic ray intensity to tttat obtained from force-field.Solid line /G.U./ indicates Ahe ratio obtained by numericalinvestigation ©f Gleeson and Urch /1973/.
Inspection of Pig.l a/owa that the predicted ratios de-scribe the general character of those obtained by Gleeson andUrch /1973/, although the/present calculation seems to over-estimate the deviations rom unity.
•sotropy. in the preafent model, in contrast to the force-ield solution, gradieftts of <po and <p, give rise to radialstreaming, too. The calculated anisotropy
is directed outwttude, however,
-Ftt)• /c /22/
if P>P--, and inward if P<P--. Its ampli-ains Xi below 0.03 per cent.
A technique based on time-reversal and determiningthe moments of rfnergy loss has been presented. Deviations fromforce-field solution are qualitatively well described. Toachieve quant^ative agreement further refinement and consi-dering higher/momenta are needed.
Referencest
Pisk, L.A./ Axford, W.I. 1969, J. Geophys. Res., 74, 4973Gleeaon, 2.J., Axford, W.I. 1967, Ap. J., 149, L115Gleeeon,/L.J., Axford, W.I. 1968, Ap. J., T** ••"•-Gleeson/L.J. 1971, Astrophys. Space Sci.,Glaannn/ T.-.T. Il-nnV. T H 1973 ""^ '
1011471e Sci., 2£, 387
192
KINEMATICAL ANISOTROPY OF NON-COHERENT RADIATION
A. Geranios and N.J. Martinic
Max-Planck Institut fur Kernphysik,
Heidelberg, Fed. Rep. Germany .
The anisotropy of a radiation flux ( of particlesand waves) that arises from a change of systems of re-ference when both are intertial is investigated. A com-pact form of the anisotropy as a function of the directionaround the relative velocity between the frames of reference,the physical parameters of the radiation, and the solid angleof the directional detectors is given. A comparison with thecurrent Compton-Getting effect formulae is discussed.
1. Introduction. The motion of a detector affects the intensity of cosmicradiation that is supposed to sense. This motion can be defined with respectto the cosmic isotropic radiation. The above anisotropy that comes from a kine-matical origin competes with another anisotropy that may appear from dynamicalsources, i.e. due to space-time energetic changes by four potentials of thecomponents of the cosmic ray gas. The general anisotropies that appear in timeprofiles of the data come then, concurrently from acceleration mechanisms ofparticle radiation and gravitational interaction with the cosmic radiation aswell as from relative motion between systems of reference.
The interplanetary stationary background radiation in a frame moving withthe solar wind is particularly important, due to our understanding of the trans-port process of the particle radiation. The current formula for the anisotropy,without taking into account the anisotropies from diffusive origin, of the in-terplanetary radiation is given by Cleeson and Axford, 1968, and Forman, '1970.
The general feature of the anisotropy that arises from relative motiondetector-background radiation is an increase of the intensity,J, in the direc-tion of the bulk velocity of the radiation as seen by the detector, providedthat the exponent of the isotropic radiation power-law spectra remain smallerthan a fixed number (2 for relativistic gas and 1 for non-relativistic one).The amplitude of the anisotropy in the relativistic gas (less than \X for cos-mic rays) is proportional to the ratio relative velocity and the velocity of theparticle that forms the radiation. For non-relativistic gas the anisotropy ex-hibits dramatic fluctuations of the mean intensity.
Quantitatively we define the differential directional intensity of partic-les or photons as the undirectional rate of radiation passing through an unitof area normal to the direction of incidence when the radiation has energiesin a range dT+T and T. Obviously this definition is not covariant due to thequantities used to-define it. Covarian tly the intensity, J, comes from thefour-vector particle flux (Lindquist, 1966) that in an inertial system coin-cides with the standard flux across a unit area nomal to the momentum per unitsolid angle and unit total energy.
2. Anisotropies of the cosmic ray gas. In order to explain part or all ofthe observed anisotropies in the cosmic radiation it has been introduced an*angle dependence around a 'fixed' direction of the intensity of the gas.<• -Thisrepresentation of the generally observed anisotropies is sufficient to para-metrize anisotropies of kinetnatical origin. A superposition of more than one
193
direction would need another 'spatial' angle to represent the anisotropy.We Bumnarize the experimental data. For particle radiation in the energy
range 1012 - lO1^ eV, the sideral anisotropy, i.e. a streaming of cosmic radia-tion in a direction fixed in the galactic space, has an amplitude of le-s thanO.IX (Fenton,' 1975). In what follows we call amplitude, in a fixed direction,the ratio between the semidifference and semi sum of the intensity of the radia-tion in the above direction and its antidirection.
The direction is defined when such an amplitude is maximum. We talk oftenof phase instead of direction, when the streaming of cosmic rays remains in aplane. For underground detectors which are effected by primary particles withthreshold energies of equal or larger than 17 GeV, the sideral anisotropy thathas the same amplitude as before reveals variable phase from year to year(Swinson, 1971 and 1976). The basic difficulties of the data treatment in thisenergy arise from a seasonal modulation of the solar anisotropy, i.e. the mea-sured sideral anisotropy may not be genuine. The sideral anisotropy in thesecounters present a component with phase at 18 hr ST ( local sideral time, thatis to say, we have, synchronized the aideral clock with the solar time at 00 UT.during the autumnal equinox). Another component of the sideral anisotropy has .a phase of 06 hr ST or, 12 hr out of phase with respect to the former component. :(For this two-way anisotropy see Jacklyn, 1966). [To feel these phases in our context of relative frames we indicate that the jmotion of our solar system is roughly directed toward 18 hr ST. (a= 18 hr, \5 » 30°). Swinson, 1971, claims that one is to sense with threshold energies iof 100 GeV to avoid the marking effect of the solar modulation when working !with underground telescopes. >
In the range of neutron monitors (threshold rigidities, 1 GV) and with me- j.son telescopes the solar anisotropy reveals an amplitude of less than 1%. The :nucleonic component as seen by the neutron monitor network shows a well-de- ,fined phase at 18 hr LT, i.e. a macroscopic anisotropic streaming overtaking ;the terrestrial kepplerian motion around the sun. (See Pomerantz and Duggal, j1971). i
The particle anisotropies whose time profiles reveal a much larger ampli- Itude than \X, depend on their spectra and are related with the microscopic, ii.e. local, electromagnetic configuration of the interplanetary cavity. Satel- jlite data of these events starting with proton energies of I MeV and electron !ones of 40 keV are available, and some phenomenological classification as a jfunction of their time scales has been attempted. (See McCracken and Rao, 1970). •
For photon radiation the anisotropies are of the same order as before, [viz. less than 1Z. The 3°K background radiation exhibits the streaming in the jdirection 13 hr ST. (Conklin, 1969). The X-ray background with energies ofaround 10 keV has been measured by Schwartz, 1970.
3. Distribution functions. To define covariantly the distribution functionin order to deduce the gas flux we use a quasi-Euclidean frame which is locallyat rest with respect to streaming of the gas. The phase space is then the tan-gent bundle over the space-time manifold. The distribution function of the cos-mic ray gas, F(ft,fk), is the ratio between dN particles which cross a volumespace-like element dV at x, whose four-momentum is p and the hypersurfaceelement dP in the momentum space.
dN = F(x,p-)(-p\m)dVdP (I)
The scalar product fi.m in the quasi-Euclidean space is needed in order to makeF independent of the unit time-like vector ffl that is perpendicular to dV.Choosing m =0,0,0,0) we obtain
dN = F(x,p) Ep d£ dfi dV (2) :
The corresponding particle flux, $, across a unit, area normal to p, is :
194
/p dP F = ;p p dF dfiF (3)
(cf. Lindquist, 1966).4. Lorentz transformation. The flux four-vector d $a ( « = 1,2,3,4) per
unit of solid angle as well as for an energy window dff is
pap F dff (4)
where, as before p c 2 = E 2 - Eo and the £ o the rest mass of the particles ofthe gas.Let E two systems of reference; one is related to the other via a three
velocity Be. The components of the four-vectors p a or d<j>atransforms as followsunder the Lorentz homogeneous group.
<P±), = Y « P ,
( P + ) X = (pjj.(5)
E. ->,)
The 1 and the J_^symbols mean the components parallel and perpendicular tothe three-vector B.^ ^If we call u = (B.p )/Bp and £ = RE /cp as two dimensionless parametersfrom (5) we ~ obtain ~
P = (in2 ( $1 + B2 »l ± 2 ^ VJ ) (6)2 -1/2
Y in (6) is the Lorentz factor, y = (1-B ) . Equation (6) converts into thecosine theorem in the non-relativistic limit, i.e. y = I and tir- = 0. Similarlyto (6) we obtain for the flux per unit of solid angle end energy
2 2 2 ''2
F p d£ dfi = F p d£ dfl (1+Y (••••)) (7)
Assuming the direction B as the only source of an isotropy we can callda + = 2ndy± , and from (5)
dn = dfi_ Y(i± C P_ *V + 2C3/2
(8)
(9)
calling J± =we obtain
(10)
If we assume that 1 is the system in which the background radiation is iso-tropic, i.e.
->J.(P+,E (p ))= J.(£~.) , and assuming
J +(£ +)^T +E , where T is the kinetic energy, then
J_(p_,£_(pJ) = J+J£_) J2U_ u_) (11)
dropping the minus subscripts we obtain for a relativistic gasO-. c 1 —^ 1 1 •> O ~2
(12)
where n
195
and for non-relativistic cosmic ray gas
The above formulas are also valid for photons with a power-law spectrum equalto v~ e(cf. Schwartz, 1970). In such a case 5 = S and the expression (6)re-duces to the Doppler effect, and
,-(2+e)J2(photons) = ( Y ( 1 + B U ) ) (14)
5. Discussion. The current approximations (Gleeson and Axford, 1968;Forman^ 1970; Balogh et al. 1973; and Ipavich, 1975) coincide with the one de-rived from the exact formulas (12) and (13), except for the low energies, atthe order claimed by these authors. For non-relativistic gas one should addthe term (5y2_i) £- to the expressions obtained by Balogh et al., and Ipavich.However, due to the form of (13) the 0(52)-approximation is sound only forH = 0 . The 0(5^)-approximation foru=* 1 for instance for e = 3 and £; = 0.2is poor.
According to section 4,we have assumed that fl is fixed in, space and y+ isthe actual cosine oE tihe angle between g and p ; the other cosine y_, isthe one between 13 and-p_.This geometrical interpretation is the source of the non-symmetry of the signs in the homogeneous Lorentz transformation formulas. How-ever, The funstion ^ ( V J - ) has to be symmetric, i.e. independent of the signof the moving frame, if"written as a function of the direction of motion ofeither frame I + or Z^ when assuming one or the other as the moving frame wherethe measured radiation is isotropic. This is the case if one uses u = ± u t inJ2 and interprets it as the cosine of the angle between the unidirectional flux(the intensity) and the direction of the motion of the moving frame.
Finally we discuss the anisotropy of the cosmic background radiation (thisLime the adjectiv. cosmic means extragalactic) of =3°K. This blackbody radiationexhibits an anisotropy due to the motion of the earth in this sea of radia-tion. If we assume at Z+ that the intensity is isotropic, then
J + (P+» £+(p+)) = 3 + (.£+) = J+ (h \>+), where h is the Planck constant and v the
frequency of the photon with linear momentum p + = hv+/c. This intensity is pro-portional to the Planck photon density function measured in units of (numberof photons)/(cm sr. Hz). Then, the covariant distribution function , F+
(photons) is proportional to (exp(p+c/ki+)-|)"' where T + is the temperatureof the blackbody and k the Boltzmann constant. Using the property that F+ isscalar and with the transformation property of p + we obtain
+which is a symmetric formula in li= + p ± if tof the right hand is considered .the temperature of the moving frame where the blackbody radiation is isotro-pic. The p-dependance of the intensity is given by the y-dependance of F ifin its argument the temperature has been written by the moving blackbodytemperature given by the above equation.
Acknowledgements. We thank Prof. H.J. Volk and Dr. F.C. Jones for theiradvise and discussions. The authors acknowledge the economical support of theAlexander von Humboldt (N.J. M.) and the Max-Planck (A.G.) foundations.'
REFERENCES
Balogh, A., Webb, S., and Forman, M.A. : Planet. Space. Sci., Z\_, 18ol, (1973)Conklin, E.K.: Nature, 2 2_, 972, (1969)Fenton, K.B.: Cosmic Ray Conf., Munich, _M_, 3907, (1975)Forman, M.A.: Planet. Space Sci., 8 , 25, (1970)
196
Cleeson, L.J., and Axford.W.I.: Astrophys. Space Sei. 2, 431, (1968)Ipavich, F.M.: Geophys. Res. Lett., l_, 149, (1974)Jacklyn, R.M. : Nature, jMJ.» 69o> U966)
: Ann. Phys., 2tf, 487, (1966), and Rao, E.R.: Space Sei. Rev., J_l_, 155, (1970), and Duggal, S.P.: Space Sei. Rev., J^, 75 (1971)Ap. J., J£2, 439, (1970)J. Geophys. Res., 13, 2075 (1976)
Lindquist, R.W.McCracken, K.G.Pomerantz, M.A.Schwartz, D.A. :Swinson, D.B.:Swinson, D.B.: J. Geophys. Res., 7£, 4217 (1971)
241
GLE-1 event is seen in Case (b) and is not seen/ in Case (a).
This confirms that this event is caused by lower energy particlf
(from solar origin) reaching only stations in po^r regions.
(5) PI-1 event is evident also in Case (a). Thisr confirms that
this event is caused by a modulation of galactyc cosmic rays. It
is concluded from estimation of amplitude and direction of the an-
isotropy that, for this event, the higher enerrgy particles deviate
eastward from the Earth-Sun (E-S) line largafr than the lower ener-
gy particles and its amplitude of the anisytropy is smaller than
that of the lower energy particles.
(6) It is clearly seen that FD-2 event id accompanied with large
N-S and longitudinal anisotropies in both Case (a) and Case (b).
It is concluded from estimation of amplitude and direction of the
1oncitudinal anisotropy that the higher energy particles deviate
largely from the E-S line, its maximyfm amplitude is smaller,.and
the time of maximum amplitude is delayed, in comparison with the
lower energy particles.
(7) PI-? event is also evident in/both Case (a) and Case (b). It
is clearly seen that this event is accompanied with N-S and longi-
tudinal (sunward) anisotropies,/as pointed out by many workers.
Acknowledgments. We thank Professors H. Elliot, A. J. Somogyi,A. G. Fenton and D. B. Swins/n for sending us their undergrounddata before publishing. We attso thank Prof. Nagashima and Dr.Fujimoto for calculation of/the coupling ceofficients for us.Thanks are due to the Dire/tors of the cosmic ray stations atwhich the cosmic ray data/ised in this study were obtained.
References.
K.fi.Bemalkhedkar, L .V.Kargathra , U.R.R e s . , 79 , 2269, 1974.
A. Inoue, K. F.urakami,id K. Nagashima, Proc . I n t . Symp. on HighModulation, 1-8 Aug. 1976, Univ
/Freeman
Agrawal ,S .P . , A.G.Ananyn, ARao and H. Razdan, J . y&eopysFuj imoto, K., S. YasuK. Kodama, I . Kondo
Energy Cosmic RTokyo, ?15 ,
Kedrano, R.A., C.JRes., 80, 1735^, 1975.
Nagashima, K., Rep. Ionos. Space Res. Japan, 2_5, 189, 1971.Rao, U.R., Space/Sci. Rev., 19, 533, 1976.Takahashi, H"., y. Chiba, K. Fujimoto, S. Yasue and ¥.. V.'ada, Pvoc.
Int. Cosndc/Ray Synp. on Hirh Knerpy Cosmic Ray Kodulation,l-P Aug. 1»76, Univ. of Tokyo, Tokyo, ?15, 1976.
V.'n-i • Data Ce/ter A for STP, Rer>. UAG-PB, Pt.II, Boulder, 1973.
of Tokyo,
, H. Hills and R.R.Vondark, J. Geophys.
242
SIDEREAL VARIATIONS AT 365 hg can"2 UNDERGROUND ANDINTERPLANETARY MAGNETIC FIELD DIRECTIONS
A.G.Fenton, K.B.Fenton and J.E.HumblePhysics Department, University of Tasmania,Hobfirc, Tasmania, Australia 7001
Abstract ' ::
Sidereal variations observed by the Poatina underground muon detectors |are analysed according to the inferred directions of the interplanetary Jmagnetic field. The results for the years 1972-76 are interpreted in terms \of a possible solar influence on primary particles of median energy about1000 GeV.
1. Introduction
It has been known for some years that the diurnal intensity variationsobserved in sidereal time by auon detectors at moderate depths undergroundshow a marked dependence on the direction of the interplanetary magneticfield (Swinson 1969, 1971; Humble et al.,1973). Thus, if a genuinesidereal anisotropy exists outside the region of influence of the Sun, theeffect is contaminated by processes occurring in the interplanetary fieldmaking it difficult to draw reliable conclusions concerning the direction andmagnitude of any cosmic ray anisotropy which might exist in our part of thegalaxy. In an attempt to obtain further information on this problem wepresent below the results of an analysis of data obtained at a much greaterdepth underground, where the median primary cosmic ray energy responsible forthe observed rauons is believed to be about 1000 GeV. A definitive result atthese energies would have an important bearing on the interpretation of thephenomenon: A relatively low cut-off observed fcr the solar influence wouldassist in distinguishing between the models proposed for the interplanetaryfield directional effect, and the existence of such a cut-off would giveconfidence when interpreting the sidereal daily variation above this energy interms of interstellar or galactic processes.
2. Observations
Interplanetary magnetic field (ipmf) directions inferred from polar..isnetometer records as proposed by Svalgaard and others (Svalgaard 1972a,iy72b; Wilcox et al., 1975; Solar Geophysical Data Bulletins) have been usedLO select days according to whether the ipmf vector was inwards or outwards .relative to the Sun. The two sets of data were harmonically analysed foreach year from 1972-76 inclusive, and for the whole 5-year period. The datawere obtained from the wide angle vertical muon detectors.totalling 3 m2
sensitive area located in an underground hydro-electric power station atPoatina, Tasmania (about 125 km north of Hobart - Fenton, 1976a). The
:••/
243
Ohrs0-1 %h
Flg.l Poatlna 365 hg cnr*mean sidereal diurnalvariations.
Fig.2 Poatlna 365 hg cm~z
annual mean sidereal diurnalvariations.
0 • 1 %
244
results are shown in Figure 1 and Figure 2. In Figure 1 the error circlesindicate the standard deviation obtained from the scatter of the dailyvectors.
3. Discussion
The mean sidereal diurnal variations (Figure 1)- are not sufficientlysignificant statistically to draw any definite conclusions; however, it maybe noted that the amplitude of the observed variation in the OUT direction islarger than that for the IN direction, i.e. in the same sense as is observedat shallow depths (Humble and Fen ton, 1977). The times of maximum for bothvectors are in agreement with the overall sidereal diurnal variation,independent of ipmf direction (Fenton, 1976b). The annual mean siderealdiurnal vectors shown in Figure 2 appear to show greater consistency in thetime of maximum for the OUT direction than for the IN direction, againsimilar to the behaviour observed at shallower depths.
In view of the poor statistical accuracy of the above results arisingfrom the relatively low counting rate of the muon telescopes, we do not feeljustified in attempting an interpretation in terms of models such as thosediscussed In the next paper (Humble and Fenton, 1977). Our conclusion isthat the results indicate some doubt as to whether the primaries responsiblefor muons observable 365 hg cm""2 below ground level are sufficiently freefrom solar influences to enable the magnitude and direction of any genuinesidereal anisotropy to be inferred with confidence.
4. References
Fenton A G (1976a) Proc.Int.Cosmic Ray Symposium on High Energy Cosmic RayModulation, pp. 92-93 and A25, University of Tokyo
Fenton A G (1976b) Proc.Int.Cosmic Ray Symposium on High Energy Cosmic RayModulation, pp.308-309, University of Tokyo
Humble J E and Fenton A G (1977) - Paper MG110, 15th Int.Cosmic Ray Conf.Plovdiv. This volume.
Humble J E, Fenton A G, Speller R D, Otaola J A, Thambyahpillai T, Dutt J C,Mathews T, Miyazaki T and Peacock D S (1973) Paper 037, 13th Int.Cosmic Ray Conf. Denver, Conference Papers 2, 976-81
Svalgaard L (1972a) Paper R29, Geophysical Papers, Danish MeteorologicalInstitute
Svalgaard L (1972b) J.Geophys.Res. JT_, 4027-34Swinson D B (1969) J.Geophys.Res. 7±, 24, 5591-98Swinson D B (1971) J.Geophys.Res. 76, 19, 4217-23Wilcox J M, Svalgaard L and Hedgecock P C (1975) J.Geophys.Res. jJO, 3685-88
303
Acknowledgement • Research reported here was suppoit-. J in p/rt by theAtmospheric Sciences Section of the National Science Foundation undergrant ATM 74-16328. Author's travel to this meeting is made possible inpart by the generous support received from the University of New Mexico,the Cosmic Ray Commission of the International Union of/Pure and AppliedPhysics, and the National Organizing Committee of this Conference. Iwish to express my deep gratitude to all of them.
References•
Abies, J. G., McCracken, K. G., and Rao, U. R., 19615. Paper tfMOD-19,Proc. Ninth Intern. Cosmic Ray Conf., London,A, 208. Publishedby the Institute of Physics and the Physical Society.
Ahluwalia, H. S., Escobar, V. I., Zubieta, M., Anfla, R., Schreier, M.,and Troncoso, 0., 1965. Paper #M0D-13, Prat. Ninth Intern CosmicRay Conf., London, 1_, 190. Published by t/e Institute of Physicsand the Physical Society.
Ahluwalia, H. S., and Ericksen, J. H. 1970. B&per #M0-70, Proc. EleventhIntern. Cosmic Ray Conf., Budapest. Acba Phys. Acad. Sci. Hungaricae,29 Suppl. 2, 139.
Ahluwalia, H. S., 1971. Paper #M0D-30, Twelfth Intern. Cosmic Ray Conf.,Hobart.'Conference Papers (University/of Tasmania), 2., 641.
Ahluwalia, H. S., and Ericksen, J. H., 19m. J Geophys. -Res., 76, 6613.1973a. yPaper #466, Thirteenth Intern.
Conferen/e Papers (University of Denver),
1973b/ Paper #468, Thirteenth Intern.Confei^nce Papers (University of Denver),
Ahluwalia, H. S., and Singh, S.Cosmic Ray Conf., Denver.2, 948..
Ahluwalia, H. S., and Singh, S.Cosmic Ray Conf., Denver.5, 3129.
Ahluwalia, H. S., 1975. Paper #HG9-i, Fourteenth Intern. Cosmic Ray Conf.,Munich. Conference Papers (Ma/-Planck-Institut fur ExtraterrestrischePhysik), 12, 4215.
Castagnoli, C. G., Marocchi, D., Elliot , H., Marsden, R. G., andThambyahpillai, T., 1975. Fourteenth International Conference onCosmic Rays, Munich. Confe/ence Papers (Max-Planck Institut furExtraterrestrische Physik)/ 4_, 1453.
Dorman, L. I., 1957. Cosmic Raly Variations. Published by State PublishingHouse for Technical and Theoretical Literature, Moscow.
Marsden, R. G., and Elliot, VI, Hynds, R. J., and Thambyahpillai, T.,1975. A preprint from /mperial College.
Rao, U. R., and AgTawal, S.W., 1970. J. Geophys. Res., T5_» 2391.Regener, V. H.. Swinson, D./B., Tricksen, J. H., and Ahluwalia, H. S.,
1970. Paper #M0-]51,/Proc. Eleventh Intern. Cosmic Ray Conf., Budapest.Acta Phys. Acad. Sci/ Hungaricae, 2£, Suppl. 2, IS".
Swinson, D., 1974. J. G/ophys. Res., 79, 36S5.
iH) CORONAL HOLES INFLUENCE COMMII K\I DAILY HARMONICS?
H. S. Ahluwalia
Department of Physics and Astronomy, The University of New Mexico,Albuquerque, New Mexico, 87131, U.S.A.
Coronal holes are identified by their low emissivity ineither EUV (Munro and Withrobe, 1973) or in X-rays (Krlegeret al, 1973a). They are seats of unidirectional magneticfields. Also, high speed solar wind streams originate inthem (Krieger et al, 1973a,b; Neunert and Pizzo, 1974;Nolte et al, 1976). Coronal holes often extend over awide range of heliolatitudes (Timothy et al, 1975). Else-where in these Proceedings we have presented results onthe long term changes observed in the amplitudes and thetimes of maximum of the diurnal, the semidiurnal and thetridiurnal variations of cosmic rays, a+ low (neutrons)and at high (underground muons) primary rigidities(Ahluwalia, 19771. We have shown that a dramatic shift toearly hours is noticeable in the times of maxima of the har-monics during 1971-72 period. In this paper we examinethe nature of the contributions of off-ecliptic cosmicrays of high enough rigidity, streaming under the influenceof large scale ordered interplanetary magnetic fieldset up by the coronal holes, to the cosmic ray dailyharmonics. Some models are presented and discussed in apreliminary fashion.
J_. Introduction. Elsewhere (Ahluwalia, 1977) in these Proceedings wereport on the existence of significant long term changes in the amplitudesas well as the times of maxima of the three cosmic ray daily harmonics,he show that these changes are observed both for the low (neutrons) aswell as for the high (underground muons) rigidity primaries. In particularit is observed that the uncorrected (for geomagnetic bending) times ofmaximum of the diurnal variation of cosmic rays for neutrons and muonsshow a remarkable systematic shift to early hours, beginning with 1971.This change is quite dramatic and is more pronounced for muons than forneutrons. Agrawal and Ananth (1973) and Duggal and Pomerantz (1975)have reported similar results using neutron data from other stations.A drastic change of similar type took place during the deep solar mini-mum of 1954 (Possener and van Heerdan, 1956; Conforto and Simpson, 1957;Yenkatesan and Dattner, 1959; Marsden and Begum, 1959). Diurnal variationduring this period became quite erratic. For some months it vanishedaltogether. Some speculations have been made regarding this anomalousbehavior of the diurnal variation (Conforto and Simpson, 1954; Thomson,1971; Antonucci, 1974). The suggested models invoke peculiar ad hocelectromagnetic conditions that were supposedly obtainable in the inter-planetary medium durii g the solar minimum of 1954. Even so, the years'"1-72 are by no means anywhere near the solar activity minimum.
Several exciting questions can be raised, based upon the results.ia- wishes to know whether there are any solar cycle related changes in
305
tue observed properties of the solar wind and the interplanetary magneticfield which may be invoked to understand the long term changes in the
I properties of the solar daily harmonics of cosmic rays, within the frame! work of available models. Recent results reported by Gosling et al
(1976) indicate that during the period 1962-74 the annual mean solar windvelocity has remained remarkably close to 400 km/s. Similarly, Marianiet al. (1975) report that although temporal fluctuations are observedin the interplanetary magnetic field components, no clear solar cycledependence is indicated for the period 1964-73. How then to account forthe observed changes in the cosmic ray daily harmonics?
One could perhaps start with solar diurnal variation which hasa larger amplitude. Also, it has been observed over a longer period oftime. One obvious approach is to try to explain the observed drasticshift in the time of diurnal maximum in 1971 in terms of lower valuesof R . Our calculations along these lines are still in progress. Itshould be pointed out though that Agrawal and Ananth (1973) have failedto reconcile the observed shift-for the diurnal time of maximum for tin-neutrons on this basis.
It has been suggested that diurnal variation has a relationshipwith 22-year magnetic cycle of the sv "orbush, 1969, 1973). Levy(1976) has proposed a model for this • ot. We would like to verifywhether the diurnal variation ":.orv^u for underground muons conforms tothe predictions of this model, it might be added that Duggal andPomerantz (1975) claim that they have b'.-en able to explain the long termchanges observed for neutrons entirely on this basis.
Bridge (1976) and Gosling (1976) report that solar wind has under-gone a remarkable transition during the 1970-74 period. During 1973-74a well established pattern is observed of high speed streams corotatingwith the sun. It appears that 1970-72 represents the transition periodfor the solar wind. One might note here that recurrent high speed solarwind streams are related to the coronal holes (Krieger et al, 1975)which are also the seats of unidirectional magnetic fields. Hereinlies a clue for yet another approach that might he fruitful in under-standing our results. It turns out that low-latitude coronal holes arcbounded on both sides by regions of high coronal green line intensity(Bohlin, 1976). It is possible therefore that the close correlationobserved by us (Ahluwalia, 1971) between the amplitude of the diurnalvariation and the corona] green line intensity at low helio-latitudes
. is indicative of the control exercised by the coronal holes on theelectromagnetic weather in the interplanetary medium. Since the coronalholes often extend over a wide range of heliolatitudes (Timothy et al,1975), it follows that on such occasions a large scale structure ofunidirectional magnetic fields must exist in space, far away from theplane of the ecliptic. Observations have not been made yet to discoverthis large scale symmetry in the structure of the interplanetary magneticfield. One should also note that solar polar field was changing polarityduring 1969-71 period (Howard, 1974). To make the situation more in-triguing Svalgaard et al (1974) have suggested a phenomenological modelwhich indicates that an interesting relationship may exist between thepolar magnetic field of the sun and the solar sector structure. If trip
306
OFF-ECLIPTIC COSMIC RAYSTREAMING MODELS
this must again lead to a large scale ordering of the interplanetarymagnetic field. We have perhaps failed to recognize this broad symmetryin the interplanetary magnetic field because the data obtained so farare only representative of the situation close to the plane of theecliptic. It appears to me, therefore, that off-ecliptic cosmic raysmust make a significant contribution to the solar anisotropy of cosmicrays observed on earth. This effect will probably be more apparent for""high rigidity cosmic rays. In this paper we examine the nature of thiscontribution in terms of some simple models.
. Off-Ecliptic Cosmic Ray Contribution to Solar Anisotropy. Severallausible models can be constructed t j accommodate various modes of
streaming of off-ecliptic cosmic rays.These models may havevarying amounts ofcomplexities builtinto them. Let usconsider some simplemodels. FollowingSubramanian andSarabhai (1967) andQuenby and Lietti(19681, let us as-sume that a.symme-trical cosmic rayparticle densitygradient (Vn) existsnormal to the planeof the ecliptic.Some of the stream-ing patterns of off-ecliptic cosmic raysin the large scaleordered interplane-tary magnetic field Figure 1(B) are shown in Figure 1. Off-ecliptic cosmic rays will therefore contri-bute to the solar anisotropy observed by detectors located on the rotatingearth. The different modes of contributions arising from the correspond-ing models of streaming are illustrated in Figure 2. Streaming patternsfa), (b) reproduce the model of Subramanian and Sarabhai and Quenby andLietti. Clearly, a great deal of flexibility is available in accomo-dating departures of the amplitudes and times of maximum from thatpertaining to the corotational anisotropy. Various degrees of sophisti-cation can be incorporated into these models. For example, magnetic fieldsmust inevitably have some kinks in them, of various scale sizes, soscattering must result. Again, as active regions evolve on the sunthere is bound to be some large scale reordering of off-ecliptic magneticfields. Some gradients might also exist in the magnetic fields. Thenthere is the interplanetary electric field £ 'Ahluwalia and Dessler,19f2). One also notes that the plane of the ecliptic is inclined withrespect to the solar equator. In addition, one notes that the rotational:IM< of the earth is in. ' 'u'd with respect to th'e plane of the ecliptic.
307
OFF-ECLIPTIC COSMIC RAYCONTRIBUTIONS TO
SOLAR ANISOTROPY-~—"-• • INDICATES OFF-ECLIPTIC CONTRIBUTION
TO SUN _^ * TO SUN _
C.A. INDICATES COROTATIONAL ANISOTROPY
(a,b) (c) (d)
Also, the geomagnetic field is deformed. All these factors will eiverise to additional temporal effects. It should be noted here that there
• is no known reasonwhatsoever to expectthat a stable sym-metrical particledensity gradientshould exist normal »—»«-»————-—.—«•-»—-»«——»-————»—«.to the plane of theecliptic. A flexi-bi l i ty is thereforeavailable for in-troducing particledensity gradientsof different typesinto the models ofstreaming. One canthen make a de-tailed comparisonof the predictionsof the models withthe data. We be-lieve that thiseffort might leadto a unified theoryof the anisotropiesof solar origin,
which contribute Figure 2to the solar daily harmonics. Such a study might also make i t possibleto draw certain inferences regarding the broad scale ordering of theinterplanetary magnetic field and i t s temporal variation, over a solar«™ 7£ e Sc l n f e r e n c e s may b e compared with the predictions of the modelproposed by Svalgaard et al (1974). We are now in the process of for-mulating detailed plans for undertaking some aspects of this potentiallyproductive area of research.
Acknowledgement. My travel to this meeting is made possible in part bythe generous support received from the University of New Mexico, theCosmic Ray Commission of the International Union of Pure and AppliedPhysics (IUPAP) and the National Organizing Committee of this ConferenceI am deeply grateful to all of them.
References. • ' •
Agrawal S. P., and Ananth, A. G., 1973. Thirteenth Intern. Cosmic Ray, . • ' D e n v e r - Conference Papers (University of Denver], 2, 1005
Ahluwalia, H. S., 1977. Fifteenth Intern. Conf. Cosmic Rays PlovdivConference Papers, in these Proceedings
Ahluwalia, H. S., and Dessler, A. J . , 1962. Planet. Space Sci., 9, 195Antonucci, E., 1974. ELDO/ESRO Sclent. Tech. Rev , 6, 17 ~Bohlin, J. D., 1976. Phys. of Solar Planet. Environments. Proc Intern
Symp. on Solar-Terrestrial Phys., 1, 114.Bridge, H. S., 1976. Phys. of Solar Pllnet. Environments. Proc Intern
Symp. on Solar-Terrestrial Phys., .1, 47.
308
Conforto, A. M., and Simpson, J . A . , 1957. Nuovo Cim., <S, 1052.Dorman, L. I . , 1957. Cosmic Ray v a r i a t i o n s . . Published by State Publishing
House for Technical and Theoret ical Literature, Moscow.Duggal, S. P . , and Pomerantz M. A., 1975. Fourteenth Intern. Cosmic
RayConf., Munich. Conference Papers (Max-Planck I n s t i t u t furExtraterrestr i sche Ptys ik ) , 4 , 1209.
Forbush, S. E . , 1969. J. Geophys. Res . , 24, 3451.Forbush, S. E . , 1973. J. Geophys. Res . , 78, 7933.Gosling, J. T.; Asbridge, J. R.; Bame, S. J . , and Feldman, W. C , 1976.
J. Geophys. Res . , 81_, 5061.Howard, R., 1974. Solar Phys. , 3J, 283.Krieger, A. S . , Timothy, A. F . , and Roelof, E. C , 1973a." Solar Phys. ,
23, 123.Krieger, A. S . , Timothy, A. F . , and Roelof, E . C , 1973b. Solar Phys.,
29, 505.Levy, E. H., 1976. J. Geophys. Res., 81_, 2082.Mariani, F.; Diodato, L., and Moreno, G., 1975. Solar Phys., £5_, 241.Marsden, P. L., and Begum, Q. N., 1959. Phil. Mag., £, 1247.Monroe, R. H., and Withrobe, G. L., 1972. Astrophys. J., 126_, 511.Neupert, W. M., and Pizzo, V., 1974. J. Geophys. Res., 79_, 3701.Nolte, J. T.; Krieger, A. S.; Timothy, A. F.; Gold, R. E.; Viana, G.;
Lazarus, A. J.; Sullivan, J. D., and Mclntosh, P. S., 1976. SolarPhysics, £6, 303.
Possener, M., and van Heerden, I. J., 1956. Phil. Mag., 1_ (Series 8), 253.Quenby, J. J. and Lietti, B., 1968. Planet. Space Sci., ljb, 1209.Subramanian, G., and Sarabhai, V., 1967. Astrophys. J., 169, 417.Svalgaard, L.; Wilcox, J., and Duvall, T. L., 1974. Solar Phys., 3_J_, 157.Timothy, A. F.; Krieger, A. S., and Vaiana, G., 197:.. Solar Phys.,
42, 135.
Tliomson, D. M., 1971. Planet. Space Sci., 9, 1169.Venkatesan, D., and Dattner, A., 1959. Tellus, 7, 16.
333
Times of proton Increases aregiven from Slmnett 72
334
INTERPLANETARY ELECTRONS:WHAT IS THE STRENGTH OF THE JUPITER SOURCE?
Walker F i l l i u s , Wing-Huen I p , and Paul Knickerbocker
Un ive r s i t y of C a l i f o r n i a , San DiegoLa Jol la , California USA
Abstract
Because there is not enough enformation to support a rigorous answer, weuse a phenomenological approach and conservative assumptions to address thesource strength of Jupiter for interplanetary electrons. We estimate thatJupiter emits ~ 10 - 1 0 ^ electrons s~^ of energy > 6 Mev, which source maybe compared with the population of ~ 3 x 10*8 eiectrons of the same energy inJupiter's outer magnetosphere. We conclude that Jupiter accelerates particlesat a rate exceeding that of ordinary trapped particle dynamical processes.
Introduction.
Almost all non-solar electrons of energy < 20 Mev found in interplane-. ry space are produced in the magnetosphere of Jupiter. This source was.tisuspe-Lad until, as the Pioneer 10 spacecraft approached Jupiter, theelectron fluxes increased drastically within 1 AU of the planet. (Chenetteet al, 1974; Teegarden et al, 1974). It was then discovered that electronincreases previously observed in the orbit of earth were tied to the relativepositions of earth and Jupiter, and that these electrons originated atJupiter, too (Teegarden et al, 1974; Krimigis et al, 1975; L'Heureux andMeyer, 1976; Mewaldt et al, 1976). The interplanetary propagation of theseparticles has been the subject of many papers and much lively debate (Gold etal, 1976; Gold and Roelof, 1976; Jokipii, 1976; Smith et al, 1976; Chenetteet al, 1977; Conlon, 1977; Conlon and Simpson, 1977). Additionally, variousauthors have tried to deduce the existence and length of a Jovian magnetotailfrom observations of these particles (Krimigis et al, 1975; Mewaldt et al,1976; Pesses and Goertz, 1976), but there is disagreement over this interpre-tation of the data (Pyle and Simpson, 1977). In this paper we address thequestion of how many energetic electrons per unit time Jupiter supplies tointerplanetary space and we consider the significance of this number relativeto the magnetospheric source region and the particle acceleration mechanism.
Instrumentation.
We will use data from the Cerenkov counter in the UCSD Trapped RadiationDetector package on Pioneers 10 and 11. This sensor counts electrons ofenergy > 6 Mev and nucleons of energy > 480 Mev/nucleon. (Fillius andMcllwain, 1974b; Axford et al, 1976) During the planetary encounter, its re-sponse is overwhelmingly dominated by trapped electrons, but in interplane-tary space a special procedure is needed to distinguish between cosmic raynucleons and electrons. This procedure makes use of the pulse height spec-trum (3 integral channels are available) and takes advantage of thedifference in the pulse height spectra of nucleons and electrons. Let N.and E i be the counting rates in channel i caused by nucleons and electrons,respectively, so that
S. = N, + Ei i + E i (i = 1,3) ( 1 )
335
where S. is the total counting rate. Define a.. • . . / ':. and 0.. = E./ E..
Far from Jupiter E. « N., and we can determine a.. from a.. ss S./ S..
Close to Jupiter, fluctuations in the electron flux are much greater than
fluctuations in the nucleon flux, and B.. can be determined by a linear re-
gression between S. and S.; P.. =a o S./d S.. After the a's and P's have
been determined, the electron (or nucleon) counting rate in a given channelcan be evaluated by solving two of the simultaneous equations (1). DefineE.. as the electron counting rate in channel i evaluated by solving equations
i and j. One gets
(2)
There are three ways to evaluate the e lec tron counting rate of a part icularchannel; E . . , E . . , and 0 . . E . . . Because of s t a t i s t i c a l f luc tuat ions and
ij 3.K . 1J JKimperfections in the procedure, the results differ s l ightly. As these errorsare reduced by averaging the three results, the data shown in this paper arethe average of three solutions for channel 1.
Interplanetary Electron Fluxes.
Figure 1 shows the interplanetary electron fluxes obtained by using thisprocedure. Each data point i s averaged over a ten hour interval. The periods
INTERPLANETARY ELECTRONS FROM JUPITER
UCSD CERENKOV COUNTER
ELECTRON ENERGY >6MeV
1972 1973 1974 1975
r
2 £4o S j
r0 L
1976
1972 1976TT1F 4,5 007
336
used to determine the a's and the S's are marked by horizontal bars. The nuc-leonic background typically corresponds to ~ 5 cm'^g-lj aiui the apparentlynegative electron fluxes are due to the limits of resolution of the subtrac-tion procedure and statistical fluctuations. The data record starts at launchand continues through encounter with gaps for several solar particle eventsand the Jovian magnetosphere. Gain changes ( ~ 10%) occurred in the detectorsat encounter, but these have been compensated for. The planetary encounteroccurred in December, 1973 and December, 1974 for Pioneer.10 and Pioneer 11respectively, and the two smooth reference lines superimposed on the data areinversely proportional to the distance between the spacecraft and Jupiter.It is clear that the appearance of electrons at the spacecraft is variable andimpulsive, but the intensities are highest near encounter.
Figure 2 shows the electron fluxes plotted vs distance to Jupiter on log-log coordinates. Some of the impulsiveness has been smoothed out by taking
RADIAL OISWNCE FHo« JUPITEH («ii running 27-day averages, and the in-0Q5 oi os iQ so bound and outbound passes for both
ELECTRONS OF JOVIAN ORIGINM
RADIAL DISTANCE FROK JUPITER
27-DAY RUNNING AVERAGESELECTRON ENERGY >6MtVUC5D CERENKOV COUNTER
i 10°
spacecraft are plotted together. Itis clear that a 1/R dependence (whereR is the distance from the observationpoint to Jupiter) describes each passwell. A 1/R-dependence has previouslybeen noted for the peak fluxes byChenette et al (1974) for Pioneer 10inbound, and by£yle and Simpson(1977). Because of negative excur-sions after nucl^eon subtraction thisplot cannot be extended beyond ~ 2 AUfrom Jupiter, but as mentioned in theintroduction, £here is plenty of evi-dence that the electrons extend as faras the earth's orbit. Using simultan-eous data from Pioneer 11 and earth-bound Imp 7, McDonald and Trainor (1(1976) deduced an intensity gradientof ~ 150%/AU betveen the two space-craft. Being a two-pointobservation, this gradient can as wellbe quoted as a power law, and their
result is equivalent to a 1/R-dependence also.
RAOIAL 0I5TANCE FROM JUPITER ( R J
Figure 2
The two dashed lines are the same reference lines seen in Figure 1. Thedata from three of the four passes are intertwined and are equally well rep-resented by a single line, while the Pioneer 10 outbound data are clearlyhigher by about a factor or two. Although it is incidental to our argument,this difference is certainly attributable to a better connection via the pre-dominantly azimuthal interplanetary field lines between the source region andthe spacecraft on the dawn side of the'planfet. What is significant to us isthat there is bad connection on the other three passes, in which the space-craft are more or less radially upstream of Jupiter in the solar wind, wherethe electrons must propagate across the interplanetary field lines.
The Source Strength.
It is impossible to get a firm value for the source strength without
337
more data or a full understanding of the propagation characteristics andparameters. However, by combining a phenomenological approach with conser-vative assumptions, we arrive at a value which suggests a significantrelationship between the source strength and the population of the outermagnetosphere:
> population of the outer magnetospheresource strength RJ I_I . z I
rotation period of the planet
Because of the simplicity of our approach, we believe this relationship willstand even after the numbers have been refined or changed using betterknowledge.
The simplest approach to the source strength is to estimate the numberof electrons in interplanetary space and divide by their residence lifetime.For the spatial distribution of electrons we choose the 1/R-dependence shownin Figure "3:
• P(R) = JQ /c^/lOORj ) ; 5 < JQ 13 c m ' V 1 (3)
where J is the time-averaged omnidirectional flux. Now these measurements.weremaSe on the dawn and daylight sides of Jupiter, but not over the polesor on the dusk and night sides. However, the noon side should be the mostdifficult for the electrons to get to, and so it is reasonable to suppose thatthe noonside profile is a lower limit. Furthermore, there is only a factor oftwo difference between the relatively accessible and inaccessible profilessampled, and this is a minor factor. Equation (3) is thus a conservativeestimate based on what information we do have. Integrated over a sphere outto the noise threshold of our data at 2 AU from Jupiter, this density profileyields an estimate of ~ 10 3 0 particles, and to 5 AU, ~ 1031 particles.
To proceed to the source strength, we need to divide by the particles'sresidence lifetime in the integration volume. The impulsiveness of the datain Figure 1 gives a hint, but a better measure is .provided by a solar eventwhere the sourc^is known to be a delta function in time. Electrons gener-ated in the*4j*£ust, 1972 solar flares were monitored by Pioneer 10 at 2 AU,and they decayed exponentially with a lifetime of ~ 1.5 days. Using thislifetime we^estimate that the source strength is ~ 1 0 ^ - 10^6 electronssecond"^.
A second approach to the source strength is to imagine a surfa.ce enclos-ing the Jovian magnetosphere and to estimate the net flow of particlesoutward through that surface. This flow can be expressed by the integral
I JQ ? A (4)
where 9 is measured, from a normal to the surface and ? is the anisotropy withrespect to the surface normal. Only in the Pioneer 10 outbound pass was ourdetector oriented so as to measure | . From a preliminary analysis, theaverage value is about 6% near Jupiter, and it decreases as the spacecraftrecedes from Jupiter. If we use this value for the average anisotropy, takethe average omnidirectional flux from equation (3), and integrate over asphere at lOORj, the result is a source strength of ~ 10 electrons s"1.
338
If electrons are channeled out of the magnetosphere is some preferentialdirection (e.g. from the polar caps ~, or down the magnetotail), our spacecrafthas probably missed the main stream. Then our recourse is to take the surfaceof integration out so far that the escape channel looks like a point in thecenter and the electrons are relatively homogeneous over: the surface. In sodoing we note that, because the density and anisotropy both fall off inverselywith R, particles are conserved only if the surface grows as something likethe second power of R. Thus ah integration over a spherical surface at, say,2 AU should yield the same result as above.
The Population of the Jovian Magnetosphere.
In the outer magnetosphere of Jupiterthe population of electrons of energy > 6 Mevnumbers 3 X 10^8 plus or minus an order ofmagnitude. Figure 3 shows four radial pro-files of this region made by the same detec-tor used for Figures 1 and 2. Large temporaland/or local time differences are apparentamong the four passes. The number-above wasobtained by integrating the electron densityrepresented by the dashed line over the vol-ume of a dipole field between 25 and 100R .The volume is probably somewhat less thanthis because the field lines are actually notdipolar in this region, but seem to be dis-tended centrifugally. However, a generousestimate serves our purpose well, and adipolar geometry is probably the bestapproximation near the equator where the fluxtubes have most of their volume, anyway.
El ICTRONS OF rSEBI I >CMtV
OUTER JOVIM, MAJNE tOSPHtRE
UCSO CERCMOV OEHCIOR
Discussion.
20 2 4-We have obtained estimates oflO2°s~l for the source strength of > 6 Mevelectrons, and ~ 3 X 10^8 for the populationof Jupiter's outer magnetosphere. As therotation period of Jupiter is ~ 10 hours,this generation rate matches or exceeds thecapacity of the outer magnetosphere in lessthan the planetary rotation period. Althoughthere are other possibilities, these numberslend credence to the hypothesis of McKibbenand Simpson (1974) that the outer magneto-sphere empties and fills with electrons everyrotation. We conclude that Jupiter acceler-ates particles at a rate exceeding those ofordinary trapped particle dynamical processes(e.g. inward diffusion by violation of the third adiabatic invariant), andremarkable acceleration Mechanisms are needed to produce this source rate.One possibility, suggested earlier by Fillius and Mcllwain (1974a), is thatthe electric field of up to 360 megavolts associated with Jupiter's rotationcouples by means of differential rotation and parallel electric fields to thecharged particle population.
20 M 100RADIAL 0I5KNCE IR.l
Figure 3
33l
Ac knuv> . > . .;ument
This work was supported by NASA through contract NAS 2-6552 and grantNGR 05-009-081.
References
Axford, W. I., W. Fillius, L. J. Gleeson, and W. -H. Ip, Ap. J. 210, 603, 1976.Chenette, D. L., T. F. Conlon, and J. A. Simpson, J. Geophys. Res. 79, 3551,
1974.Chenette, D. L., T. F. Conlon, K. R. Pyle, and J. A. Simpson, Ap. J. 215,
L95, 1977.Conlon, T. F., submitted to J. Geophys. Res., 1976.Conlon, T. F., and J. A. Simpson, Ap. J. 211, L45, 1977.Fillius, R. W., and C. E. Mcllwain, Science, 183, 314, 1947a.Fillius, R. W., and C. E. Mcllwain, .7. Geophys. Res. 79, 3589, 1974b.Gold, R. E., and E. C. Roelof, submitted to J. Geophys. Res., 1976.Gold, R. E., E. C. Roelof, and S. M. Krimigis, submitted to J. Geophys. Res.
1976.Jokipii, J. R., Geophys. Res. Let. 3, 281, 1976.Krimigis, S. M., E. T. Saris, and T. P. Armstrong, Geophys. Res. Let. 2,
561, 1975.L'Heureux, Jacques, and Peter Meyer, Ap. J. 209, 955, 1976.McDonald, F. B., and J. H. Trainer, Jupiter, T. Gehrels, Ed., pp 961,
University of Arizona Press, Tucson.McKibben, R. B., and J. A. Simpson, J. Geophys. Res. 79, 3545, 1974.Mewaldt, R. A., E. C. Stone, and R. E. Vogt, J. Geophys. Res. 81, 2397, 1976.Pesses, M. E., and C. K. Goertz, Geophys. Res. Let. 3, 228, 1976.Pyle, K. R. , and J. A. Simpson, Ap. J. 215, L89, 1977.Smith, E. J., B. T. Tsurutani, D. L. Chenette, T. F. Conlon, and J. A.
Simpson, J. Geophys. Res. 81, 65, 1976.Teegarden, B. J., F. B. McDonald, J. H. Trainor, W. R. Webber, and E. C.
Roelof, J. Geophys. Res. 79, 3615, 1974.
340
POSSIBLE 1EECHAHISK FOR ENRICHMENT OP SOMR COSKIC RAYSBY HELIUK-THREE AHD HEAVY E^GLEI
Ibragimov I . A . , Kocharo/ G.E.
Some tens of events with anomelou/ lerge f lux of •'He nucle ii n eo lar cosmic rays (SCR) ea co^ptredf with the protons and oC-p a r t i c l e s are too«n to the present moment.
Large number of these events wMich were detected independen-t l y by the vaxioua s c i e n t i f i c groups means,that the new physicalphenomenon i s found and needs in terpret ing . Available experimen-t a l data on ^He-rich events are discussed in our papers / 1 , 2 / ,where i t i s shown, that the hypothesis proposed i n the current l i -terature » the enriohment of soZar ac t ive region by hie from deepinner layers of the Sun; the / r e f e r e n t i a l acce lerat ion of ' He-n u c l e i and heavy elements; pecul iar anysotrcpy of acceleratedp a r t i c l e s and kinematic of nuclear react ion can not explain evensome of the general c h a r a c t e r i s t i c s . More important of them are:the very large r a t i o of h/lium-3 t o helium-* (up t o 8 ) ; l i t t l eor no H and % ; enrichment of the SCR by heavy elements;largevariat ions of the r a t i o / o f protons to ot-par i c l e s from event toevent; a tendency to bis associated with small western hemisphereo p t i c a l f l ares on the/Sun. The d e t a i l e d consideration of possibleexplanations of Xhaad events shown / 3 / that i t i s very importantto search such mechanism of acce lerat ion which has e f f i c i ence JJwhere Z - i s the charge of p a r t i c l e , A- the mass of number (n>2.In t h i s paper we propose the new mechanism for enrichment of SCRby %e and heavy/nucle i , which i s based on pre ferent ia l inject ionof these nuc l ey i n t o a main acce lerat ion process due to nonl ine-ar e f f e c t s in ycurbulent plasma. According to the modern ideas ,s o l a r f l are s ^re located in upper chromosphere or c o r o n a , i . e . i nhighly ionized and rare plasma, where the condit ions e x i s t f o rdevelopment/of various I n s t a b i l i t i e s and therefore for the p l a s -ma turbulence / 5 / . Due to nonlinear interact ions of plasma waveswith the f luctuat ions of the e l e c t r o n density and decay of mer-ging wav/s, excitation of others plasma oscillations is folio*
353
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D15 (1977) 2963of the Fourth
on High-Energy
i .I:
3B-:
THE MUON CHARGE RA1iu AND ITS RELATIONTO PRIMARY MASS COMPOSITION
A.K. Lee and E.C.M. Young
Department of Physics, University of Hong Kong,
Hong Kong.
Using the scaling theory and the ISR data, themuon charge ratio in the near vertical directionfor the energy range between 50 GeV and 4000 GeVhas been calculated numerically under variousassumptions about the mass composition of primarycosmic rays for energies greater than 1 TeV. Theresults are compared with experimental values andthe form of the primary spectrum discussed.
1. Introduction. Measurements of the charge ratio of cosmic raymuons have been made in recent years with improved precision and theenergy range extended to the TeV region. Most of the measurementshave been obtained with magnetic spectrographs, especially in thelower energy region. For example, the Durham group (Boxendale et al.1975) has reported results with particularly good statisties up tomuon energy of 2 TeV, but the uncertainty in the higher energy regionis still rather large. The Armenia group (Asatiani et al. 1975)has measured the muon charge ratios up toA TeV with a magnetic spect-rograph at high altitude. At still higher energies, the charge ratioscan only be derived from indirect measurements. Thus the Utah group(/shley et al. 1975) has obtained the charge ratios up to - 8 TeV fromunderground muon measurements.
The muon charge ratio is related to the mass composition andthe shape of the cosmic ray primary spectrum and to the nature ofhigh energy hadronic interactions. Using the scaling theory and theISR data, the variation of the charge ratio with muon energy can becalculated for an assumed pximary spectrum. Early calculations ofthe muon charge ratio base^ on the scaling theory were done by Frazeret al. (1972) and Garraffo et al. (1973) who gave the predicted valueswhich were higher than those observed. Several other authors havesince produced theoretical predictions usin^ recent ISR data, butthey still show rather divergent values. (See e.g. the review byKitamura, 1975) .
In the present work, the charge ratios for near vertical muons•• calculated by assuming the validity of scaling under various• .'••umptions about the mass composition of the primary spectrum. The
-,fnsitivity of the mass composition to the muon charge ratio is thenexamined and the likely form of the primary spectrum with energygreater than 10 1 2 eV/nucleon is dismissed in the light of the measuredmuon charge ratios.
355
2. The Primary Spectrum. Recent measurements of the primary cosmicrays (see e.g. the summary by Ramaty et a l . 1973) of energy up to10 u eV/nucleon show that the differential energy spectrum of protonsand a particles has an exponent of about -2.75 and that the ironspectrum appears to be much flatter with an exponent in the range -2.0to -2.4. Direct measurements of the primary spectrum at higher energiesindicate that the proton spectrum falls off rapidly at energies aboveabout 1012 eV (Grigorov et al. 1970), whereas the spectrum of otherelements continues to have about the same exponent. It is of interestto investigate the steepening of the proton spectrum and the ratherflat iron spectrum from the muon data.
The mass composition of the primary spectrum provides the prototi-to-neutron ratio which in turn is manifest in the muon charge ratio.In the'present calculation, the primary composition adopted is thatgiven by Saxena (1972) for energies less than 10lz eV and the protonfliix used at this energy is £hat derived from the proton spectrum ofRyan et al. (1972). For primary energies greater than 101 eV, twoalternative spectra are assumed: (i) the proton spectrum of Ryan etal . continues to energies greater than 1012 eV and (ii) the protonspectrum steepens suddenly at 1012 eV(as suggested by Gregorov et al.
' 1970) with an exponent of -3.5 for the differential proton spectrum.To see the effect of the iron group nuclei, two values for the ex-ponent of i t s differential spectrum (-2.2 and -2.75) have been used.I t is assumed that al l other nuclei heavier than proton and lighterthan iron have a differential spectral exponent equal to -2.75 foral l energies.
10
Muon Momentum (OeV/c)
Figure 1. Comparison of measured and predicted chargeratio of cosmic ray muons in the neat verLicaldirection. The measured values are fromDurham, Armenia and Utah groups. Curves A,B and C are predictions for various assumptionsof the primary spectrum. See text forexplanation.
356
3. The Muon Charge Ratio. The method of calculating the expectedmuon charge ratio, based on scaling and the I.S-R. data of inclusivereactions, for a particular primary spectrum has been considered bymany authors (see e.g. Erlykia et al. 1974). Essentially the fluxesof positive and negative pions and kaons are calculated by solvingthe respective diffusion equations. It is assumed that the scalingfunctions for hadron-air nucleus Interactions are the same as thecorresponding ones for hadrcn-proton interactions. The effectiveratios for ir /TT~, K+/K~ and K~/it~ as derived from I.S.R. data, turnout to be 1.44, 2 and 0.14 respectively (Ayre et al. 1973) and wehave adopted these ratios in the calculations. The contributionsfrom both the plan decay and the kaon decay have been considered.
The predicted variation of the charge ratio with muon energy forthe various assumptions about the mass composition of the primaryspectrum is shown by che curves A, B and C in Figure 1, together withthe experimental values given by the Durham, Armenia and Utah groups.Curve A is derived from an assumed primary spectrum with a differentialexponent of -2.75 for all the nuclei, including proton and iron. CurveB corresponds to a primary spectrum with an iron spectral exponent of-2.20 and that for proton and all other nuclei of -2.75. Curve C isthe result of an iron spectral exponent of -2.20 and that for protono: -3.5 for energies above 10lz eV.
4. Discussion. Figure 1 shows that the muon charge ratio is quitesensitive to the mass composition of the primary spectrum. The effectof the variation of the spectral exponent for the iron spectrum canbe seen from curves A and B. However, both A and B are not inconsist-ent with the measured values, although curve A see! is to give betceragreement. Until the statistical accuracy of measurements in theTeV region is greatly improved, there will be dif iculty in drawingfirm conclusions. However, curve C lies clearly 1 elow the measuredvalues and this suggests that a sudden steepening of the proton spect-rum for energies greater than 1012 eV (Grigorov et al. 1970) is notconsistent with the muon data unless scaling does not hold for postI.S.R. energies. Unfortunately the muon charge ratio measurementsare rather difficult to make in the TeV region and it is precisemeasurements at energies in this region that more valuable informationabout mass composition of primaries can be obtained.
Reference
Ayre, C.A. et al., 1973, Proc. 13th Int. Conf. on Cosmic Rays, 3, 1822.
Asatiani, T.L. et al., 1975, Proc. 14th Int. Cosmic Ray Conf., 6, 2023.
Ashley II, G.K. et al., 1975, Proc. 14th Int. Cosmic Ray Conf., 12_, 4282.
Baxendale, J.M. et al., 1975, Proc. 14th Int. Cosmic Ray Conf., 6_, 2011.
Erlykin, A.D. et al., 1974, J. Phys. A., 7, 2059.
357
. razer , W.R. et a l . , 1972, Phys. Rev. D, 5_, 1653.
Garraffo, Z. et a l . , 1973, Nucl. Phys. , B53_, 419.
Grigorov, N.L. et a l . , . 1970 , Sov. J . Nucl. Phys., U_, 588.
Kitaraura, T., 1975, Proc. 14th In t . Cosmic Rays Conf., ^ i . , 3925.
Ramaty, R. et a l . , 1973, Science, JjSO_, 731.
Ryan, M.J. et a l . , 1972, Phys. Rev. L e t t , , 2£, 985.
Saxena, Y.C., 1972 J . Phys. A., JJ5_, 1502.
358
STADY OF THS ENRGY SPECTRA. OF THE COSMIC RAY MUONS,Y -QUANTA, AND KADRONS IN THE / > 2 TeV RANGE.
T.P.Amineva , M.A.Ivanova, K.V.Mandfritskaya, E.A.Osipova,I.V.Rakobolskaya.N.V.Sokolskaya, N/l .Tulinova, A.Y.Varko-v i t skaya , L. Kuzmichevi V.I.Zatsfepin, G.T.Zatsepin.
I n s t i t u t e of Nuciftar .rnysics Moscow St^rbe Universi ty
Moscow II7254 USSR. A b s t r a c t .
The spectrum Of cosmic ray muons/at sea l eve l and spectra ofY-quanta and hadrons at the dep/h 60 g/cm in the s t ra tosphe-
r e are measured a t the energies U2 - 30 ) TeV. As comparedwith our ear ly work ( Amineva e t / a l 1973, Amineva et a l 1975 )t h e present resmTbs are obtained/on the bas i s of la rger s t a t i s t i e s )
At p resen t , the t o t a l expo/ i t ion of the chymbers for detecting!the cosmic ray muons has reacted 700 ton.year and.the t o t a l numbedof the detected events with Energies higher than 2 TeV i s 2500.
2 / 2
The chamber of 0.5 m area lias been exposed at a 60 g/cm in the
stratosphere during 360 honrs. All the electron-photon cascades
( EPC ) which originated At the depth of more then four cascade
units ( A t ^ 4 ) were considered as hadron-jets. The total num-
ber of such events is 2P8. 726 events with A t < 4 have been de-
tected, 5OJ6 of these events being ft - quarta.
As was noted in out previous works ( Amirava et al 1973, and
Amineva at al 1975 )/an increase in xhe energy spectrum exponent
was observed for thfe events with A £ < 4 and also muons, and a
difference was found between the spectrum exponents for the events1
with A"t>4 and /at. <• 4. These effects are confirmed at pre-
sent work, with^enlarged statistics.
The first problem to be clarify is that the observed effect
are not a consequence of technique of X-ray emulsion measuremens.
In our eamy works the calculations of the iiPC development
made by Nishamura (1964- ) were used. The detailed study of the
core apprommation in the J5PC theory .was made by Guzhavin et al
( 1974 )yv/ho calculated more accurately the lateral distribution
of the cascade electrons. In the present work we have used these
calculations and have studied a number of experimental methodical
effects'. First of all, the possibility of underestimating the
energ res in the high-energy range due £0 insufficient knowledge
415
10
to
416
THE COSMIC RAY NEUTRINO-INDUCED BACKGROUNDIN THE SOLAR NEUTRINO EXPERIMENT
A.W. Wolfendale
Physics Department, University of Durham, England
and
E.C.M. Young,
Physics Department, University of Hong Kong.
At very great depths underground, the limit to thedetectability of solar neutrinos is set by thepresence of cosmic ray muon and electron neutrinos.Attention is directed to the magnitude of the cosmicray neutrino-induced background iji the Brookhavensolar neutrino detector in which the target materialis C2CI1*. Recent estimates of the cross sections ••for 37ci(Ve,e~)37Ar and 37ci(v y~)37Ar as a funtionof neutrino energy and the cosmic ray neutrinospectra are used to set a limit to this background.
1. Introduction. The problem of measuring the solar neutrino flux inorder to test solar models is well known. The discrepancy betweenobservation and the supposedly well established theory is sometimesdescribed as the 'solar neutrino puzzle'. Specifically, the recentresults of the Brookhaven solar neutrino experiment (Davis and Evans,1976) give-an average neutrino capture rate above the cosmic ray back-ground of 1.3+0.4 SNU (SNU = solar neutrino unit, 10~36 captures per sec.per 37ci atom). The experimental upper limit of 1.7 SNU can be compared tothe predicted rate of 4.7 SNU, based on a 'standard' solar model, given inthe recent work of Bahcall (1977).
The Brooiihaven neutrino detector is situated underground at a depthequivalent to 4400 hg cm"2 of 'standard rock' and the detection of theneutrinos depends upon the reaction 37cx(v>e~j37^ri However, there areother processes which can produce 37Ar and these constitute the backgroundeffects. At the depth of the detector the main source of background isdue to cosmic ray unions but there is a small contribution from cosmic rayneutrinos. The muon background decreases rapidly with the depth under-ground, and thus can be practically eliminated if the detector is situatedsufficiently deep underground. The cosmic ray neutrino background is,however, constant with depth and it will set a limit to the detectabilityof solar neutrinos and other extraterrestrial neutrinos. The presentapparent deficiency of solar neutrinos makes it all the more important tohave accurate estimates of the sources of background.
2. The Neutrino Cross Section. In the earlier estimates of the back-ground (Davis, Wolfendale and Young, 1972) attention was f ocussed upon thedominant source, i.e. the muon background. The cosmic ray neutrinocontribution was only approximately estimated as the cross section for the
417
reaction 37Cl(v,e~)37Ar for the relevant energy region (0.1 - 1 GeV) wasnot wellknown. In our earlier work, a Fermi gas model for the nucleusand the neutrino cross section for free nucleons were adoped with allowancesbeing made to account for the exclusion principle and the recoil protonescape. It nowappears that in this fashion the neutrino background mayhave been considerably overestimated and the predicted background can onlybe regarded as an upper limit.
Recently Domogatsky et al. (1976) have reported shell modelcalculations of the cross section for the reaction 37Cl(v,e )37Ar forneutrino energy up to 300 MeV. In this work, the authors have used anenergy transfer cutoff of 8.79 MeV to avoid neutron emission and assumedthe purity of the <|(ld3A, ) 53/2+, T = -y configuration for the 37C1 groundstate and the corresponding state in 37Ar. However, there- seems to besome doubt about the latter point and such an energy transfer cutoff wouldignore transitions from higher states. Both points would tend tounderestimate the calculated cross -section. In the absence of furtherexperimental or theoretical confirmation, the cross sections should beregarded conservatively as a lower limit.
3. The Neutrino Spectra. The cosmic ray neutrino background arises fromthe reactions 37ci(vu,v~)
37Ar and 37Cl(ve,e~) 37Ar. The main contribution
cosies from neutrinos in the energy region 100 - 500 MeV. The neutrinospectra (vu + ve) in this energy region are affected by the local geomagneticcutoff rigidity of primary cosmic rays (see e.g. Young, 1973). Theneutrino spectra for energy below 1 GeV have been calculated by Tain andYoung (1970) and recently by Choi and Young (1975) for some geomagneticlatitudes. The Brookhaven neutrino detector is situated in the HomestakeMine in South Dakota, U.S.A. (44°21'N, 103°46'W) where the local verticalrigidity is about 1.9 GV. The neutrino spectra appropriate to this locationhave been calculated, the geomagnetic effect being taken into account.
4. Results and Discussion. Using the cross sections given by Domogatskyet al. and the calculated neutrino spectra, the background due to cosmicray neutrinos (v,, + \>_) has been estimated to be 5.4 x 10"1* per day per10^ gallons of C2CI4 for the Brookhaven neutrino detector. This is shownin Figure 1 together with the predicted muon background as a function ofdepth. Figure 1 also shows the recent experimental total capture rateincluding background (Davis and Evans, 1976) and the total predicted rate(Bahcall, 1977). The predicted rate for the pep neutrinos only is alsoshown as this is the lowest capture rate that is consistent with thehypothesis that nuclear fusion is the source of solar energy. It can benoted that if the same detector were situated at a depth of at least7000 hg cm"2, the union background would be drastically reduced to theextent comparable to the cosmic ray neutrino background level. At such adepth the signal from the pep neutrinos alone would be at least an orderof magnitude greater than the expected total cosmic ray background.
418
hreà Je hedte,
t-tlJ for PEPnentrincs
Figure 1. Ar production rate vs. depth.
The 'average measured rate' is an estimate only - there isdoubt about the actual value because of the possiblerejection of certain experimental runs for technicalreasons.
The key to the cosmic ray neutrino background levels is
(1) the Fermi gas model prediction of our earlier workDavis et al., 1972)
(2) The present predictions using the cross sections ofDomogatsky and Eramzhyan, 1976).
The actual level is between (1) and (2), probably muchnearer (2).
References
Bahcall, J.N., 1977, preprint.
Choi, M.C., and Young, E.C.M., 1975, 14th Int. Cosmic Ray Conf., 6>, 2134.
Davis, R, Jr., and Evan, J.M., 1976, Brookhaven National LaboratoryReport 21837.
419
Davis, R. Jr., Wolfendale, A.W., and Young, E.C.M., 1972, Proc. Neutrino•72, Balatonfured, I, 77.
Domogatsky, G.V., and Eramszyan, R.A., 1976, Neutrino 76 ConferenceReport.
Tarn, A.C., and Young, E.C.M., 1970, Acta. Phys. Hung., 2!9_, Suppl. k_, 307.
Young, E.C.M., 1973, 'Cosmic Rays at Ground Level1, (ed. A.W. Wolfendale,The Institute of Physics, London), 105.
420
EXPERIMENTAL STUDIES OF THE ACOUST/C DETECTION
OF PARTICLE SHOWERS*'
L. R. SulakHarvard University
Cambridge, Mass. 021/8 (USA)
and
T. Bov.en, B.Pifer, and P. Polakos, Unive/sity of Arizona; H. Bradner,
Scripps Inst i tute of Oceanography; W. y. Jones, Louisiana State University;
0. Learned, University of Wisconsin; / . Armstrong, M. Bregman, M. Levi,
and J . St ra i t , Harvard University; V. L inscot t , Syracuse University; and
A. Parvulescu, Hawaii Geophysics i / s t i t u t e
reSUitS ! r O m B r o o k h a v e n National Laboratory and Harvard5 U r e r ° d U C e ^ b y e n e r 9 e t l " c P™tons depositing energy Vn
suggests that energy depositions as smallbe o b s e r ^ b l e by this technique Sd Jtat l S "
e rS P r ° d U C e d b y u l t r a " h i 9 h ™rW Particles
Subnvittyd to the 15th International Cosmic Ray Conference, Sophia, Bulgaria,
13-26/August, 1977
