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VOLUME a

PLOVDIV* "*V ,W* BULGARIA AUGUST 13-86,1377 15" International Cosmic Ray Conference

CONFERENCE PAPERS VOLUME a

OG SESSION

BULGARIAN ACADEMY OF SCIENCES

PLOVDIV. BULGARIA AUGUST 13-26,19(77- Ill

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 12 volumes. Volumes from 1 to 9 include the original contributions, 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 their abstracts. Volumes from 10 to 12 include the invited and rapporteur lectures, as well as late original papers. Volume 12 contains the general contents of the volumes, an authors' index and other references. All papers included in the present publication are exact reproductions of the authors' original manuscripts. The Secretariat has not made any corrections or changes in the texts. The original contributions 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 texts of 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 adopted at the cosmic ray conferences, which also coincide with the sessions. Volume 1 - OG (Origin) Session Volume 2 - OG (Origin) Session Volume 3 - MG (Modulations and Geophysical Effects) Session Volume 4 - MG (Modulations and Geophysical Effects) Session Volume 5 - SP (Solar Particles) Session Volume 6 - MN (Muons and Nutrinos) Session Volume 7 - HE (High Energy Physics) Session Volume 8 - EA (Extensive Air Showers) Session Volume 9 - T. (Techniques) Session The 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 to the success of the Conference and have made possible the publication of the present 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 of Sciences, without whose diligent work the publication of the proceedings would have been impossible.

Acad. Christo Ya. Christov Chairman of the National Organizing Committee I\

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.N. 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 C.J.Waddington (USA), Professor A.W. Wolfendale (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), Professor G. 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 SECRETARIAT Institute for Nuclear Research and Nuclear Energy Sofia 1113, 72 Btvd Lenin Telephone: 7341 Telex: SOFIA BAN 22424 TABLE OF CONTENTS

VOLUME 2 - ORIGIN

COSMIC RAY SOURCES

OG-112 Search for Anisotropy of Cosmic Ray Muons Y.Kamiya, S. I ida, S. Shibata andl.Kondo (Abstract)

OG-113 Enhancement of the High Energy Part of the Cosmic R^yS Flux of Nuclei J. C. Jodogne (Abstract)

GG-114 Contribution to the Galactic Cosmic-Kay Flux from Pulsars J. C. Jodogne (Abstract)

OG-115 About the Role of the-Center of the Galaxy as the Source of Cosmic Ray^.'-" Ya. M. Khazjfn and V. S. Ptuskin

OG-116 Stellar Death and Cosmic Rays ^^^W. D. Arnett and D. N. Schramm (Abstract)

OG-117 Nucleosynthesis and the Origin of Galactic Cosmic Rays 10 D. N. Schramm and W. D. Arnett OG-1T8 The-€oronal4onizationJlIodeL..F^^ Sources ___.————-— -14- Mr-Ga^s^TEa P. Goret (Abstract)

CG-119 Cosmic Rays from Pre-Main Sequence Stars 15 H.Reeves and C.J.Cesarsky

OG-120- Selective Injection as an Accessory of Fermi Acceleration in Supernova Remnants ,20-- M. M. Shapiro and RTSilberbeig^

CG-121 Structure of Pre - Supe r nova ,Sta-rs"Srid^roduct ion of" Black--- Holes as Meired-frSmNeutrino and Hardphoton Pulses _Ms^frSHapiro and R. Silberberg

CG-122 High-Energy Cosmic Neutrinos and Photons from Point Sources, and Implications for Galactic Confinement 26 i/ R. Silberberg and M. M. Shapiro

OG-123 Nature of Galactic Cosmic Ray Sources 30 R. Cowsik and M. A. Lee (Abstract)

CG-124 - Nearly Loss-Free Escape of Cosmic Rays froirrSupernova Remnants 31 S. J. Schwartz and S. Street OG-125 Avoiding Adiabatic En urther Developments S. J. Schwartz, J. Skill

OG-126 Corpuscular and liatlon of Supernova and Radiocarbon s Atmosphere V.A.I v (Abstract)

OG-127 Pulsars and Cosmic Bays In thet)ense Supernova Shells V. S. Berezinsky and O. F. Prilutsky

OG-128 Propagation of Cosmic Bays in Extragalactic Radio Sources * J. A. Earl

COSMIC RAY INTERACTION

OG-129 Light Elements Production by Galactic Cosmic Rays-the yt State .of Affairs H. Beeves and J. P. Meyer

OG-130 , Deuterium Production by Cosmological Cosmic Rays ^ T. Montmerle

OG-131 Some Additional Indications of the Contribution of Interstellar Helium to Cosmic Ray Spallation G. M.Raisbeck and F. Yiou

OG-132 Experimental Cross Sections for the Pickup of Electrons by Relativistic Nuclei G. M.Raisbeck, H.J.Crawford, P. J. Lindstrom, D. E. Greiner, F. S. Beiser and H.H.Heckman

CG-133 Cro^Sections for bL-roL-* Be at 400 60fit and lOCKMeV F. YiouSG. M.Raisbeck and H. Quecho/ n / OG-214 Cross Section Measurements for Pnalauction of Stable Isotopes of Ne ancPAx by High-Energy Spallation of Al, Sc, Ti, Fe, Co, NvandCu, S. Regnier

CG-212 IsotoDe Production Cross j^ctib^s from Fragmentation of at Relativistic Energies H.J.Crawford, F.S. Bjeser, B. Corl^JH. H. Heckman, D. Greiner and P.J. I^ndstrom (Abstrac

OG-223 Isotope Production Cross Sections from Fragmentation of 14N at Relativianc Energies P. J. Lindstroni, F.S. Bieser, B.Cork, H.Crawford, H. H. Heckmsm and D, Greiaer Vll

OG-134 Calculations of Fragmentation Cross Sections of Nuclei In High Energy Collisions 83 E. Jullusson (Abstract) / / OG-135 Modification of\ Semiemptorfea l Equations for Calculating Partial Cross Sections of p-Nucleus Reactions 84 R. Silberberg and pm.Tsao

OG-136 Calculations o^NucIeu^rNucleus CrosB Sections and the Attenuation of Complex Cosmic Ray Nuclei in the Atmp&phere \ 89 R. Siljaiferberg and C. H. Tsao\

OG-137 Cross Sections for Production of "Boron Isotopes in Carbon Spallation: Propagation of the Light Cosmic Ray ^ Nuclei 95 * Pierre Fontes x OG-138 Transport of Cosmic Rays in Supernova Remnants 101 G. Morfill and M. Scholer (Abstract) /

OG-139 The Energy plectrum of Cosmic Ray/Leaving a Supernova Remnant \ ./ 102 M. Scholer an^G. Morfill (Abstract) s IMPLICATIONS 05 THE COMPOSITION OF COSMIC RAYS / / OG-140 Ionization States and\heOrigin of Low Energy (1-30 MeV/amu) Cosn^fc Ray Nuclei 103 N.Durgaprasad and ^Bicwas

OG-141 About the Ihfluendtfof the Ionization Losses on the / v Abundance of Gosmic Ray SecQndary Nuclei 109 Ya. M. Khazanr / \ 44 OG-142 Cross Sections for Spallation Production of Ti: Application to Determining Cosmic kay Acceleration Timpr 115 GyM. Raisbeck and F. Yiou (Abstract)

26 OG-143 Cross Sections for the Production of A1 from Targets / of Si, Al and Fe Irradiated by Protons of 600 MeV IIP V V G.M.Raisbeck, C.Menninga, R.Brodzinski and N. Wogman

O G-144 A Two Zone Cosmic Ray Propagation Model and Its Implication of the Surviving Fraction of Radioactive Cosmic Ray Isotopes 347 M. Simon, R. Scherzer and W. Enge OG-145 A Two Zone Cosmic Ray Propagation Model and Its / Implication of the Source Composition and of the Energy v Dependent Abundance of Cosmic Ray Nuclei 125 M. Simon

OG-146 Silicon, Sulphur, Argon\Calciui3^-Puzzling Thougits on a Key Quartet 131 M. Casse and J. P. Meyar \

OG-147 Realistic Uncertainties on Galactic Abundances and . / Significance of the Cosmic Ray Source Composition 137 / * J. P. Meyer and H. Reeves -13 OG-148 Mass Composition of Primary Cosmic Rays above 10 eV 143 J. Olejniczak, J. WdowczyKand A. W. Wolfendale

OG-149 Comments Regarding Hierarchical Models of Cosmic / Ray Origin 148 K. Sitte

SIDERIAL VARIATIONS OF COSMIC RAYS

OG-150 Time Variation of Small Showers 153 C.Aguirre, R.Anda ano^D. Andreiie&i (Abstract)

OG-151 Sidereal Anisotropy of.Srfi^l Air Showers Observed at Mt. Norikura \ 154 K. Nagashimay^Tsakakibara, X, Fujimoto, Z. Fujii, H. Uenoaatfl. Kondo \

OG-152 Year to Year Variation of Sidereal Anisotropy of Cosmic . /Rays 160/ V M. Ichinose

OG-153 Some Thoughts^n Musala Anisotrop^; Pitch Angle Distribution or 166 J. Kota and A. J. Sdijiogyi (Abstract)

OG-154 Further Evidences of\he Ajusotropy Observed at Musala Station 167 T. Gombosi, J.Kota, A^kSomogyi, A.Varga, B. Betev, L. Katsarski, S. Kavlaltov and I. Kirov (Abstract)

OG-155 Search for Sidereal Variations^ the Muon Flux Using the Deis-Spectrometer (Abstract) 168 O.C.Allfcofer,/G.Bella, W.D.Dau\H.Jokisch, G.Klemke, Y.Oren, E.QOJhr and Y.Yeivin (Abs

OG-156 Measurement of Variations of MS with fVpv Number of 347 Particles V.Vj/lexeyenko, A. E. Chudakov, LM.Kogai, A„R. Mikhelev and N. S. Miranova (Abstract) OG-157 Investigation of the Sidereal Anisotropy of High Energ^r v Muons 170 V.V.BoW, V. G.Kirillov-Ugryumov, R. P. Kokoujfn, A. A. PetAjkhin, v-v- Shestakov and Yu. A. StepanOv

OG-209 Spatial Distribution of Cosmic Ray Muons ab^rve 200 GeV 175 A. R. Bazer-Bachi, G. Vedrenne, W. R. Sheldon and J. R. Benbrook\( Ab s trac t)

OG-211 Operational Characteristics of the Utah Anisotropy Detector 176 D. E. Groom, H. Emerge son, D. J. Cutler and J. F. Davis ,11 12 182 OG-158 Origin of Cosmic Rate in the Rarige 10 - 10 eV J. L.Osborne, A.W. Wblfendale-and J.Wdowczyk

OG-159 Does Cosmic Ray AnisotBppjr Vary with Time? Additional Results for th^ears 1959-1960 188 J. Linsley (Abstract) / \

/ \ 189 OG-I6O Anisotropy of Superhigh Energy, Cosmic Rays D. D. Krasilnikov, ,

OG-162 Air jShower Directions from the Sydney Air^Shower Array 196 A.IJ. Bray, L.Horton, R. J. W. Lake, C. B. A^McCusker, y. S. Peak, J. Ulrichs and M. M.Winn (Abstract)

OG-163 Cosmic Ray Intensity Annual Variations for the Last (/ Several Centuries 197 V V. A. Dergachev, G. E. Kocharov and S. K. Tleugaliev

PROPAGATION OF COSMIC RAYS

10. OG-164 The "Be P^blem Revisited 203 v G. M. Raisbecftsand F. Yiou

OG-165 Lifetimes of Cosml rs in the Energy Range 5-50 GeV/n 208 F. Le Guet

OG-166 Chloringy36 and the CosAic Ray Escape Lifetime. PreaedtStatus \ 213 \ Meyer, M. Casse and P^Goret

OG-167 Stability of Horizontal Equilibria of the Galactic Gaseous Disk 219 / M. Lachieze-Rey, E. Asseo, C. J. Cesarsky and R. Pellat OG-168 Parker Ihstability and CosrrHp R^yEscape from the Galactic Disk 224 E. Asseo, C. J. Cesarsky, ^ L^ieze-Rey and R. Pellat

OG-169 The Two Tier Model of Cosmic Ray Escape from the Galaxy 229 J M. M. Shapiro and R. Silberberg

OG-170 Gosmic Ray Propagation: Energy-Dependence of Leakage J Mean Path Lenght 234 P. Fontes,J.P. Meyer and C. Perron 1/ \ f OG-171 Constraints of the Cosmic Ray/Halo Dimensions 240 F. C. Jones and F. W. Stecker /

OG-172 The Formation of a Cosmic sRay Electron Halo 246 R. Schlickeiser and K. O. Thielheim (Abstract)

OG-173 Comments on tfte Dynamics of Interstellar Hydrogen and Cosmic Ray Acceleration' 247 K.O. Thielheim (ABstract)

OG-174 Synchrotron RadiationSfrom the Galaxy 248 C.E.Jakel, K.O.ThielK^im andH.Wiese (Abstract)

\ 249 OG-175 Contribution of Pulsars totoe Flux of Galactic Gamma Rays A. W. Strong and A. W/ . Wolfe^dal\ e (Abstract) OG-176 Cosmic Ray Escap^ from the Galaxy 250 E.Juliusson / \ I OG-177 The Effects of the1 Nonlinear Interactions of Cosmic Rays with the Plasma jfoinds from the StarS of Various Classes 255 L. I. Dorman (Attract) / OG-178 Interactions ofjthe Cosmic Rays of the Internal and External Grigin with th$ Expanding Shells of Supernova 256 L. I. Dorman ^Abstract) \ \ OG-179 / \ 257 Compound-Diffusion of Cosmic Rays in the Galaxy V. S. PtuskiA \ OG-180 / V Diffusion Radioactive Nuclei and the Cosmic Ray Agte in the 263 Large Hs^o Model \ V. L. Prphchep, V. S. Ptuskin and Ya. M. Khazan i OG-181 On the /Propagation of Cosmic Rays in the Galaxy 267 A. A. Aitmuhambetov, A. G. Zusmanovich, E. V. Kolomeets and O. V. Krupennikov \l

OG-182 Spectra of^Nuclear Secondaries in Fermi Type Accelerating^ Processes* / 272 \ R.Cowsik (Abstract) \ / OG-183 Acceleration of Cosmic Rays at Shock Fronts 273 W\l. Axford, E. Leer and G. Skadron (Abstract) / \ ' OG-224 Corrections to the Theoretical Cross Sections iJx the \ / Pickup of Electrons by Relativistic Nuclei / 274 L.W. Wilson / \ / COSMIC RAYS OF ULTRA HIGH ENERGIES

OG-184 Arrival Direction Distribution of Muon.Selected EAS 280 P.R. Blake, W. F. Nash and I. C. Presip&tt

OG-185 " \ / 285 Primary Proton* Spectrum to 30 Te¥ T.K. Gaisser, F^Siohan and G. B.^odh (Abstract)

OG-186 Upper Bound on MetagalactiivicUfigciiauLHcJ Fr^uJJuAx VJofJ Infrared Diffuse Radiation \ 286 V. S. Bere~msky and Si I. Grijjfor'eva \ / 16 OG-187 Arrival Directions of Cosmic Rays Above 6.10 eV 292 A. M. T. Pollock, R. J. O.Aeid and A. A. Watson

OG-188 Some Implication^ of Obsmife Ray Arrival Direction } Measurements 298 A. M. T. Pollock and A. A. Wats\n 17- OG-189 The Energy Spectsum of Cosmic^ay Particles? above 10"' eV 303 G. Cunningham, d. M. T. Pollock, S. J. O.Reid. and A. A.Watson /

OG-190 Ultra High Energy Cosmic Rays frotai Evolving Sources 309 V. S. Berezin^ky and S. I. Grigor'eva \

OG-191 \ On the Oristn and Propagation of Ultra High Energy Cosmic Rafys \ 315 P. Kiraly/Abstract)

OG-192 Origin off Ultra High Energy Cosmic Rays \ 316 N. R. Stapley, A. W. Wolfendale and J. Wdowczyk \\ \ \\\

\COMPOSITION OF LOW ENERGY COSMIC RAYS \ OG-193 Low-Energy Particles in Interplanetary Space During Quiet Times at War Minimum 320 G. Gloeckl^r, D.Hovestadt, B.Klecker and C.Y.Farv (Abstract) \ / \ 3 OG-194 Deuterium and He in Low Energy Cpsmic Rays/ 321 R. A.Mewaldt, VE. C. Stone and R. E. Vogt (Abstract) \ j OG-195 Temporal Variations in the Composition of Lbw Energy Cosmic Rays \ / 322 R. A.Mewaldt, E.G.Stone and R. E. Vogt (Abstract) \ / OG-196 The Isotopic and Elemental Composition of Cosmic Rays Below 30 MeV/nuc \ / 323 R. A. Mewaldt, E. C. Stone and R. E. Vogt (Abstract) \ i / f OG-197 Exploration of the Anomalous N-Q-Ne Component at Higher Energies (E 2 100 MeV/uj) 324 F.W.O'Dell, J.Kidd, N. Seemari, M. M.Shapiro, R. Silberberg and C. H. Tsap / / OG-198 Energy spectra and AbundaiifcsR of Carbon to Nickel Ions in -199 the Low Energy (8-100 Mej/amu) Cosmic Rays Observed in the Skylab Experiment / 327 S. Biswas, N. Durgaprasad, J.'Nevatia, S. Sarkar and V. S. Venkatavaradan /

OG-200 Lexan Track Detector on Skylab - Results on Energy Spectra and Composition of Jf> £ Z£ 28 Nuclei at Low Energies (8-160 MeV/amu)/ 333 C. Bagola and U. B. Jayanthi (Abstract) / OG-201 The Anomalou^Component of Low Energy Cosmic Rays During the Present Solar Minimum - A Comparison of Observation^ with Model Calculations \ 334 B. Klecker/D. Hovestadt, G. Gloeckler and C. Y. Fan (Abstract)' / . \ OG-202 On the rfistory of the Discovery of Cosmic\Rays 335 I. V. Dprman \

OG-203 A Technique to Determine the Charge State ot the Anomalous Low Energy Cosmic Rays \ 341 J/B. Blake and L. M. Friesen \

OG-204 /The Quasilinear Kinetic Theoiy of Charged-Partlcle / Acceleration in Alternating Magnetic Fields \ 347 M. F. Bakhareva Mil \. V C/G-205 Charged ParticlL e Acceleration i>a Alternating Magnetic Fields and OrigiH of the Low Energy Cosmic Rays ^ 352 M. F. Bakhareva \ " \ \ , OTHERS

OG-206 Cosmic Ray Spallation Effects tp^iSO's 357 J. Baldwin, A. Boksenberg, jfiKlBurbidge, R.Carswell, R.Cowsik, J.Perry and-A'.Wc^fe (Abstract)

OG-2Q7 Mechanisms of Jtffcerstellar Dust Barticle Destruction 358 V. S.Berezinsky and O. F.Prilutsky\

OG-2Q8 Subcosmic Rays and Their Role in the Spnce 364 L. I. Dorman \ \ 9

"Stellar Death and Coafnic Rays" W. D. Arnett and D. fif. Schramm Enrico Fermi Institute, Un/versity of Chicago Chicago, Illinois 60637

The composition of matter/processed by a supernova can be read as a history/of the conditions to which that material was subjearced. The cosmic rays may provide a uniquely valuable sample of such material. Quantitative evolutionary calculations have been done which give the properties of a pre-supernova star. Implications if these results for abundances, particularly iron-g/oup nuclei, will be discussed. In addition, estimates will be made of v-line emission from newly synthe/ized matter. Yields of processed matter for severafl .interesting choices of stellar mass will be presenter, and the effects of hydrodynamic phenomena discussed.

This work is Supported in part by U.S. NSF Grant AST 76-21707 and/the University of Chicago. b&MoofH 10

Nucleosynthesis and the Origin of the Galactic Cosmic Rays David N. Schramm and W. David Arnett Enrico Fermi Institute, University of Chicago Chicago, Illinois 60637

If supernovae are the source of galactic cosmic rays and are the site of nucleosynthesis, then the cosmic ray abundances shouid tell us something about the source. Previously (Arnett and Schramm 1973, Hainebach, Norman and Schramm 1976) showed that the cosmic rays seemed to show a different average over sources than the solar system (meteorite) abundances. In particular the solar system abundances seem to be reproduced by a mass-weighted average over all supernovae ejecta whereas the cosmic rays are more like the typical supernovae ejecta. New work showing that mass loss makes a significant effect on massive star evolution as well as more Helium- core models have improved our ability to make relevant averages over initial stellar mass functions. In addition, the implications of the work of Chevalier (1976) on the supernova remnant Cas A have been interfaced with the model and will be discussed. A hybrid model including botn preferential acceleration and nucleosynthetic enrichment may be necessary to totally explain all observations.

]_. Introduction. It is well established that the evolution of massive stars (M £ 7 Mg) leads eventually to a star with an Iron-Nickel core surrounded by concentric shells of primarily Silicon, Oxygen, Neon, Carbon, Helium and a Hydrogen envelope (c.f. Arnett and Schramm 1973 and Schramm and Arnett 1975). It has been shown by Arnett and Schramm (1973) and more recently with greater detail by Arnett (1977) thatfcif these stars blew up and became supernovae, the mass average of the ejecta of these stars gave a reasonably good fit to the observed solar system abundances (Cameron 1973) of the heavy elements from Carbon to the Iron Peak. It was also noted that the differences between the galactic cosmic ray composition and the solar system might be due to a different way in which cosmic rays sample the supernova ejecta (Arnett and Schramm 1973 and Hainebach, Norman and Schramm 1976).

In particular it was shown that the C/0 ratio in the cosmic rays being near unity was more easily understood if the cosmic rays preferentially sampled the lower mass end of these massive stars. Similar beneficial results occurred when one considered other heavy elements such as Ne. It was thus proposed that perhaps the cosmic ray composition was more indicative of the typical supernova (M ^ 12 MQ) rather than the mass-weighted average M ^ 25 MQ. This might have been understood if each supernova accelerates the same amount of cosmic rays regardless of the mass of material actually ejected. 11

2 . Type of Average Over Different Mass Stars. One of the points of this paper is to mention that recent work by Arnett (1977) filling in the compositions for some mass stars which were previously interpolated or extrapolated through now indicates that the weighting function for the cosmic rays may be somewhat more subtle than just the "Typical Supernova". However, it should be remembered that detailed compositions are still quite uncertain particularly with regard to the C/0 ratio which is sensitive to the still poorly known reaction rate for 12C (a y) 160. In addition, the processing of the material during the explosive ejection may significantly change its composition (c.f. Hainebach et al. 1976). The basic fact still remains that higher C/0 ratios are obtainable with lower mass stars.

3 . Mixture Prior to Acceleration. Accelerating the heavy element- rich mantles of these massive stars can explain much about the heavy tlement composition of the cosmic rays. However, it must be remembered that the cosmic rays, while enriched in heavy elements relative to the solar system, are still predominantly Hydrogen and Helium. This latter fact is easily incorporated into the supernova model if acceleration does not occur until after the mantle of the star has been mixed with its envelope and perhaps some interstellar media. (In fact, the degree of such mixing is directly related to the Nitrogen abundance in the cosmic rays, since the N came via that fraction of the envelope which was CN processed.)

Such a mixture prior co acceleration is exactly what occurs in the Scott and Chevalier (1975) model where acceleration occurs via a second order Fermi process, which happens when the particles bounce off the magnetic knots such as are observed in the Cas A supernova remnant. Hainebach et al. 0976) have developed a consistent model utilizing the Arnett and Schramm (1973) supernova model and the Scott and Chevalier (1975) cosmic ray acjeleration model. However, it should be noted that any acceleration mechanism will suffice so long as the material accelerated is a well-mixed sample of mantle plus envelope with possibly some interstellar medium. In order for such a mix to occur, the acceleration probably does not take place until at. least a few years after the supernova itself. This will mean that primary electron capture nuclei with lifetimes less than a few years should not be present in the cosmic rays (c.f. Casse and Soutoul 1974).

4_- Role of Preferential Acceleration. It should be remembered ttat some model of this type seems to be required since nucleosynthetic enrichment of the source seems to have occurred as is clearly shown by the r-process nature of the ultra-heavy cosmic rays (Blake, Hainebach, Schramm and Anglin 1977). Hainebach et al. showed that the r-process to s-process ratio implied by their model for these ultra heavy cosmic rays should be K 10 which is consistent with observation. Wefel et al. have gone on to show that this r-process enrichment does not apply to the region between A -v 60 and A ^ 80 because the core Helium burning s-process occurring in the massive stars will contribute s-process material to this atomic mass range.

Recently Blake et al. (1977) have gone on to show that to completely explain the current Sk.ylab experimental results of Price and Shirk (1975) for the ultra heavies requires not just an r-process enhancement, but also some preferential acceleration. Preferential acceleration is not capable of 12 producing the "Pt" peak dominance, which is such a characteristic of the r- process; however, the high Actinide to Pt ratio of the cosmic rays compared to the low Actinide-Pt ratio in the solar system material seems to imply preferential acceleration (presumably dependent on first ionization potential) since both Actinide-Pt ratios should be due to the same r-process nuclear physics and the only difference should be the * 10? yr cosmic ray age versus the 4.5 x 109 yr solar system age, and this later age effect is easy to correct (Blake and Schramm 1974).

If preferential acceleration seems to have affected the ultra heavies, then it probably also affected the other heavy elements. In particular, Shapiro and Silberberg (1977) have pointed out that the addition of self- consistent preferential acceleration does seem ^o help the fit of the massive star mantle ejecta to the observed cosmic ray composition. (Of course, some of these differences might also have been made up for by explosive processing of the supernova ejecta.) It had also been noted by Hainebsch et al. that the massive star models tend to imply Helium enrichment in the cosmic rays relative to the solar system. Such an enrichment is observed by Webber and Lezniak (1974) using a rigidity-dependent cosmic ray spectrum. However, if one feels the spectrum is not rigidity-dependent, then the cosmic ray Helium may be low, which Shapiro and Silberberg (1977) use as another argument favoring the influence of preferential acceleration on the determination of the cosmic ray source spectrum.

5. Location of Mass Cut. One major question in supernova theory is the location of the "mass cut" separating that material which falls in to make a neutron star from that material which gets ejected. It is at this mass cut that the extreme neutron enrichment necessary for the r-process probably occurs. It is also just above this mass cut that the e-process, which creates the Iron peak elements, probably occurred (Hainebach, Clayton, Arnett and Woosley 1974). We know that for the solar system Iron peak the bulk of the ejected material had a low neutron enrichment since solar system Iron is dominated by 56Fe. However, it may be that typical r-process source gets a somewhat higher neutron enrichment in its ejecta. Evidence for this would come if the cosmic rays showed a large amount of 58Fe.

Summary. The basic scenario that supernovae are the cosmic ray sources seems to be in reasonably good shape. Massive star models syn- thesize the bulk of the heavy elements up to the Iron peak in quiescent nuclear burning shells. These shells are ejected and explosively processed in the supernova explosion. The detailed elemental and isotopic composition of the ejecta will vary with the mass of the presupernova star. While the solar system heavy element composition can be reasonably well understood by the summation of all the ejecta of such supernova with the different masses weighted in this sum by the Sal peter (1955) mass function, the galactic cosmic rays appear to not be representative of such a total mass average.

In order to understand the overall composition, including the Hydrogen and Helium, it is necessary that the heavy-element supernova mantle be mixed with the Hydrogen-rich envelope and perhaps some interstellar gas prior to acceleration. Acceleration thus does not occur until at least a few years after the supernova explosion and perhaps not for a few hundred years. 13

The injection and acceleration process may also preferentially select material from this mixture since some features of the observed abundances seem to be best fit by preferential acceleration. However, the need for enrichment in the cosmic rays of recently synthesized nucleosynthetic products is shown by the r-process dominance in the ultra-heavies, particularly the supremacy of the Pt peak to the Pb peak.

]_. Acknowledgments. We would like to thank our former collabora- tor J. B. Blake, K. Hainebach and 0. Wefel for their contributions to this work. This work is supported in part by U.S. - NSF Grants AST 76-21707 and AST 76-20253 at the University of Chicago, and in part by the Shirley Farr Fund and the Enrico Fermi Institute Research Fund.

References

Arnett, W. D. 1977, Ap. J., submitted. Arnett, W. D., and Schrairm, D. N. 1973, Ap. J. (Letters), 184, L47. Blake, J. B., Hainebach, K. L., Schramm, D. N. and Anglinr J. D. 1977, Ap. J., submitted. Blake, 0. B., and Schranm, D. N. 1974, Ap. and Space Sci., 30, 225. Cameron, A. G. W. 1973, in Explosive Nucleosynthesis, ed. D. N. Schramm and VI. D. Arnett (Austin: University of Texas Press). Casse, M., and Soutoul, A. 1974, Symposium on Measurements and Interpreta- tion of the Isotopic Composition of Solar and Galactic Cosmic Rays at Durham, N. H. Hainebach, K. L., Clayton, D. D., Arnett, W. D., and Woosley, S. E. 1974, Ap. J., 193, 157. Hainebach, K. L., Norman, E. B., and Schramm, D. N. 1976, Ap. J., 203, 245. Price, P. B., and Shirk, E. K. 1975, 14th Int. Cosmic Ray Conf., 1, 268. Sal peter, E. 1955, Ap. J., 121, 161. Schramm, D. N., and Arnett, W. D. 1975, Mercury, 4, 16. Scott, J. S., and Chevalier, R. A. 1975, Ap. J. (Letters), 197, L5. Shapiro, M., and Silberberg, R. 1977, Bull. Am. Phys. Soc. Webber, W. R., and Lezniak, J. A. 1974, Ap. and Space Sci., 30, 361. Wefel, J. P., Schramm, D. N., and Blake, 0. B. 1977, Ap. and Space Sci., in press. THE CORONAL IONIZATION MODEL

FLARE STARS AS COSMIC RAY SOURCES ?

M. Casse and P / Goret Service d1 electr onique physique/ Centre d' Etudes Nucleaire- s de Saclay ,/France Thcorctical [7] Experimental Q Both Q]

In recent years , as suprfrnova or pulsar theories of the origin of Galactic Cosmic Rays (G. C. R)/had problems in giving a self-consistent picture of the cosmic ray sources, alternative models were proposed . These models start from the observation that the abundance'biases of the G.C.R source with respect to ordinary galactic matter seem correlated with the atomic properties of me elements . This view is supported by the observation that the same feamires probably show up in the Solar Cosmic Rays . We briefly recall our /coronal-type ionization model and discuss of the relevant physical conditions . These conditions are likely to be encoun- tered in common astr ophysical sites . We tentatively consider the extent to which powerful eruptive ^tar s (flare stars) could contribute to the supply of the G. C. R .

Present address :/California Institute of Technology - Pasadena

Coordinates: 1.8.1/ Cosmic Ray Sources

Mailing address: P. GORET DPh/EP/ES - Bat 28 Centre d'Etudes Nucleaires de Saclay B.P. 2 - 91190 Gif-sur-Yvette (France) bCjrWODfrt

COSMIC RAYS FROM PRE-MAIN SEQUENCE STARS

H. Reeves and C.J. Cesarsky Service d'Electronique Physique, Centre d'Etudes Nucleaires de Saclay (France)

To reach the Main Sequence, stars transform a part of their gravitational energy into rotational energy, which must then somehow be evacuated. This energy is likely to be released through magnetic interaction with the galactic field. It seems plausible that part of this energy is transformed into cosmic rays. The rate of gravitational energy released by stars presently contracting toward the Main Sequence is evaluated. We show that within large uncertainties an acceleration efficiency of a few per cent may be enough to account for the energy requirement of galactic cosmic rays in the solar vicinity.

I. INTRODUCTION The case for the origin of cosmic rays in supernovae or supernovae remnants is no more as strong as it was before. The case was based on three points: a) the energy requirements were best satisfied by the large supernovae power, b) the overabundances of heavy elements could be accounted for by "in situ" nucleosynthesis, c) supernovae were known through their synchroton emission to accelerate particles to relativistic speeds. The realisation that important adiabatic losses must be associated with the emergence of cosmic rays (Wentzel 1973, Kulsrud and Zweibel 1975, Cowsik and Wilson 1975) has weakened the first point. The correlation of overabundances of chemical elements with their first ionization potential (Casse et al 1975),thereby opening the possibility of preferential acceleration as being the source of the overabundances - has weakened the second point. The absence of proof that heavy particles - and not only electrons - were participating in the emission of radiation has weighted against the third point. In view of the difficult situation met by the SN origin theory it seems worthwhile to consider other sources. Here we ,, consider young stars evolving toward the Main Sequence (MS). Simple considerations show that when a rotating star contracts at fixed angular momentum it speeds up until the rotation energy becomes comparable to the gravitational energy, thereby impeding further contraction. At typical rotational velocities as imparted from the differential rotation of the galaxy a protostellar cloud would reach the limiting equa- torial velocity at many times the present solar radius. In the same fashion, if the magnetic field lines were frozen in the interstellar gas, stars with solar masses could hardly form. The loss of angular momentum and of magnetic energy probably 16 occurs through processes involving hydromagnetic wave generation, resis- tive plasma instabilities and turbulence, all phenomena which can be accompanied by acceleration of particles. Thus an appreciable fraction of the gravitational energy released by a Pre-Main Sequence Star (PMS) must have transited through a rotational and a magnetic mode.

II. GRAVITATIONAL ENERGY RELEASED BY NEW STARS Our first task is to evaluate the gravitational power released by all stars presently contracting toward the Main Sequence and to compare it to the power required to maintain the Galactic Cosmic Rays (GCR) against escape and ionization losses. The energy required to replenish cosmic rays in the solar neighborhood is:

dW =3. 1039(Wcr) (H/lkpc) erg/pc2year , . dt (lev) (T/15. 10 years) ^ 1 where H=I000 pc seems a reasonable estimate for the equivalent width H (twi.ce the half width) of cosmic rays, given the recent discussion by Baldwin (1976} Wcr is the cosmic ray energy density; T is the containment time. For local cosmic rays, recent evidence on abundances of radioactive isotopes indicates that T~l. 5. lO^years (Garcia Munoz et al 1977, Webber et al 197 7); the containment time in other region is unknown. Salpeter (1955) has attempted to derive from the luminosity function ox stars in the solar environment, the dependence of the birth rate of stars on their mass, M ( in units of the solar mass) obtained a law of the form: f ( M) dM<*M~2* 35 dM for M > 0. 8. For lower mass stars, whose lifetime on the main sequence is longer than the age of the galaxy, it is impossible to derive a birth rate from the luminosity function without using a model of galactic evolution. As the luminosity function is smooth in this mass region, any model that supposes that the star formation rate was higher in the past than it is now leads to a birth rate function with a (suspicious?) bump in this region ( Schmidt 1963).

In a recent study Smith et al (1977) attempt to interpret existing radioastronomical data, as well as data on galactic abundances of elements, in terms of a model of galactic evolution where the star formation rate at a given location on the disk is proportional to the surface density of gas at the power k; the required birth rate of stars of MO decreases as • k increases the best models are obtained for k = 0. 5 to 1. The present birth rate of stars, according to Smith et al, can be approximated by:

N ( M ) dM = f (M) dM = C j 10_9dM /pc2yr (3) CLCT ——- M2- 35 where the star masses and radii are in solar units. 17

C1 = 1. 58 for M) 1 C2 (0. 5) = 0. 47

Cf \ C2 M for C2 I1) = °'23 ^ We want to compute the gravitational energy released by all stars as they approach the MS. For stars with M>0.4 the contraction time toward the MS is much smaller than the age of the galaxy: we need then only to multiply the present birth rate by the total gravitational energy released a GM2, where R is the MS radius andor~2 for the sun. From stellar models (Allen 1973) we estimate the mass dependence of the function GM2/R on the MS to be«M1,28 for M)>0.4 and ec M for M<0.4. First we consider the contribution to the gravitational energy release from stars with M> 1 for which the observational uncertainties are the smallest: dWgrav C N (M) GM2 dM = 4. 8 x 1Q4° erg (5) dt M» 1 1J R pc^yr For smaller mass stars we shall have to introduce explicitely the time dependence of the stellar formation rate in the galaxy in order to incorporate the effect of the contraction time to the MS . Following Schmidt (1963) and Salpeter (1955) we write the birth rate function of stars as dN (M, t) = f (M) g (t) dM The function g (t) depends on the present gas to mass ratio and on the exponent k defined before. The case k=l seems particularly well suited to account for the distribution of metallicity in stars ( Fowler 1972, Pagel and Patchett 1975) and with long lived radioactivities (Reeves and Johns 1976). As. shown by Vigroux et al (1976) in the solar vicinity we have tiien g (t) = e (instant recycling approximation),is determined by g (tg) = e"tg/T= ^Mgas y 0. 1 in the solar neighbourhood^ g is the age of the galaxy. The case k= 1/2 ( not incompatible with observations) would give a g (t) decreasing with time at a rate between a linear decrease (corresponding to k-0) and an exponential decrease (k=l). For M< 1 we write dff(t) = f M2 N (M) dM (6) dt / R c/M/c/M^1l ? , -r J The contraction time tc is given by (

f3. 4 x 10 erg pc y for k = 1 , 40 -2 -1 , , 4.2 x 10 erg pc y for k = 1/2 18

Both values are slightly over estimated due to the fact that we should have used here a time dependent radius. However as they are at any rate slightly smaller than the contribution from M> 1 this overesti- mation is of no importance for our discussion. The total gravitational energy release obtained from the present discussion based on the birth function given by Smith et al (1977) is then _dW ~ 8 x 104°erg pc~2yr_1 (7) dt The presence of planets of various sizes in our solar system clearly shows that in multiple systems the contraction time is much

smaller than the radiative contraction time tc used in this work; this is especially important for us since Jupiter for instance is known to be (still today) a powerful cosmic ray emitter. This opens the possibility of an extra contribution which in absence of an appropriate birth rate function we can not evaluate at the present time. Neglecting for the moment the contribution from multiple systems and using'%or the cosmic ray power required to account for the observations in the solar neighbourhood,we find that stars contracting toward the MS are required to transform in relativistic particles about four per cent of their gravitational energy release in order to account for the GCR.

III. DISCUSSION a) The chemical composition of the cosmic rays . One important piece of information for our discussion is the fact that most of the overabundances appearing in the GCR also appear in the solar cosmic ray abundances (Webber 1975). This shows that some mechanism exists which preferentially accelerates certain elements and/or sorts them according to their rigidity (Casse et al 1975) and transform a thermal solar type composition in a fast GCR type composition. Furthermore the similarity between the radio and optical energy fluxes (~10-^) during flares at the surface of eruptive K, M stars and the sun suggest that the same mechanism takes place in these various stars (Lovell 1974). The fact that the flares are many orders of magnitude more powerful than in the sun is of relevance to the case (Casse 1976). b) Conclusion. The contribution of T Tauri stars (P. M. S stars) and flare stars to the galactic cosmic rays have been considered, by a number of persons (Ginzburg and Syrovatskii 1964, Lovell 1974, Casse 1976). Here we have shown that the gravitational power released by contracting stars is some twenty to thirty times larger than the power required to maintain the GCR. Since the formation of individual stars implies the transformation of at least a part of this power in rotation and in magnetic modes which must themselves be dissipated, it is not un- reasonable to believe that fast particles may be accelerated in those stars, which could contribute in an important way to the observed GCR flux. 19

REFERENCES

Allen, C. W. , 1973, "Astrophysical quantities", The Athlone Press. Casse, M. , Goret, P. , and Cesarsky, C.J. ,1975, 14th Cosmic Ray Conf. 2, 646. Cowsik.R. , and Wilson, L.W., 1975, 14th International Cosmic Ray Corn., 475. Garcia-Munoz, M. , Mason, G. M. , and Simpson, J. A. , 1977 " The age of the Galactic GoSmic Rays derived from the abundance of ^Be. Preprint. The University of Chicago.

Ginzburg, V. L. , and Syrovatskii, S.l. s Page 192 "The origin of Cosmic Rays", Pergamon Student Editions, 1964. Kulsurd,R., and Zweibel, E. , 1975, 14th International Cosmic Ray Conference, 2, 465. Lovell, B., 1974, Phil. Trans. R Soc. Lond A 277 , 489. Pagel, B. E. J. , and Patchett, B. E. , 1975, MNRAS 172, 13. Fowler, W. A. , 1972, in "Cosmology, Fission and other matters; a memorial to G. Gamow, Colorado Assoc. Univ. Press. Reeves, H. , and Johns, O. , 1976, Ap. J. 206, 958. Salpeter, E. E. , 1955, Ap. J. , 121, 161. Schmidt, M. , 1963, Ap. J. , 137, 758. Smith, L., Biermann, P., and Mezger, P. G. , 1977, Astron. and Astrophys. in Press. Vigroux, L., Audouze, J., and Lequeux, J., 1976, Astron. and Astrophys. 52 , 1, Webber, W.R.', 1^75, 14th Int. Cosmic Ray Conference, Munich 5, 1597. WSifcar, W.R. , Lezniak, J. A., Kish, J.C., and Simpson, G.A., 1977 10 "A measurement of the abundance of cosmic ray Be and its implications for the cosmic ray age" Preprint. University of New Hampshire. Wentzel, D. , 1973, Astrophys. andS.S. , 23 , 417. 20 j

SELECTIVE INJECTION A.S AN ACCESSORY OF FERMI ACCELERATION IN SUPERNOVA REMNANTS

M. M. Shapiro and R. Silberberg Laboratory for.Cosmic Ray Physics Naval Research Laboratory Washington, D. C. 20375

Certain features of the composition of cosmic rays—the Ar/Ca ratio at the sources and the He/H ratio in energy per nucleon intervals—favor ionization potential effects as an accessory to nucleosynthesis. The ratio of Ar to Ca abundances in cosmic-ray sources is calculated to be 0.1+ ± O.b with the newly measured cross sections of iron measured by Lindstrom et al. On the dither hand, a value of ~1.3 is expected on the basis of sdlar wind measurements of the Ar/He ratio, as well as from arguments based on nucleosynthesis. Alternative explanations/ (reduction of the heavier oxygen burning products S, Ar ajid Ca) are explored, and an experimental test to resolve/the problem (measurement of the 36Ar/4°Ca ratio) is suggested.

1. Introduction. There have been two classes of explanations of the source composition of cosmic rays: Al) Nucleosynthesis (e.g., Hainebach et al., 1976; see also Shapiro and Silberberg, 1970 and references therein on p. 376). (2) Injection near 104 °K, dependent on ionization potential (Havnes, 1971, Kristiansson, 1971, and Casse, 1975).

We point out some experimental observations which suggest that process (l) is supplemented by process (2), especially in the case of certain noble gases like Ar and He. Trie relative abundance of Ne is also consistent with this interpretation. J

2. Data favoring an accessory contribution to the composition of cosmic rays that depends on ionization potential. The ratio of Ar/Ca abundances at cosmic ray sources is b.k ± 0.U, while a value of ~1.3 is expected from in- terpolation between S/and Ca, as well as from arguments based on nucleosynthesis (Woosley et al. 1973) and the composition of the solar wind (Geiss, 1975). /

Likewise, the Contribution of effects due to ionization potential is favored by the He/H ratio of cosmic rays 0.05 at the same velocity or energy per nucleon), if we adopt a velocity-dependent acceleration mechanism and injection mechanism at the sources. Scott and Chevalier (1975) propose such a scheme—a/second order Fermi process that accelerates cosmic rays in supernova shells^. (With a rigidity-dependent acceleration, or possibly with rigidity-dependant injection, the He/H ratio fits the value calculated by Hainebach et alt. (1976) from nucleosynthesis and interstellar mixing.)

Recently/Blake et al. (1977), have proposed accessory effects that depend on the first ionization potential to explain the observed ratios of Pb/Pt and U/Pt in cosmic rays.

3. Data chat present difficulties for effects depending on ionization potential. / Sufficient cooling of supernova remnants (104 °K) appen.TR to take 25

/ & Table 3. Summary of high-energy pulses from/supernova.

prompt shock hig m-energy nucr.eosyn, Type V x or "V u.v. v } n "Y "Y lines

Carbon deto- 3 nation^ sub- I supernova - - - X c e I X p / w w w X f?P / I-B or II // leaky box X 5 X X X X closed halo X w w w X 4 9 black hole X - } - — —

£L / x denotes "yes", w denotes 'Vafek signal", - denotes "no", p denotes prompt (< 1 sec), s denotes "slow" (delayed » hours to 1 day), ? denotes that production of the signal is question- able, and is to he verified/experimentally. ^No pulsar or neutron star/formed. / Assumed an old, slowly rotating white dwarf, with very weak magnetic field, collapses without the carbon detonation process. The existence of type I is uncertain, and can be determined by methods/proposed in this paper. d / If Colgate's acceleration mechanism is valid, expect x- or Y-ray burst, especially for type I. e j The columns for high-energy v and y appear similar, yet the information content differs—the electromagnetic cascade is greatly affect eel by the magnetic field.

6 . Conclusions. Measurements of the time intervals between high-energy neutrino and photon ^pulses, and of the various signal strengths, permit estimation of the size of the supernova progenitor, tests of pulsar origin for particles above 10f5 eV, tests for black hole formation, and of galactic confinement models such as the leaky box and the closed halo.

7. References^ Arnett, W, D.,n.976, Internat. Symp. on Structure and Content of the Galaxy and Galactitf Gamma Rays, Goddard Space Flight Center, Greenbelt, MD., p. 286. Clayton, D. a., 1973, in Gamma-ray Astrophysics, edited by F. D. Stecker and J. I. Trompka, NASA SP-339, P. 263- Colgate, S.A., 197^, Ap. J. 187, 333. Kahn, F. Dj, 1975, lith Internat. Cosmic Ray Conf., Munich, Rapporteur Papers, 11, 3560. Silberbeafe, R., 1976, Proc. 1976 DUMAND Summer Workshop, Univ. Hawaii, p. 55. Tammann/G. A., 1976, Proc. 1976 DUMAMD Summer Workshop, Univ. Hawaii, p. 137. bQWOQIte 26

HIGH-ENERGY COSMIC NEUTRINOS AND PHOTONS FROM POINT SOURCES, AND IMPLICATIONS FOR GALACTIC CONFINEMENT R. Silberberg and M. M. Shapiro Laboratory for Cosmic Ray Physics Naval Research Laboratory Washington, D. C. 20375

The power input into highly relativistic electrons at the Crab pulsar nearly equals the neutron star's rate of energy loss due to spin-down, (a) Assuming that, a newly formed pulsar is an efficient accelerator of cosmic rays (» 10$ efficiency), and (b) adopting Ruderman's estimates of the initial pulsar spin-down rate x 1040 to 1043 ergs/sec), we calculate the rate at which • neutrinos are detected. In 1011 tons of water, in U months, and for E ^ H TeV, one can expect ~ 6 x 10s to 108 neutrino events from a supernova at 10 Kpc, and 1 to 500 from 7•5 Mpc; about 1 supernova per year occurs at the latter distance. These ra~es correspond to the range of estimated values of the original rate of spin-down. For the closed galaxy model of Peters and Westergaard, the required rate of energy input into cosmic rays is less by about two orders of magnitude. In the latter case, only galactic supernovae are likely to generate observable fluxes of neutrinos. Strong radio galaxies like Cen A are powerful emitters of gamma rays between 1011 and 1012 eV, and Cen A should yield ~ 10 neutrino events per year in a 1011 ton detector.

1. Introduction. Berezinsky (1976) has proposed that young supernova shells serve as an interaction medium for high—energy cosmic-ray protons. During the first four months the shell is sufficiently dense for protons to interact, generating TT- and K-mesons which, upon decay, yield neutrinos. The mesons generate electromagnetic showers in the supernova shell. While cosmic rays at energies below 1015 eV can be explained in terms of the promising acceleration mechanism of Fermi (19^9, 195*0, further developed by Scott and Chevalier (1975)» those above 105-5 eV require a different source-. Direct acceleration at the pulsar appears promising.

A detector size of ~ 1(P tons suffices for exploring neutrino emission from galactic supernovae, but ~ 1011 tons are required even for rudimentary studies of extragalactic ones.

3. Neutrinos from Supernova Shell Showers. The energy spectrum of neutrinos from supernova shells should exhibit time-dependent features, changing from ~ E-1 to ~E°. During the first days, the shell is sufficiently thick for the protons to undergo many successive collisions, becoming degraded in energy by several orders of magnitude. Also high-energy pions will then interact (rather than decay). After 2 months, only a single interaction is likely, with a pion (and neutrino) energy distribution resembling the flat or multi-fireball distribution of cosmic-ray jets.

A limitation in detecting point sources is the omnidirectional neutrino background, largely due to atmospheric neutrinos below energies of 1014 eV. 27

The angle between the incident neutrino and the outgoing charged lepton (L) is 6 ~ 8 x 10"3/ [E (TeV)] ^ radians (l) Lr V

i.e. ~0.5° at 1 TeV, and this is effectively the cone which determines the background contribution. In four months and for the corresponding solid angle of « 10 4 steradian, the atmpspheric background of near-vertical v at E > 1 TeV is ~ 1 count in 1011 tons of water.

Table 1 shows the expected number of neutrinos detected frojn supernova shell showers, at distances of 10 Kpc (to the galactic center) and 18 Mpc (to the Virgo cluster).

Table 1. Number of neutrinos detected in 1011 tons water, in U months, for 1Q% energy-conversion efficiency into cosmic rays (E > U TeV).

Frequency Supernova Number of Neutrinos Per Year Distance (Kpc) [initial Spin-down Rate (ergs/sec) 1043 k x 104o-J

~ 0.C8 10 108 6 x 105 1 7-5 x 103 300 1 ~ 18 20 x 103 1*0 0.2

Gamma-rays from shell showers. The emission of gamma-rays starts about 2 weeks after the stellar collapse; an electromagnetic cascade reaches the surface of the shell even when the shower has passed through about 20 radiation lengths of matter. The high-energy cascade, however, is appreciably suppressed by synchroton emission in the magnetic field when the shell is about one month old, ~ 5 x 10-2 gauss as evaluated from eq. 29 of Ruderman (1972). Obscuration by the diffuse gamma ray background is rather serious: in 107 sec, per m2, within a cone of resolution only 1° in diameter, some 103 photons with E > 100 MeV arrive.

Table 2. Number of gamma rays (£ ^ 100 MeV) incident on 1 i?, in months, for 10$ energy-conversion efficiency into cosmic rays.

Frequency Supernova Number of Photons Per Year Distance (Kpc) [initial Spin-down Rate (ergs/sec) 43 4 10 h X 10 °]

~ 0.08 10 U x 107 2 x 105 1 7.5 x 103 80 O.k ~l8 20 x 103 10 0.1 28

5. Fluxes for a closed galaxy model. For the closed galaxy model of Peters and Westergaard (1977)> the required energy conversion efficiency is much lower. Accordingly, the expected number of neutrinos and gamma rays from supernova shells is less. The energy conversion efficiency X for various galactic confinement models can be estimated from the following equation (Silberberg, 1976):

e = v T Ew X f / V, (2) where e is the measured energy density of cosmic rays (at energies E > 1015 eV) = 1+ x 10"4 eV/cm3, (Wdowczyk, 1975) v is the frequency of supernovae in the galaxy, ~ 1 in 13 years (Tammann, 1976), Ew is the energy output of a pulsar due to loss of rotational energy, (about 1051 ergs), f is the energy loss of cosmic rays due to adiabatic deceleration on pushing their way out from the vicinity of the pulsar; from Cowsik and Wilson (1975) , one can estimate f ~ 0.01. The galactic confinement time T (and the corresponding path traversed in the galaxy) at energies near 1015 eV is poorly known. For the leaky box model, extrapolating the E-0"3 energy dependence of the (Li, Be, B)/(C,0) ratio to 1015 eV, T » 105 years (and the path length x « 0.1 g/cm2) for the disk model, and T « 5 x 106 for the halo model. In a model having energy-dependent confinement in the sources up to ~ 100 GeV/u, x may be taken to be «1 g/cm2 at energies up to 1015 eV; the values of T are then higher by one order of magnitude. For the closed galaxy model, T = 108 to 109 years. % The confinement volumes V are 5 x 1066 cm3 for the disk modeL and « 2 x 1068 cm3 for the halo model. For the leaky box model, (with either disk or halo confinement), X « 0.1, and it would be about 2 orders of magnitude lower for the closed galaxy model. An independent expression for the energy conversion efficiency, that does not depend on the uncertain assumptions regarding confinement time and adiabatic deceleration, is given by:

E = X F E (U months), (3) V v w where E^ is the energy input into neutrinos (to be measured), F is the fraction of pion and kaon energy going ultimately into neutrino^ *« 0.5, and EW(U months) is the rotational energy loss in the initial U-month period. An estimation of X from Eq. 3 provides a test of the closed galaxy model of Peters and Westergaard (1977).

6. Neutrino emission from strong radio and y-ray sources. There are powerful radiogalaxies (Cen A, Cyg A) whose intrinsic radio fluxes exceed that of our own galaxy by factors of ~103 to ~ 10 6. Cen A is also known to be a powerful gamma-ray source at energies near 10 MeV, and even as high as «1 TeV. Other strong sources of synchrotron radio emission and of y-rays are galactic supernova remnants like the Crab nebula, Cas A and Vela. If we assume that the ratio of neutrino flux from a source to that of our galaxy equals the ratio of the corresponding radio emissions, r = source ^ radio flux, source /. x v-flux, our galaxy radio flux, our galaxy ' one can expect values of H » 10~3 to 10"2 for the above sources. The neutrino fluxes (at 1 TeV) to be expected in a detector of 1011 tons are shown in Table 3. It can be seen that the neutrino events from strong point sources considerably exceed the statistical fluctuations of the atmospheric background. • 29

Table 3. Neutrinos expected to be recorded per year in 1011 tons of water.

„ , , Counts/year, for Atmospheric background vU} R = 10"* R = 10"3 v + v vertical v e |x e

1 TO T 30 ± 5. 5 3 ± 1.7

At lower energies, below 1 TeV, the conditions for detection are poorer due to lower collimation of the charged leptons that are produced.

7- Conclusions. The prospects for detecting high-energy neutrinos (E > 1 TeV) from point sources, e.g., supernova shell showers and strong radio sources, galactic as well as galactic, are promising. However, large detector sizes, ~ 1011 tons of water are required. These could be attained with an acoustic array for detection of particles.

8. References.

Berezinsky, V. S. 1976, Proc. "1976 DUMAND Summer Workshop, Univ. Hawaii, p. 229. Cowsik, R. and Wilson, L. W. 1975, Conf. Papers, lUth Internat. Cosmic Ray Conf., Munich, 2, U55- Fermi, E. 19^9, Phys. Rev. 75., 1729. Fermi, E. 1951*, Ap. J. 119, 1. Peters, B. and Westergaard, N. J. 197T, to be published. Ruderman, M. 19T2, Am. Rev. Astron. Astrophys. 10, U27. Scott, J. S. and Chevalier, R. A. 19T5, Ap. J. (Letters) 19T, L5. Silberberg, R. 1976, Proc. 19T6 DUMAND Summer Workshop, Univ. Hawaii, p. 55. Tammann, G. A. 19T6, Proc. 1976 DUMAND Summer Workshop, Univ. Hawaii; p. 137- Wdowczyk, J. 1975, Phil. Transac. Royal Soc. (London) A. 277, ^3. 30 Katdre

R. Cowelk and M. LM

* Tata Institute of ftandamarttal Research, Bombay 5, India + Department of Kysics, Washington pniversity, St. Louis, Mo. 63130

Theoretical X

Aesuaing that cosmic rays originate ixi discrete sources distributed on the galactic plane, we discuss their oronagation including effects due to spallation energy loas and dirnisiv*-. leakage at the surface of the galactic disc. The unique correspondence between the position of the •break' in the electron spectrum and the yaLae of L/H ratio ie lost in this spatially dependent calculation. We can use the obscured spectrum of electrons to say that there should be at least active sources of cosmic rqjrs in the galactic plane. /

Fluctuations in t>ia positionI s of the nearest sources oroduce effects similar to that in the ohenomenological model recently put forward by- Peters. In the context of the naet-ed leaky box model of COWBUC and Wilson, we predict the )£-rajr luminosities of the galactic comic-ray sources.

Co-ordinates^ 00 1.8.

Mailing Address: Dr. K. Cowslk Tata Institute of Fundamental Research Hani Bhabha Road Bombay 400005, Ih-iia &QWO0/W 43

RiLaAiU AiiD CuBMIG RAYS IN THE! DENSE SUPERNOVA SHELLS. V.SJBerezinsky and. O.F.Prilutsky Institute for Nuclear Research, Academy of Sciences of the USSR.

Cosmic rays (c.r.) injected "by a young pulsar in the dense supernova shell are considered. The maintenance of the Galactic- c.x. pool by pulsar production is shown to have a difficulty: adiabatic energy losses of c.r. in the expanding shell demand a high initial c.r. luminosity of pulsar, which resulta in too high, flux of -radiation produced through TT0-decays (in ex- cess over diffuse # -ray background) .

I.Pulsars and accelerated particles in supernova shells. The supernova explosion is usually thought to result in blow out the shell and in the oroduction of a rotating magnetic neutron star (pulsar) whose magnetic dipole radiation can effectively accelerate the particles (Gunn and Ostriker 1969, Kulsrud et.al. 1972, Rees and Gunn 1974). If the pulsar braking is caused, by magnetic dipole radiation, its luminosity decreases as 2 3 Lmd(t)=Lo(l+t/ "Cm )~ , where *Uw=3c I /4fW*.Q.0 , X is the moment of inertia, M is the magnetic moment and is the initial angular velocity ( S^L.q'V IO^s * is usually assumed). The number of protons with the energy =E/Bq injected per sec. in the shell by pulsar is

2 (2f +I) Q(£ ,t)=( * -I)( V Lo /E* )(l+t/ Tmr E " (I.) where Eq is the minimum energy in. the spectrum and. }\ is the fraction of energy of a magnetic dipole radiation transferred to the accelerated protons, We shall consider the supernova shell with M=IM q expanding with. the constant velocity u I.I09cm/s untill it sweeps up the mass of interstellar gas equal, to the initial, mass of the shell. The protons accelerated by pulsar are continuously injected in the shell. Their total number £ in. the shell is governed by equation

- Q (£ ,t) -ccr n tt) N p f - co-p h fct)N p fe W -H c>t p (2) 44 where n(t)=3IV'4ir nuR^t) is the particle density of the shell, R(t) is its —26 2 radius, nig is the mass of hydrogen atom, si 4*10" om is pp-croas-section and dk =>l/2 is the fraction of energy retained by a projectile pra- toib in the collision. We take the solution of Eq.(2) at. £ I in the form: »P, (3) 0 where ¥ (t); is the total energy of protons, in the shell, with individual

energies higher than Eq. Inserting (3) into (2) we get

2 w (t) dKp /« =Lo(i+t/rm)" - t) - ife ^ P <*> vhdio ^•ps^r —1w - -

The expanding shell filled with c.r. can be characterized, by the following four specific moments (ages). 1) The moment t ^ from which on the decay time of chained pions with. Lorentz—factor becomes less than the time between two nuclear collisions t

\ 41T UJGU / \ w

2) The moment t ^ since which on the shell becomes transparent for ^-quanta: /2 2 JM tjf „ y = 2.8 10 (m/M©—^) sec (7) 2 4ir u crax_& J 3) The moment t , given by Eq.(5) since which on adiabatic energy losses begin to dominate over those due to nuclear collisions. 4) The moment t^ when the mass of interstellar gas captured by the shell becomes equal to the initial mass of the shell:

I f 3 M \ 1/3 9 I/3 tbX u Us?firJ a 6,510 } se° (8) In Eqs (5)-(8) =1.7 IO'^g/cm3 is the mass density of interstellar m gas, radius of the shell at t=tb is Rj, =utb and at t>tfe is R(t)<>> t , where m=2/5, M is the mass of the sh' ell (M=IMQ will be used), 45

2fi 2 —26 2 (f =4.10" cm and (j^f =2.5 10 cm are pp- ancl. TTp-crosa-sectiona rea- pectively, X^ =2.6 10 a is T -life-time and. xrad=62g/cnr: is the radiation length for hydrogen shell. The solutions of 3q. (4) ares A) T4 to. At t to, V„(t)- ALfl+t/x )"2 t3/ti P ° (9)

At t » tb WpC"t)= Wp(t0)R*(t0) /R*(t)

where W (t ) .is defined "by continuity condition at t si t ^ . B) * <<

At t < to. Wp(t)= (10) t)= At t >> t b V C) T» u

At t < t^ wp(t)= t)= At t» tb V (II) At t»X. Vt)= 2.Upper hounds on the c.r. initial luminosity of a pulsar. The c.r. initial luminosity of a pulsar is limited due to the following: I) the V -radiation from all extragalactic supernova shells must not exceed the diffuse tf -ray background and 2) nuclear energy losses of c.r. in the shell are limited by observed optical radiation of supernova (light curves). The y -radiation of the shell is mainly produced through decays of

r.eutral pions generated in pp-collisions. At t > ty the shell is transparent for Jf -rays as far as pair production in Coulomb field of a nucleus is concerned. But for high energy y -rays 100 GeV) it remains still . + — opaque due to the reaction H + ^ e + e at the collis^ons®with the thermal photons ( .) . The tf -radiation with E^ h 100 GeV becomes more effective when periphery of the shell is cooled to the temperature it originates from the outer parts of the shell. This suppresses 8"-radiation with Ej >, 100 GeV in comparison with E^ >, 100 MeV, If emission of the light in the shell is generated due to c.r. nuclear collisions, the factor of suppression increases. Calculation of y -radiation of the shell (E^ 100 MeV) and comparison of the total IS -flux from extraga- 46 lactic supernovae with observed. diffuse y -radiation at llj 100 MeV (Berezinsky, Prilutsky 1976) result in the following upper limits

4 44 7 ( S) Sjj/2.I0" >( VL/I0 )(T/I0 ) < 0.6 at ia TCU (12) 4 44 ( S) SE /2.I0- >( > Lq /IO ) < 0.5 at X » where S) gjj (in Mpc "Vears-"*") is the average rate of extragalactic supernova explosions, >Lq is in ergs/s and. "C is in s. The light curves of su- 43 44 riernovae yield ALq< I0 -I0 ergs/s. 3. Pulsars and c.r. in the Galaxy. To provide the Galactic pool, of c.r. 50 a supernova must produce c.r. with the total energy 1.10 ergs. This energy c.r. must retain to the moment of exit from supernova shell. It occurs when the c.r. pressure in the shel•j l 2 falls down to the pressure of interstellar magnetic field: 3W /4ffR^ ~ H /81T , where Rq is the radius of the shell at the moment of the exit. At R > E c.r. begin diffusing in c the interstellar medium instead of expanding as gas and therefore they d.Q not suffer any more the adiabatic energy losses. Inserting W (t )=W in p c p Eq's (9)-(II) we shall find the value of ^ which is to "be compared with the upper limit (12) derived from 2T-ray background and with. 43 44 ALq < I0 -I0 ergs/s, derived, from-the optical observations of supernovae. Then we comn e to the following conclusions in the cases A)—C): A) T < to, =1.3-10 s. If the total energy of c.r. at the moment of exit 50 from supernova shell is V 1.10 ergs and extragalactic rate of supernova P I T T explosions is V sjr Si 2.10 Tip c^years"" (Talbot 1976, Tammanm 1976) , the total flux of TS -radiation with E* 70 MeV from supernovae is ~ 1000 7 8 times higher than observed one. B) to, tfe .At 10 <• <• 2.10 sec there is the contradiction with X -ray background and also, with optical g radiation at t t^ 150 days after supernova explosion. At (1*2) .10 s -flux from, supernovae is only 3 times higher than diffuse one but too high optical luminosity togethepr with, rjhape of light curve remains a serious contradiction. At Z > 2.10 see it ia difficult to reconcile the large initial luminosities which axe necessary to provide the Galactic c.r. intensity with the observed luminositie10 s of pulsars. For pulsar in Crab (the present luminosity L(t)~ 10 exgs/s and age ti^IOOO years) the value 42 "C'v 2.10®s results in the initial luminosity L0 ~ 2.I0 exgVa instead of 47

^v LQrv/ 1.5" IO^ergs/s necessary to provide the Galactic-c.r. intensity. C) X > t =6.5- I09s. In this case at t>t (when c.r. do not undergo the •' • 1 - c adiabatic energy losses) pulsar almost retains it's initial luminosity and as a result near the half of kinetic, energy of pulsar can "be transferred to the Galactic c.r. In. this case the initial pulsar luminosity was not much higher than one observed now and a pulsar produces c.r. with the same efficiency during IOQO-IOOOO years of its life. The' idea that old pulsars arcs the maim. c.r. sources meets no difficulties in adiabatic energy losses and. in tf -radiation of the dense supernova shell. 4. Conclusions. Generation of the bulk of c.r. in the Galaxy by young pulsars meets the serious difficulty. At usually accepted, braking time of n pulsar ( X'k. (1+3) .10 s) adiabatic energy losses, of c.r. in the expanding supernova shell demand the high initial luminosity of pulsars (Kulsrud and Zweibel I975» Cowsik and Wilson 1975)» which results in the total y -radiation (through H° -decays in the shell) from extragalactic pulsars exeeding the observed flux of diffuse 2f -radiation in 100 MeV range. The hypothesis of c,r. acceleration by young pulsars can be tested by measurement of tf -radiation (with E x 100 MeV and E y 100 GeV) as well as neutrino radiation during 3-5 months, after supernova explosion.

References Berezinsky V.S. and Prilutsky O.F. 1976 Proc^Int.Conf. "Ueutrino-76" Cowsik R. and Wilson L.W. I975 Proc. 14-th Int. Cosmic Ray Conf.. 2, 475 Gunn J.E. and Ostriker J.P.I969 Phys. Eev. Lett. 22,728 Kulsrud R.M., Gunn J.E., Ostriker J.P. 1972 Phys-Rev .Lett. 28,636 Rees M.J. and Gurni J.E. I974 Mon.Not. 167,1 Talbot R.J. 1976 Ap.J,. 205,535 Tammann G.A. 1976 Proc. Workshop "DUMAKD-76" (Ed.A.Roberts.) 137. bQMoom

PROPAGATION OF COSMIC RAYS IN EXTRAGALACTIC RADIO SOURCES

James A. Earl

Department of Physics and Astronomy, University of Maryland College Park, Maryland USA 20742

The transport of charged particles which are scattered by random magnetic fields while they propagate along the diverging lines of force of a spatially inhomogeneous guiding field is described by the Boltzmann equation. Nearly rigorous solutions, based upon a matrix formulation of this problem, lead to a new interpretation of radio galaxies. A radio source is formed when electrons from a galactic explosion move coherently outward along the strongly diverging lines of a large scale guiding field centered on the galaxy. Far from the center, where the divergence becomes weak, the electrons are scattered into two slowly evolving, nearly isotropic, clouds which constitute the twin lobes of a typical source. In the early coherent phase, electrons are transported without adiabatic energy losses in static magnetic fields and without serious Compton/synchrotron energy losses in the relatively short time they take to reach the lobes. In the diffusive phase, the radio polarization is perpendicular to the source axis and the structures nearest the center, which are old ones that have drifted inward, have a steeper spectrum than those further out. In radio trail galaxies, where the velocity of the galaxy through an ambient medium exceeds the drift velocity of the diffusive clouds, this spatial variation of the spectral steepness is reversed. Thus, several basic observational features of extragalactic radio sources are explained in terms of fundamental transport theory.

1. Introduction. Scattering by magnetic turbulence plays a crucial role in the propagation of cosmic-rays. In many circumstances, this scattering is sufficiently intense that the familiar phenomenon of diffusion adequately represents the spatial and temporal evolution of a cloud of charged particles. However, these diffusive effects, which embody the lowest-order solution of the transport equation, are accompanied by higher-order effects which are negligible when the scattering is intense but which can become important when the scattering is weak. The effect of the next higher order beyond diffusion is the coherent propagation of a bunch of particles within which the density can be represented by a Gaussian profile whose center moves with a characteristic velocity while its width increases with time at a rate characterized by a coefficient of dispersion CEarl 1974; Kunstmann and Alpers 1977). Adiabatic focusing has a profound effect upon both the diffusive and the coherent modes (Earl 1976a) , for particles are deflected not only by the longitudinal forces exerted by random fields, which lead to pitch-angle scattering, but also by those exerted by perpendicular components of a spatially inhomogeneous guiding field, which lead to a systematic alignment of trajectories along the guiding field. In a strongly diverging guiding field, where systematic alignment overwhelms random scattering, coherent propagation replaces diffusion as the dominant mode of particle transport. This qualitative change occurs with striking abruptness as focusing is intensified. However, the diffusive mode always 49 persists as a Gaussian feature that drifts toward stronger fields with a relatively small velocity in the direction opposite to that of the coherent feature. To designate this focused diffusive propagation, I use the term pseudodiffusive to distinguish it from focused coherent propagation which I call the supercoherent mode.

To illustrate these basic modes of focused transport, John Bieber has prepared Fig. 1, which shows "snapshots" of density F0 vs distance z at several instants of time . t - 14 following the injection of a bunch of particles. These profiles, which were calculated with the aid of the 12 program described in Paper SP-39, represent comprehensive solutions of the Boltzmann equation which 10 include all significant effects. In the bottom profile, t = 0, a narrow Gaussian spike of particles appears at the point of injection z = 0. Because its angular distribution corresponds to coherent propagation with a characteristic velocity of ^0.6V, this spike moves to the right />A ' into weakeT guiding fields without changing its shape, but its amplitude * decays so rapidly that the spike is 3 no longer visible after t = 2. In the second profile, t = 1, a small "back porch" appears behind the spike. J\ 2 In the fourth, t = 3, this feature develops into a clearly defined Gaussian which moves toward the right A 1 at ^0.5V and which decays into insig- v/AH h- 1 LH h- nificance by t = 10. This is the A supercoherent disturbance. In turn, q = l.5 0 it develops a "back porch", which is 1 visible in the fourth profile, t = 3, V/AL >1.0 and which develops into a feature that - i 4— -. propagates toward the left into -10 -5 10 stronger guiding fields. This is the pseudodiffusivs disturbance. As the Figure 1 importance of focusing, measured by the focusing length L, increases relative to that of scattering, measured by the scattering length (V/A), the supercoherent pulse persists longer and the pseudodiffusive profile appears later, until, in the limit of strong focusing, the supercoherent mode becomes dominant. Because this change in the qualitative nature of particle transport occurs quite abruptly at a specific value of the focusing parameter (V/AL), I call it the supercoherent transition. In the discussion that follows, and in Earl [1976b), these fundamental aspects of focused transport find expression in the basic structure of radio galaxies. Moreover, these aspects also correspond closely to certain well known features of solar particle events. In a sense, these interplanetary phenomena serve as a "laboratory" experiment to test the theory.

2. Interplanetary Propagation of Energetic Particles. In "scatter-free" propagation of kilovolt flare electrons, an impulsive burst of particles, usually followed by a slowly decaying tail, arrives at Earth with an average velocity parallel to the field of O.SV (Lin 1974). Wc interpret these events as supercoherent propagation of electron bunches in the diverging fields near the Sun. In the solar system, the parameter (V/AL) is not constant, for L «(r/2), where r is the distance to the Sun. Moreover, the radial dependence of (V/A) undoubtedly leads to additional variations of (V/AL). Consequently, there is a point at which the nature of interplanetary propagation changes from supercoherent to diffusive, for the focusing parameter must eventually pass through the supercoherent transition by virtue of its inverse dependence upon r. In this situation, shown schematically in Fig. 2, solar particles propagate supercoherently to a fairly abrupt transition (wiggly line) beyond which the propagation becomes diffusive.

The region of focused diffusion, beyond the wiggly line, can be further divided, by the dashed line, into a region near the transition in which maximum intensity occurs just after onset and a region far from the sun in which the intensity reaches a broad diffusive maximum well after onset. t The crucial point is that the profiles illustrated in Fig. 2 correspond qualitatively to well known types of solar events. On a more quantitative level, Linda Ma (1977) has demonstrated that most profiles observed after 51 r1 arcs un the western limb are accurately described by the predictions of focused transport theory. This good agreement is evidence for the basic validity of the theory.

The Structure of Extragalactic Radio Sources. Double radio sources, between which there is usually found un optical galaxy, are among the largest and most energetic, phenomena of astrophysics, but there is still no generally accepted explanation of these remarkable objects. The interpretation put fcrth here, which adopts a widely held view that the radiating electrons gain their energy within the central galaxy, describes the symmetrical transport of those electrons to great distances from this source and the subsequent o\ol-.ition of the clouds they form there, but it does not attempt to describe their acceleration. This interpretation, which is illustrated in Fig. 3, re-ts on the assumption that a large-scale magnetic field, which threads through the galaxy, extends far into intergalactic space to form a diverging guiding field along which focused transport occurs. Here, the basic morphology uf tiie double sources arises, in much the same way as in interplanetary propagation, when two bunches of electrons move rapidly out in opposite directions to .^upercoherent transitions where they form relatively long-lasting clouds which constitute the actual radio sources.

ftADIO LOBE GALAXV rAD,q LQflE Figure 3

A major objection is that the strong anisotropy of the supercoherent mode might be rapidly attenuated by collective effects (IVentzel 1974). Because the characteristic time for the growth of waves is much shorter thin the duration of the supercoherent pulse, the steady-state picture, in which wave effects limit streaming velocities to the Alfven velocity, is applicable. However, this growth rate may be overestimated, because it appears in the same quasilinear picture in which scattering is too intense. In any case, the supercoherent mode can persist in the presence of scattering, including that generated by the particles themselves. The interplanetary analogy may be relevant here, for Jovian bursts do persist while generating waves (Smith ct al. 1975).

Underlying the symmetry of double sources is the symmetry of the guiding field, which arises because Maxwell's equations guarantee that as many lines of force diverge out from a local condensation as converge into it. For example, if the central galaxy is surrounded by an expanding medium, the field would develop a radial pattern analogous to that of the interplanetary field. Alternatively, the energetic particles themselves may play a role in extending the field radially. Within these bilateral configurations, electrons 52 propagate and radiate in similar magnetic environments on opposite sides of the source. No matter how the electrons are accelerated, scattering within the central galaxy, which makes them isotropic there, ensures that the two bunches contain equal numbers of electrons. When these bunches hit the supercoherent transitions, particles are rapidly scattered into two clouds. Because these cloulds contain equal numbers of isotropically distributed electrons and because their pseudodiffusive evolution is slight during the time required for light to travel between them, the two lobes of the radio source appear to have nearly the same luminosity regardless of the angle between their axis and the line of sight. The axis is perpendicular to the E-vector of the polarized emission from the clouds. These predicted symmetries are the same as those observed by MacDonald, Kenderine and Neville (1968), who found that the intensity ratios of double sources in the 3C catalog are strongly clustered near unity and that the polarizations are strongly clustered around the direction perpendicular to the axis.

In pseudodiffusion, the peak of the radio profile moves toward stronger fields. Thus, if a series of discrete explosions occurs in the central galaxy, clouds from earlier events drift inward where they appear as weak secondary lobes lying on the axis between the relatively intense lobes from later events. The following double sources with well-marked lobes each resolved into a close pair have been reported by MacDonald, et al. (1968): 3C 53.1, 3C 61.1, 3C 184.1 and 3C 234. If the explosions occur frequently or if the acceleration is continuous, electrons drifting inward form a continuous bridge between the lobes. Clear-cut examples of this behavior are 3C 46, 3C 1.1\-1, 3C Zo-", 3C 430, and 3C 452. Because the Compton/synchrotron mechanism has more time to act on the electrons in these inner components, their radio spectrum is expected to be steeper than that of the outer Icbes. This prediction is i' accord with the finding of MacDonald, et al. (1968) that the emission from between the main components has a steeper spectrum than the source as a whole.

Radio trails (Wellington, et. al. 1973) ai*e believed to delineate magnetic fields dragged out behind as the central galaxy moves through a stationary medium. In this magnetospheric configuration (Jaffe and Perola 1973), the velocity of the galaxy may exceed the drift velocity of the pseudodiffusive Gaussian. Consequently, electron clouds from successive explosions are strung out in a trail behind the primary lobes which form, as before, as supercoherent transitions moving with the galaxy. This interpretation predicts that the radio emission from the tail decreases in intensity systematically with distance from the galaxy while its spectral slope increases. These are the effects found by Miley (1973) in 3C 129 and NGC 1265.

The probability of observing a double source in its supercoherent phase is small, but it is reasonable to expect that a few are currently in this phase. If such a source is viewed perpendicular to its axis, it appears as two relatively compact radio lobes moving apart with a velocity slightly less than twice the speed of light. This superluminous velocity of recession is smaller than the velocities of 4c and 6 c found in 3C 279 and 3C 273 (Cohen et al. 1971; Whitney et al. 1971). However, the apparent velocity of recession is enhanced when the axis is not perpendicular to the line of sight (Rees 1967). 53

4. Suirjrory. The model of extragalactic radio sources propsoed here is similar to previous interpretations (Longair, Ryle, and Scheuer 1973), which assume that relativistic particles carry energy from the central galaxy to the radio lobes. Unlike these interpretations, which invoke local acceleration within the lobes, the radio waves are emitted here by the same electrons that transport the energy. Fundamental characteristics of this transport, which takes place in the same magnetic fields that are required to explain the synchrotron emission, give r^se to the basic morphology of radio sources. Specifically, the emission .is confined to an axis because electrons propagate parallel to magnetic field more readily than perpendicular to it. Symmetrical lobes appear on this axis because electrons are deposited at the supercoherent transitions far from the central galaxy where they propagate diffusively. The slow drift velocities which characterize this propagation explain the secondary structure between the main lobes and establish a relationship between double sources and radio trail galaxies. The supercoherent propagation by which electrons reach the lobes proceeds at superluminous velocities of recession comparable to those observed in some quasars. Except for relatively slow changes which may occur in powerful sources due to particle pressure, only static magnetic fields are involved. Consequently, the adiabatic energy losses that embarrass interpretations in which electrons are transported within expanding clouds of thermal plasma do not occur in the present model. Finally, the basic features of focused transport are confirmed by interplanetary observations. In retrospect, it seems surprising that the analogy between the scatter-free propagation of solar electrons and the intergalactic transport of radio emitting electrons had not been recognized.

This research was supported by the National Aeronautics and Space Administration under grant NGR-21-002-066.

References

Cohen, M.H., Cannon, W., Purcell, G.H. , Shaffer, D.B., Broderick, J.J., Kellerman, K.I., and Jauncey, D.L., Ap.J., 170, 207 (1971). Earl, J.A., Ap.J., 188, 379 (1974). Earl, J.A., Ap.J., 205, 900 (1976a). Earl, J.A., Ap.J., 206^, 301 (1976b). Jaffe, W.J., and Perola, G.C., Astr. andAp., 26, 423 (1973). Kunstmann, J., and Alpers, W., Ap.J. in press (1977). Lin, R.P., Space Sci. Rev., 16, 189 (1974). Longair, M.S., Ryle, M., and Scheuer, P.A.G., M.N.R.A.S., 164, 243 (1973). Ma, L. , thesis, University of Maryland (1977). MacDonald, G.H., Kenderine, S., and Neville, A.C., M.N.R.A.S., 138, 259 (1968). Miley, G.K., Astr. and Ap., 26_, 413 (1973). Rees, M.J., M.N.R.A.S., 155, 345 (1967). Smith,. E.J., Tsurutani, B.T., Chenette, D.L., Conlon, T.F., and Simpson, J.A., J. Geophys. Res., 65 (1975). Wellington, K.J., Miley, G.K., and van der Laan, H., Nature, 244, 502 (1973). IVentzel, D.G., Ann. Rev. Astr. and Ap., 12, 71 (1974). Whitney, A.R., Shapiro, I.I., Rogers, A.E.E., Robertson, D.S., Knight, C.A., Clark, T.A., Goldstein, R.M., Marandino, G.E., and Vandenberg, N.R., Science, 173, 225 (1971). Afy WOO 4*6

LIGHT ELEMENTS PRODUCTION BY GALACTIC COSMIC RAYS:

THE STATE OF AFFAIRS

H. Reeves and J . P. Meyer

Service Electronique Physique, Centre d'Etudes Nucleaires de Saclay, France

In the light of recent measurements of light element abundances in meteorites, in the Sun, in stars and in the interstellar medium, their production by spallation reactions induced by observed high energy galactic cosmic rays is rediscussed. The requirements of low energy fluxes (unobservable at earth) are specified. Other interpretations are considered.

I- THE NEW PICTURE OF THE Li Be B ABUNDANCES Recent abundance determinations of Beryllium and boron on meteorites and on stars (including the sun) are used together with older measurements to select a set of abundances in various astrophysical locations for all three elements lithium, beryllium, boron . Particular care has been taken in the evaluation of the associated uncertainties .

Two new independant studies of meteoritic beryllium abundance by Eisentraut et al (1971) and Quandt and Herr (1974), bearing on one C2, two C3 and one unclassified carbonaceous chondrite, have appeared. From all the data we estimate that the C2-C3 abundance of Beryllium is 0. 36 0. 13. We consider that this value should be also representative of the CI abundance in view of (i) this absence of fractionnation between C2's and C3's (ii) the small degree of fractionnation of Be between all classes of chondrites (Mason 1971, Quandt and Herr 1974), and (ixi) the refractory character of Be, like all other earth-alkaline elements. For the sun , the non-LTE center-to-limb study of Chmielewski et. al (197 5), though based on a single line, yields a very reliable value. These authors give a thorough discussion of the various sources of systematic error (non LTE effects; atmospheric model; continuous opacity; blends; f-values, whic!. are very accurately known).

Boesgaard et al (1974, 1977) found an abundance Be=0. 10 in units

of in both Vega and in the Hyades (average over 6 stars) while Dravins and Hultqvist (1977) got Be=0.25 on Alpha Cen A. The more comprehensive LTE Study of 38 F and G stars by Boesgaard (1976b) yields an average Be abundance of 0. 13 0. 04 (see also Boesgaard and Ghesley 1976). The check that the Be II line is formed in LTE conditions on Vega (Boesgaard et al 1974), together with the correct LTE abundance obtained for the (comparatively cool) sun, show convincingly that non-LTE effects do not seriously effect the abundances obtained. In view of the spread of the observed abundances, we shall adopt an uncertainty factor of 1.6.

The Boron abundance has been the subject of a lot of controversy. 55

TABLE 1

OBSERVED AND ADOPTED "GALACTIC11

Li, Be, B ABUNDANCES

(in units of 10"10 of H )

(Figures in parenthesis indicate error factors)

Li/H Be/I-I B/'H

Meteorites CI, C2 22. +4. 0. 36 + 0.13 15. (2.)

Meteorites E4 19. ±8. 0.14 (?) 5- ( ?)

Solar CI. 10 £ 0. 03 0.14 (1.6) 2- (2- )

Stellar 10. (2.) 0.13 (1.6) 1.5 (2.)

1 S M 15. (?) ^f 1it*. ?

Adopted 10. (2.) 0.14 (l.fc) "Galactic" 2. (2.)

Fig. 1 56

We first consider carbonaceous chondrites. The three independant studies reported in Mason (1971) and Cameron et al (1973) use completely- different techniques and yield for 5 carbonaceous chondrites of all 3 types very similar values, all consistent with B=58 +_ 16. The absence of significant decrease of the B abundance from CI to C3 chondrites is puzzling for such a volatile element (which does show the standard fractionnation pattern of volatile elements between other classes of chondrites). Contras- ting with this concordance, two recent studies agree on much lower boron abundances in carbonaceous chondrites: (i) Weller et al (1976), who cross check two independant techniques, get B =22 + 8 for CI, 10 + 3 for C2 ?.nd 7.5 + 3 for C3 carbonaceous chondrites, in agreement with the standard fractionnation pattern of volatile elements; (ii) by another technique, Curtis et al (1976) get preliminarily an abundance ^12 for C3 carbonaceous chondrites. Discrepancies by factors or 3 to 8 are found between these and the older measurements on the same meteorites. Here we shall tentatively adopt the new C.1 -C2 values, i.e. B = 15 within a factor of 2. If the higher older values were the correct ones the differences with respect to solar- stellar and enstatite chondrites abundances which we shall discuss below would be even larger than with the adopted values. Until recently one had only upper limits on theB abundance on the sun. Engvold (1970) derived B<3 based on molecular lines in Sunspots, while WO hi (1974) and Hall and EngvOld (1975) derived respectively B<2 and B< 1.8 (B<1.2 +0.6 for systematic errors) based on atomic B I lines. The latter study discusses the possible systematic errors and should be considered quite reliable. Very recently Kohl et al (1977) obtained a po- sitive observation of another B1 line, yielding B = 4 within a factor of 2 due to systematic errors ( mainly to the continuum position error). Based on the marginal agreement of this value with Hall and Engvold's upper limit, we adopt B = 2 within a factor of 2 on the sun .

A B abundance has been obtained for one star. In their detailed study of a BII line on Vega Praderie et al (1977) get B = l. 5 within a factor of 2, taking into account non-LTE effects and the errors associated with f-values, blends, continuum position. . .

II. DISCUSSION OF THE OBSERVED ABUNDANCES (Fig. 1). From a study of this data the following statements appear reasonable. A comparison between stellar and solar value shows that neither beryllium nor boron have been burnt to any extent at the surface of the sun, while lithium has been destroyed by a factor of one hundred. This information is important for the history of matter mixing in the sun, and for the theory of surface convective zones of pre Main Sequence and Main Sequence stars. The carbonaceous chondrites of type 1 and 2 are enriched in boron by one order of magnitude over the stars and the sun. There are good indications that beryllium may be enriched by a factor three. 57

There is a remote possibility that lithium may be enriched by a factor of two. The similarity of this pattern with the case of the pegmatites is worth mentionning (Hurlbut 1970). A case is made that enstatites of type 4 have abundances of these elements which are closer to the stellar values than the carbonaceous chondrites. III. ORIGIN IN TERMS OF SPALLATION REACTIONS Comparison is made between observations and the theory of the origin of these elements by galactic cosmic ray bombardment of interstellar matter. The isotopic ratios of lithium cuid boron generated by the high energy component of this radiation (as observed in the vicinity of the earth) are not large enough to account for the meteoritic observations. The hypothetical pie sence of intense fluxes of low energy cosmic rays (perhaps confined in limited regions) is considered. The boron isotopic ratio can be obtained from a low energy component with an injection spectrum steeper than the High energy G.C.R spectrum. This suggests that the astronomical source of these particles is not the same as the source of the observed G.C.R. The origin r$ay be related to pre-Main Sequence stars. Uncertainties in theo^ + d-cross sections prevent us from stating whether these low energy particles could also account for the Lithium isotopic ratio - and hence for the origin of lithium-7- or not. At present time, we are not very hopeful.

IV. CONCLUSION In summary the observed G. C.R plus a tail of low energy particles with an injection spectrum in power of kinetic energy with exponent of four 10 iS or more will generate the isotopes ^Li 9Be B £, in agreement with the observations (stellar ratios of boron/beryllium and stellar ratios of lithium/ beryllium coupled with meteoritic isotopic ratios). It is not yet clear whether this mechanism will account for one half or all of the lithium-7.

REFERENCES

nocsgaard, A.M.. 1974, Astron. Astrophys. 34^ 9. Engvold, D., 1970, Solar Phys. ]_1_, 193. Uoesgaard, A. M., 1976, Astrophys. J. ZIP. 466. Hall, D.N.B. ct al. , 1975, Astrjphys. J. 197 , 513. BoesgEiard, A. M. et al. ,1976, Astrophys. J. 210, 475. Hurlbut, C. S. Jr. , 1970, "Minerals and Man" Random House Cameron, A. G. VV. ct al., 1973, Nature Z43. 204. N. Y. , p. 72. Chmielcwski, Y. et al. , 1975, Astron. Astrophys. 42, 37. Kohl, 1. L. , et al. 1977, Astrophys. J. Letters, Z1Z.. L lOl. Curtis, D, B. et al. , 1 976, to appear in Meteoritica. Mason, B. , 197 I, Handbook of Elemental Abundances in Dravins.D. et al., 1977, Astron. Astrophys. 55. 463 Meteorites (Gordonand Breach). Eisentraut, K. J. et al. ,1971, Analystical Chemistry. 43, 2003. Praderie, F., et al. 1977, Astrophys. J. in press (May 1977). Quandt, U., etal., 1974, Earth Planet. Sci. Letters, 24j 53. Weller. M. R. et al., 1976, Preprint Cal. Tech. OAP-467. Wohl.H. , 1974. Astron. Astrophys. 34, 41. 58

DEUTERIUM PRODUCTION BY COSMO LOGICAL COSMIC RAYS

T. Montmerle

Service d' Electronique Physique, Centre d1 Etudes Nucl6aires de Saclay (France)

Among the various low-energy interactions that take place at high redshifts (E~100) between a (hypothetical) flux of cosmological cosmic rays ("CCR" : protons and a particles), and the ambient gaseous medium, deuterium production is interesting in view of the relevance of this element to big-bang cosmology. The production cross-sections are discussed in detail. The abundance of deuterium produced by this process is computed by normalizing the CCR flux so as to account for the ~1-100 MeV y-ray background spectrum. The resulting D (and' ->He) abundances may reach ~ 20"Jo of their observed value. It is also shown how the results can be compared with those obtained recently by Epstein et al. on deuterium production by "pregalactic cosmic rays". 1. COSMO LOGICAL COSMIC RAYS AND LIGHT ELEMENTS In. the framework ol the "CCR hypothesis", discussed in a cDxtipanion paper (these proceedings, OG-17, hereafter Ml, and refs, therein), we have presented a derivation of the light element production by pp, pa and arc reactions, at low energiesj with the purpose of taking the abundances of light elements as observational constraints on the possible existence of CCR. In particular, we have shown that it is possible to account at the same time lor the observations of the I-100 MeV y-ray background spectrum^ and of the 7 Li abundance, although difficulties arise with the. "^Li/^Li ratio. On the other hand, because of their very low yield, nuclear y-rays (arising from the decay of excited states of light nuclei) are not a strong observational constraint, but their flux is nevertheless compatible with the CCR. hypothesis (see these proceedings, OG-45)"\ Now the observed abundance of D is 31 2±lxl 0"'^(e. g. ,• Vidal- Maajar et al. 1977), i.e., times the observed abundance of ?Li. Since the production cross-sections for D and 7 Li differ by a factor of ™50 at most (see below), it can be anticipated that it is a priori impossible to account for the observed deuterium abundance by the abovementioned CCR interactions. Nevertheless, since D is strongly relevant to big-bang cosmology (see, e.g., Reeves 1974, Epstein 1977), it is of interest to compute the abundance of this element in the framework of the CCR hypothesis. This has been done in a recent paper (Montmerle 1977a, and refs. therein), but more details will be given below (§ II). The results will be discussed in the light of other recent work (§ III). 59 3 Note that the abundance of CCR-produced He nuclei will not be explicitly computed. Because of very similar production cross- sections, the results obtained here for D are essentially the same for %e (see also Epstein 1977). More precision is not required, since %e is much less relevant to cosmology because of the many-*possible production and destruction mechanisms (e. g. , Reeves 1974).

II. DEUTERIUM PRODUCTION a) Cross-sections. The cross-section ^ij-jj^E1, E) for production of a particle of energy E by interaction between a particle i of energy E' and a particle J at rest will be written approximately as :

(see Ml, eq. 2-3). Vi The most important reactions giving rise to deuterons are presented in Table 1 along with their "code names" ; the cross-sections appearing in eq. (2-1) are noted a^n)(E'). These' cross-sections are rather well known up to high energies (Meyer 1972). Those corresponding to the reactions listed in Table 1 are depicted in fig. 1. We Table 1 examine now Reactions giving rise to Deuterium in turn the main d-producing reac- Reaction "code name" cross-section "X^ tions, focusing on their ~ TZ + j HI iTTT" ® p + H -»- d + i: ppd a. 0.25 kinematics A to make sim- ? + He| fd+d+p (2) 0 plifying appro- a + H ximations lea- 4 , „ p + He) , . 0.48 ding to expres- U i k- -pi aj3) sions of the a ' J d+T p c up form (2-1). The . T I (+) Moving rie nucleus corresponding values of \(nJ are gathered in Table 1 and the uncertainties on the results due to these approximations will be discussed in §II.b. The cross-section o^3 for the "ppd" reactions is strongly peaked around 600 MeV. As in the case of the aa reaction, the kinematics lead to XpH = 0.25 : the deuterons-produced have a typical energy ~ 150 MeV/n. <11 The cross-section a^ for the "complex pa" reactions (i. e. the weighted sum of the cross-sections corresponding to the two reactions mentioned in Table 1) is approximately constant (="50 mb) above ~ 1 GeV : the corresponding reactions will provide most of the CCR- produced D. The energy distribution of the outcoming deuteron as a function of the energy of the incident particle (p or a) is poorly known experimentally (see the discussion in Meyer 1972), but it will be suffi- 60 cient for our purpose to make 10' :—i—rr 11 lii| r-i i ITIH| i TTi i in; 1—i i i MIL the following approximations. • (1) p(p,ifld ; If a fast proton hits a • (2) p(cyJp)d+p(a,n2p)d target, the resulting deuteron 3 (J) pk3He)d - is produced essentially at K) rest, thus 0. Conver- sely, if a fast or hits an H target, the d produced has • W3 _ / \ about the same energy per / /S : -O / nucleon as the incident or / £ • (in the lab frame), thus / 1 y J, to z 10 For the "pick-up por" o ^ I— reaction (cross-section o : 111 the energy of the secondary in• deuteron does not matter in in r V very much, since "complex o DC pa" reactions dominate (in o / \ «2w : particular, n°tje the ~ I V^ decrease of o^ above 50 1 _ MeV/n. To get an estimate 10" \ \ - of the production rate, we assume that secondary dea- terons all have the maxi- 12 10 , , I 111 11 lit 1 • mum energy allowed by the 1 t) 102 103 104 kinematics of the reactions. PROTON KINETIC ENERGY (MeV) From Meyer (1972), this leads to C11 Fig. 1 The cross-sections cr,^ for the pro- <«H = 1.7. duction of deuterons by pp and pa reactions, b) The deuterium from Meyer (1972). Further details can be abundance in the CCR found in Table 1. The cross-section for the hypothesis. The source destruction by protons a^ is als<> shown. function for the CCR- produced deuterons (see Ml eq. 2-2) is a sum o. source functions, one for each reaction. However, in the case of the complex p^He reaction which gives a essentially at rest (see above), the corresponding transport equation (Ml, eq. 2-1) can be integrated fully analytically and, after thermalization, gives to the CCR-produced D abundance D/H the contribution : (2) _ /H 02Phi' H „(E',z) dE' dz (2-2) (? W P »"•

(where n^e is the He number density of the ambient gas and 4 __is the CCR proton flux in a comoving volume). As already mentioS'ea, and as numerical calculations show, this contribution dominates deuterium production. This is also the case in the Galaxy (see Meyer 1974). 61

For a "total energy" CCR spectrum, injected in a burst at red- shift zg, fig. 2 shows that, for qo=0.1, amounts of D a priori comparable to what is observed may be obtained. However, keeping in mind the results obtained in Ml (§ III) on 7 Li, the a priori possible range of variation of the D/H ratio has to be restricted (hatched area of fig. 2) to avoid over- X \ or underproduction of 7Li. Under o these conditions, nevertheless, it is seen that up to ^20% of the observed (minimum) D abundance can be produced by CCR ; but the corresponding figure is less than ~ 10% for the y- ray normalization resulting from the Apollu {Trombka et al. 1977) and SAS-2 (Fichtel et al. 1975) data (see Ml, §111). However, a.s mentioned in 1000 1O0 10 1 Mi (§ III) and discussed in 2 The D/H ratio as a function Mirvtmerle (1977b) if one wants of z , for q =0.1. This ratio is further not to overproduce ^Li, the calculated using three different CCR flux has to be decreased by a Y~ray normalizations (see Ml these proceedings, 0G-17 ). The hat- factor at least ~ 3 ; the CCR-produ- ched area corresponds to the range ced D accounts then for ~3% only of ^Li abundance observations of the (typical) observed D abundance. shown in MI , fig. 2. Clearly, then, since little D is produced anyway,the uncertainties on the calculated D abundance are not crucial to study the possible existence of CCR. For the sake of completeness, though, we have varied the X-j factors appearing in eq. (2-1) and calculated in the preceding sections, especially in the case of the "pick-up" pa reaction in which the assumption E = E1 is kinematically the worst (as compared to other reactions). A variation of a factor of 2 either way results in a typical uncertainty of 50% at most on the final D abundance. This uncertainty is negligible when compared with other uncertainties (see Montmerle 1977b).

III. "PREGALACTIC" COSMIC RAYS In a recent review of the origin of deuterium, Epstein et al. (1976) have examined the possibility of making L by "pregalactic" cosmic rays (PCR), basically by the same reactions we have used. The PCR injection flux also appears in a burst ; it is assumed to be of the form (E + Eg)-2-^ but Eg is taken as a free parameter. Only the relative abundances of the light elements are computed. This work has been presented in greater detail by Epstein (1977). Among other results they find that, for Eg = 30 GeV/n (and for a constant density), 62 the D/^Li ratio has its observed value, and that one obtains the observed abundance of D at the cost of overproducing high-energy y-rays by a factor of ~ 103 with respect to the observed background. TMow, the PCR and CCR hypotheses are somewhat different : in particular we do not seek to find a mechanism for producing D, and our treatment of cosmological effects is more complete. Neverthe- less, the two above mentioned results can be used as a check of the mutual consistency of both treatments, at least for high redshifts . To this end, a computation of the D/^Li ratio in the CCR hypothesis was performed with Eg = 30 GeV/n. The results are displayed in fig. 3, and contrasted with the case Eg = I i proton rest mass E0 ("total 10* - energy" CCR spectrum). Although the D/^Li ratio varies with zg. it can be seen that it does lie EB= 30 GeV/n within observations, for the J range of zs that gives a fit to CD the y-ray background. On the Q other hand, it is more difficult to compare the y-ray flux estimates 10* - - when both hypotheses account for the D abundance, since neither Epstein et al. (1976) nor Epstein s (1977) state explicitly which obser- 10 - vational spectrum they use. A rough comparison can nevertheless I I 1000 10C1 10 be made. From Bonnardeau (1977), we have modified Steckers' (1973) 1+z y-ray source spectrum according s Fig. 3 The D/sLi ratio computed with a to the PCR model. As a result, the CCR injection spectrum of the form theoretical y-ray background spec- (E + E in a fashion similar to trum for Eg^ 30 GeV is not sub- the PCR model of Epstein (1977). (The stantially changed for zg> 50. Thus, curves become dotted when the corres- from § II, if is found that with ponding theoretical y-ray background respect to the theoretical spectrum spectra do not fit the observations.) normalized to the Apollo and The observational range of the D/°Li r tio lies between the thin SAS-2 data, y-rays are overproduced 1* mes horizontal by a factor ~300 in the CCR hypothe-" sis. This compares with the abovementioned factor 01 in the PCR hypothesis, with respect to unspecified Y_ray observations. Therefore, as a conclusion, both models are consistent with each other, at least within a factor of -3. Other comparable conclusions, such as concerns the ^Li/^Li ratio, are also in agreement.

REFERENCES Meyer J.P. 1974, Thesis, Universite d'Orsay Bonnardeau M. 1977, prepriat Hontmerle T. 1977a, Ap. J., to be published Epstein R.I. 1977, Ap. J. 212. 595 1977b, Ap. J., in press Epstein R.I., et al. 1976, Mature 263, 198 Reeves H. 1974, Ann. RPV. Astr. Ap. 12437 Fichtel C.E., et al. 1975, Ap. J. 198, 163 Trombka J.I., et al. i977, Ap. J. 212_, 925 Meyer J.P. 1972, Aatr. Ap. Suppl. 7, 417 Vidal-Madjar A., et al. 1977, Ap. J. 211, 91 6£?9Dom 67

EXPERIMENTAL CROSS SECTIONS FOR THE PICKUP OF ELECTRONS BY RELATIVISTIC NUCLEI

G.M. Raisbeck Laboratoire Rene Bernas du CSNSM, 91406 ORSAY, France.

H.J. Crawford, P.J. Lindstrom, D.E. Greiner, F.S. Beiser, H.H. Heckman Lawrence Berkeley Laboratory, BERKELEY, California, USA.

Cross sections for the pickup of electrons in a variety of targets have been measured with beams of 12C (150, 250, 400 MeV/n), 20Ne (250, 400, 1050, 2100 MeV/n) and 40Ar (400, 1050 MeV/n) from the Bevalac accelerator. The interpretation of the results in terms of radiative and non- radiative capture, and the implications for cosmic ray propagation studies are discussed.

1. Introduction Unstable nuclei which can decay only by the capture of an atomic electron form a unique component of the cosmic rays. Because, at high energy, these nuclei have a small probability of pocessing an electron, a study of their survival or decay can reveal important information on their conditions of formation or propagation. For example, secondary spallation products of this type can give information on the density of the propagation medium (1-4) and on solar modulation effects (3, 5) . " Primary " nuclei of this type can be used to probe the time between formation and acceleration of cosmic rays (6-9).

An important limitation of these investigations until now, has been the lack of experimental values for the atomic charge exchange cross sections for very high energy nuclei. The anergy region of interest is one in which the non-radiative process for electron pickup, which is the dominating mechanism at the lower energies usually studied, becomes comparable to radiative capture. In fact, most treatments of this problem have assumed(explicitely or implicitely)that radiative capture was the dominating process (2-9). However, because of the absence of a firm theoretical basis for non-radiative cross sections in the high energy limit, and in particular of possible relativistic effects, such assumptions have remained uncertain. The only previous experimental work in this area was restricted to charge one projectiles( 10). We report i ere on measurements with relativistic heavy ions which are directly applicable to the cosmic ray problem.

In addition to the subject outlined above, these cross sections can also have applications to other cosmic ray questions, such as permitting estimates of the " effective " charge of such particles in emulsion or plastic detectors (11), or the penetration of the earth's magnetic field by incompletely stripped ions.

2. Experiment 12 Experu nts were carried out using relativistic ion beams of C (150, 250 and 400 MeV/n), 20Ne (250, 400, 1050 and 2100 MeV/n) and 18Ar (400 and 1050 MeV/n) from the Bevalac accelerator. The electron capture and loss cross sections were determined by measuring with a spectrometer the fraction of the ions which picked up an electron in traversing a thin non-equilibrium target. 68 compared to the ratio at equilibrium in the same material. The solid targets studied included Be, C, Al, Cu and Au. A few measurements were also made with qas targets of He, Ar and air. More complete experimental details will be published elsewhere. Because the purpose of this experiment was to make measurements over as broad a range of conditions as possible, some precision was sacrificedin order to cover as many combinations of projectile, target and energy as feasible with a limited available amount of beam tima.

3. Results and discussion A few examples of the results are shown in Figs 1 and 2, which give an idea of the dependence on projectile charge (Zp), target charge (Zc) and projectile energy (Ep). Because the data are still being analyzed, these preliminary results are subject to uncertainties of perhaps a factor of 2. The (Z_)^ dependence, fig. 1(a), which is expected for either radiative or non-radiative capture (10), is confirmed. Thus the present results can be extrapolated with some confidence to other nuclei of cosmic ray interest. The linear dependence on Zc, illustrated in Fig. 1(b) shows the domination of radiative capture (at least up to Zc ^ 30 for the energy chosen) indicating a constant cross section per electron in the target. Thus one is ensured that the results can also be confidently applied to the interstellar medium where Zc is one or two (or even to an ionized medium). We have also made some attempts to measure directly the cross sections in hydrogen, by comparing targets of plastic and carbon, while only upper limits could be obtained, they are perfectly consistant with the above picture.

An initial attempt has been made to compare the results with those expected on the basis of available theory. Most of the data can be well accounted for by the predictions of radiative capture (for ex. Fig. 2(a) ). These cross sections have been calculated by using detailed balance (10) and cross sections for the inverse process, the photoelectric effect, for which a fully relativistic treatment exists. To our knowledge, no similar relativistic treatment exists for non-radiative capture. We show (as OBK-I) in Fig. 2, a " straight- forward " application of the Brinkman-Kramers formalism, (i.e. letting v=f3c) . The experimental results are in strong disagreement with such predictions. However, by recognizing that it is kinetic energy, and not just velocity which must be transferred to the electron being captured, we can try substi- 1 2 tuting S = (E/E0) / (rather than v/vQ) in the OBK expression (where E is the final kinetic energy of the captured electron in the rest frame of the target, in units of E0, the energy of the K electron in hydrogen) . The results (OBK II in Fig. 2) are in surprisingly good agreement with the data. We are still trying to determine whether there is any justification for such a crude approach.

For the cosmic ray application} however, the important point is that the light target data are adequately described by the expression for radiative capture in the energy region of interest . While we are still making some refinements to this expression, the effects will be of negligible significance

* The one exeption to this is the nuclide ^Be. Here decay becomes important only at energies low enough that non-radiative capture is predicted to dominate. However, this energy is sufficiently low that the " classical " Brinkman-Kramers predictions are expected to be valid (1). 69

Figure 1 - Capture cross sections for : (a) 400 MeV/n, C, Ne and Ar ions in carbon. The solid line indicates a (Zp)"' dependence ; (b) 1050 MeV/n Ar ions in Be, C, Al. Cu and Au. The solid line indicates a linear dependence on target charge (Z ) .

Figure 2 - Capture cross sections as a function of projectile energy for : (a) Ne ions in Al. ; (b) Ar ions in Au. The solid lines indicate theoretical estimates for radiative and non-radiative capture, as discussed in text. 70 to the cosmic ray problem. Thus previous propagation calculations which have been made on the basis of such predictions (4, 5), will be unaltered.

Some examples of these calculated cross sections for several isotopes of cosmic ray interest in a medium of interstellar composition are given in Fig. 3. They are seen to be in strong disagreement with those of Tamahane et al. (12), who considered only non-radiative capture.

4. Conclusions Experiments have been carried out on the pickup of electrons by relativistic nuclei. The results put the estimate of cross sections for the similar pickup of electrons in the interstellar medium by cosmic ray nuclei on a firm basis. Together with the relevant nuclear cross sections, such data permit a reliable and quantitative use of pure electron capture nuclei in cosmic rays as important probes of their production, propagation and modulation conditions.

References

1 - F. Yiou and G.M. Raisbeck, Astrophys. Lett. 1_, 129 (1970). 2 - D.V. Reames, Ap.J. 162, 837 (1970). th 3 - G.M. Raisbeck, C. Perron, J.Toussaint and F. Yiou, 13"3 * Int. Cosmic Ray Conf., Denver (i973) vol. 1, p. 534. „th 4 - G.M. Raisbeck, G. Comstock, C. Perron and F. Yiou, 14"* Int. Cosmic Ray Conf., Munich, (1975) vol.2, p. 560. 5 - G.M. Raisbeck, G. Comstock, C. Perron and F. Yiou, 14 Int. Cosmic Ray Conf., Munich, (1975) vol. 3, p. 937. th 6 - M. Casse, 13 Int. Cosmic Ray Conf., Denver (1973) vol. 1, p. 546. 7 - M. Casse and A. Soutoul, Ap.J. Lett. 200, L 75 (1975). 8 - A. Soutoul, M. Casse and E. Juliusson, 14th jnt. Cosmic Ray conf Munich, (1975) vol. 2, p. 455. 9 - M.M. Shapiro and R. Siiberberg, 14th Int. Cosmic Ray Conf., Munich (1975), vol. 2, p. 533. 10 - G.M. Raisbcick and F. Yiou, Phys. Rev. A A, 1858 (1971). 11 - P.H. Fowler, V.M. Clapham, V.G. Cowen, J.M. Kidd and R.T. Moses, Proc. Roy. Soc. (London) A318, 1 (1970) -th 12 - A.S. Tamahane, V.S. Venkatavaradan, J.N. Goswami and S.K. Gupta, 14 Int. Cosmic Ray Conf., Munich, (1975) vol. 2, p. 564. 71

E(MeV/n)

Figure 3 - Calculated effective " electron pickup cross sections for 55 51 44 . . . Fe, Cr anad Tx in interstellar medium. 72

CROSS SECTIONS FOR a + a + ?Be at 400, 600 and 1000 MeV F. Yiou and G.M. Raisbeck, Laboratoire Rene Bernas du CSNSM, 91406 ORSAY and H. Quechon, S.P.R., C.E.N. Saclay, 91190 GIF sur YVETTE, France.

Experimental cross sections have been measured for the reaction a + a -*• 7Be with alpha beams of 400, 600 and 1000 MeV. The results are considered in connection with the possible universal nucleosynthesis of ^Li by high energy cosmic rays. The contribution of this reaction to the observed ^Be abundance in cosmic rays is also presented.

1. Introduction Ever since nucleosynthesis of the light elements (Li, Be, B) by high energy spallation in cosmic rays was proposed (1), the potential importance of the a + a reaction as a source of Li was recognised (2, 3). The reason is that the helium abundance in both the cosmic rays and the interstellar medium 10 % that of protons) is much larger than other nuclei. On the other hand this reaction differs from the other nuclear reactions generally considered, being a " fusion " rather than a " spallation " process. It has therefore generally been assumed that the cross section for this reaction falls off rapidly with energy, becoming negligible above a few tens of MeV/nucleon (2, 3). Recent experiments (4) up to 35 MeV/n have in fact confirmed this general picture, and shown that, based on the contemporary observed cosmic ray flux, such a reaction is insufficient to explain the accepted " universal " abundance of 7 Li.

Very recently, several authors have considered other potential astrophysical sites for high energy reactions,such as early stages of the universe or explosions of super massive objects (5, 6, 7) . The advantages include the possibility of much higher interaction rates and of involving more " primitive " matter, thus avoiding difficulties with the simultaneous overproduction of the other light isotopes by spallation of heavier species. In these models, the a + a reaction is again of fundamental importance, not only for estimating the production of Li, but also for setting limits for the concurrent production of ^h in such environments. A serious limitation of these speculations has been the complete absence of experimental cross sections in the appropriate energy region. We report here on some preliminary results of such measurements.

2. Experimental 2 A liquid helium target (1.25 g/cm ) was irradiated at the " Saturne" synchrotron, with beams of 400, 600 and 1000 MeV alpha particles. The integrated flux was determined from the ^Be activity in a carbon monitor foil placed in front of the target, using cross sections for C(d,x)^Be measured in a separate experiment (8). After irradiation the helium was transferred to a second container and slowly evaporated. Both the irradiation and the evaporation containers were then rinsed separately with 0.01 N HC1 to recover the ^Be (which was found to remain completely on the walls of the irradiation container). The quantity of ^Be formed was determined by comparing the y activity of this solution with a similar standardized ^Be solution, using a Ge(Li) detector. Corrections were made for ^Be formed in the window of the target recoiling into the helium and for ^Be formed in the helium leaving the 73 target. The corrections are fairly reliable at 400 and 600 MeV, but become extremely important at 1000 MeV, resulting in a large uncertainty.

3. Results and discussion Preliminary results of our measurements (the data are still being analyzed) are plotted in Fig. 1, together with the lower energy 7Li and 7 Be results of ref.(4) . (7Li and 7Be, being mirror nuclei, are expected to have essentially identical cross sections at high energier). Although the cross sections are auite small, they are several orders of magnitude larger than expected on the basis of a simple extrapolation of the lower energy results. This ^snggrobably associated with a change in the production mechanism, with the higher rffechanisrc possibly involving TT production. While the measurements reported here are below thenthreshold 1160 MeV incident alphas) when considered on an energy/nucleon basis, sufficient energy could be available from a) Fermi momentum in the alphas b) collective effects. The possibility of such collective effects in high energy heavy ion reactions is still an open question of considerable interest.

In addition to the absolute cross sections, an important parameter in any model for Li nucleosynthesis is the production ratio 7Li/ Li. In fact this ratio has been a serious limitation to all spallation models of Li nucleosynthesis because, except near threshold, all nuclear reactions investigated have been found to produce Li with a much smaller 7Li/^Li ratio than the assumed " universal " ratio of 12.1. For^he a + a reaction, the general assumption (5-7) has been that the ®Li and Li production cross sections follow a similar high energy dependence thus encountering this same difficulty. It has even been suggested (7) that the ^Li cross section should eventually become larger than 7Li because of the larger number of particles in the final state. While such statistical considerations are indeed important in spallation type reactions, it is not obvious that they will apply in the same way to " direct " reactions involving pion production. In fact if, as seems plausible, a pion is produced via a resonance (i.e. a "delta " particle), then it is possible that the " 2 body " 7Be and 7Li production reactions such as 4He + 4He 7Be + "A" n+7r° could be enhanced significantly in comparison to the Li production where the final state is more complex. Thus it would be very interesting to also have measurements for ®Li production cross sections in the energy region covered by the present work.

4. Propagation production in present day cosmic rays For reasons indicated in the introduction, the a-d reaction has generally been ignored in propagation calculations of the expected secondary Li and Be abundances in contemporary cosmic rays. Now that experimental cross sections are available, it is interesting to make a quantitative estimate of this effect. We have therefore carried out a propagation calculation for 7Be using the data indicated in Fig. 1. The results are shown in Fig. 2, as a ratio of 'Be/C for the " standard " propagation through a 5 g/cm^ exponential pathlength distribution+ _

(The results of Fig. 2 are in fact an upper limit, since one actually needs to know both angular and energy distribution of the emitted 7Be in order to make a complete calculation. We have taken as the most conservative assumption 7 that all the emitted Be will have the maximum kinematically allowed energy - i.e. slightly less than half of the original a particle in terms of MeV/n). 74

incident 06 energy

7 Figure 1 - Production cross sections for a + a Be + x ^ Solid line is an extrapolation of lower energy cross sections of Be (open circles) and 7Li (open triangles) from Ref. 4. Solid point are present results.

in i O 4 -

a a> CD f- 2 -

100 1000 E (MeV/n)

Figure 2 - Calculated contribution of the a + a reaction to Be in contemporary cosmic rays.' 75

As can be seen by comparing the results of Fig. 2 with the production by spallation of heavier species (see Fig. 1 of OG. 164 ), the a-o contribution is quite negligible, reaching a maximum of ^0,2% at 40 MeV/n, and much less than 0,& in the high energy region. Thus, the assumption that this reaction can be ignored in such propagation calculations is seen to be completely justified. Nevertheless, it is comforting to have such an assumption resting on experimental evidence.

References

1 - H. Reeves, W.A. Fowler, F. Hoyle, Nature 226, 727 (1970) 2 - M. Meneguzzi, J. Audouze and H. Reeves, Astron. and Astrophys. 15 337 (1971) . 3 - H.E. Mitler, Astrophys. and Space Sci. J1_, 186 (1972). 4 - C.H. King, H.H. Rossner, S.M. Austin, W.S. Chien, G.J. Mathews, V.E. Viola Jr. and R.G. Clark, Phys. Rev. Lett. 35, 988 (1975). 5 - L.M. Ozernoi and V.V. Vhernomordik, Astr. Zh. 52, 1156 (1975) (English translation, Soviet Astr. 693 (1976) ) 6 - R.I. Epstein, Ap.J. 212, 595 (1977). 7 - T. Montmerle, Ap.J. (in press). 8 - G.M. Raisbeck, F. Yiou and H. Quechon, (unpublished results). 66¥9001g0 CROSS SECTION MEASUREMENTS FOR PRODUCTION OF STABLE ISOTOPES OF Ne AND Ar BY HIGH-ENERGY SPALLATION OF Al, Sc, Ti, Fe, Co, Ni AND Cu S. REGNIER Laboratoire de Chirnie Nucl6aire, ERA 144, Le Haut Vigneau, 33170, Gradignan, France.

Aboui 100 new cross sections are given for the production of 20,21, 22 , 36, 38, 39,42. . . . . _ ' ANT e and Ar in targets of Alfl1 , GSc, Ti, Fe, Co, Ni and Cu, bombarded with protons of 0. 080, 0. 150, 0. 600, 1. 05 and 24. 0 GeV. The results are in good agreement with the two-step model of Serber. They are compared with the predictions of a semi-empirical formula widely used in cosmic ray studies. 1 . Introduction. Knowledge of the cross sections of spallation reactions is necessary for a better understanding of the composition and propagation of cosmic rays. Results for the radioactive isotopes are relatively abundant, but such is not the case for the stable isotopes, owing to experimental diffi-. culties. The stable isotopes, however, represent an important fraction of the inelastic cross section foj~ nuclear reactions of the type proton + nucleus. The general characteristics of spallation reactions are now well known. For incident energies, Ep, greater than threshold, the cross sections increase rapidly with increasing Ep, pass by a maximum and finally decrease to an asymptotic value. The variations are small for energies beyond Ep = 1 GeV (which is often the energy corresponding to the maximum) and it is preferable to evaluate them from a series of measurements using the same experimental technique in a single laboratory.

Spallation reactions may be described by a two step (cascade- evaporation) model (SER 47). The intra-nuclear cascade is a succession of nucleon-nucleon collisions with emission of particles, after which a thermody- namic equilibrium is established. The uniformly excited nucleus then decays by evaporation until de-excitation is completed. Above 0. 3 GeV, TT mesorj production influences the cascade, the importance of which increases with Ep and corresponds to an increase of the excitation energy of the nucleus, thus favoring products of mass further removed from that of the target. The decrease of the cross sections above 1 GeV is perhaps due to the formation, during the p-n and p-p interactions of the cascade, of particles having an interaction probability in the'nuclear material which is lower than that of the TT mesons.

Also most of the additional energy Ep appears in the form of kinetic energy of the nucleons and mesons ejected. These variations of cross section in the 1 GeV region may contribute to the observed energy dependence of the composition of cosmic rays and-©f the mean free path,

2• Experimental Method. Very pure targets of Al, Sc, Ti, Fe, Co, Ni and Cu were irradiated at 0. 080 GeV (Louvain cyclotron), 0.150 GeV (Orsay Synchro- cyclotron), 0. 600 GeV (C. E.R.N. Synchrocyclotron), 1. 05 GeV (Saturne Syn- chrotron) and 24 GeV (C. E. R. N. Synchrotron). The total number of protons reaching the target was monitored by the 27Al(p, 3p3n)22Na reaction. 77 The small quantities of rare gases produced by the nuclear reactions were measured by means of a 60° sector, 12 cm radius mass spectrometer equipped with a gas extraction line and a calibration system and desi- gned to function in the static mode . The residual pressure obtained after out- gassing was about 10~9torr. The targets were melted by induction heating in a molybdenum crucible. The rare gases were purified in several steps, using Ti, CuO-Pd and Zr-Al getters between 200 and 800°C. Corrections were made using blank runs and data for mass discrimination, doubly-charged ions, and pumping and memory effects in the mass spectrometer. The sensitivity was frequently checked, using Ne or Ar standards. The isotopic dilution method was applied to Ne measurements. Quantities of the order of 108 to 10 atoms of each isotope of the rare gases could be measured in a routine manner, except when the gas is present in large quantities in the atmosphere or as an impurity in the target metal. 3. Results. Tables 1 and 2 give the measured cross sections, in mb. The values are cumulative for 20Ne(Na, Ne, F, O), 2lNe(Mg, Na, Ne, F), 22Ne.(F, Ne) (the 22Na contribution is subtracted), 38Ar(Ca, K, Ar, CI, S) and 39Ar(Ar, CI). The uncertainties indicated take into account the entire process of preparation of the targets, the monitoring and the gas analysis, but not the cross section of the monitor reaction or the period of 22Na. In general, each cross section is the mean of three independent measurements and the uncertainty is in the neighborhood of 10 %. It may be noted that the precision is better for the isotope ratios ( ^ 3 % in most cases). Measurements are now in progress (EUG 77) to verify the absence of systematic errors in the calibration of the experimental method, although cross sections already published for the same targets and energies are in good agreement with the present work (CUM 76, BIE 62, FOR 71, CHE 72) except for those of GOE 64. 4. Discussion. The cross sections measured in this work show a maximum at about Ep = 1 GeV. Such behaviour has already been observed with radio- 51 52 54 active products, particularly by RAI 75 for 46sCj 48v, Cr and » Mn in Fe and Ni. The excitation functions suggest that an asymptotic value is attained between 5 and 10 GeV (see fig. 1). Measurements at Ep = 3 GeV appear to be called for and are planned in Bordeaux. Unlike the cross sections, most of the isotope ratios change very little with the energy, Ep. Since the isotopic distributions of the spallation products are governed by the evaporation step, it may be assumed, as a first approximation, that the same excited nuclei are always involved for a given reaction, whatever the incident energy, Ep. "With regard to cosmic ray studies, the measured cross sections may be used to established semi-empirical formulae which will reflect the variations of the spallation cross section with the nature of the target and the

product, and the incident energy, Ep. "Unknown values may then be estimated with satisfactory precision. In this respect, it is useful to compare the results given here with the formula of Silberberg and Tsao (SIL 73) (derived from that of Rudstam) (RUD 66)), for which the parameters have been calculated using a small number of cross sections for stable products and ^vhich is frequently employed at present in astrophysics. Fig 1 shows the experimental points for the production of 39Ar in Fe. The excitation function calculated by SIL 73 (continuous line) diverges from the experimental results (dotted line) beyond about 1 GeV. The same situation is found for all of the reactions studied here.

In Fig. 2 are shown the cross sections for 36Ar and 38Ar as a function of the mass number of the target, for Ep = 24 GeV. These are compared with the 78 calculated values of SIL 73 for Ep = Eg. The calculation systematically overestimates the cross sections by more than 30 %. For the 45Sc target, in particular, the difference is more than 100 %. 5. Conclusions. The present measurements confirm the existence of appreciable variations of the cross sections of the spallation reactions for incident energies greater than 1 GeV. This result must be taken into account in the analysis of results concerning the composition of cosmic rays. Acknowledgments : I express my gratitude to G. N. Simonoff and to the team of Nuclear Chemistry of Bordeaux for encouragement and for helpful discussions. References : SER 47 R. Serber, Fhys. Rev. 72 (1947) 1008 EUG 77 O. Eugster, Physik. Instittit - Bern CUM 76 J.B. Cumming, R.W. Stoenner, Preprint submitted to Phys. Rev. C BIE 62 R.H. Bieri, W. Rutsch, Helvetica Pl^sica Acta, 35 (1962) 553 FOR 71 M.A. Forman, R.W. Stoenner, R. Davis, J.G.R. 76 (1971) 4109 CHE 72 A. Cheng, Ph. D. Stony Brook (1972) GOE 64 K. Goebel, H. Schultes, J. Zahringer, CERN 64-12 (1964) RAI 75 G.M. Raisbeck, F. Yiou, Munich OG-921 RUD 66 G. Rudstam, Z. Naturforch. 21 (1966) 1027 SIL 73 R. Silberberg, C. H. Tsao, Astroph. J. Suppl. 220 - 25 (1973) 315

E (GeV) 21AT 22AT P Ne Ne Ne

0. 080 27. 0 ± 2. 5 32. 6 - 3. 0 11.7- 1. 1

0.150 23. 0 i 3. 0 25. 0 i 3. 5 10. 5 - 1. 6

0. 600 27.0 - 1. 8 27. 9*1.8 13.9 ± 1. 0

1. 050 29.2 i 2.5 30.1 ± 2. 5 17.0 ± 1. 5

24.000 17.0 * 1.8 17. 6 i 1.7 9.4 t o. 9

Table 1

Cross sections in mb for Ne production in Al + P

(cumulative : see text) I " ' 1 "11 E (GeV) Ar 59 45Sc Ti Pe Co Ni Cu P *

36 1.43 ±0.16 0.080 35.9 ±3.2 39 13.0 ±1.0 42

36 2.85 ±0.37 1.15 ±0.17 0.0035 ± 0.0006 0. 0136 ± 0. 0027 0. 0028 ±0. 0012 0. 150 38 28.5 ±3.4 14.2 ±2.1 0. 34 ± 0. 02 0. 0581 ± 0. Q092 0. 080 ± 0. 015 0. 0126 ±0. 0026 39 12.2 ±1.5 V. 6 ±1.1 0. 179 ± 0. 014 0.0418 ± 0.0067 0. 0291 ± 0. 056 0. 0068 ±0. 0017 42 0. 034 - 0. 014 0. 095 ± 0. 014 ^0.00067 ± 0. 00014 4 a00056 ± 0. 00033 0,00017 ±U000 1 3

36 1.49 ±0,17 0.381 ±0.018 0.600 38 12.4 ±1.3 4.32 ±0.20 39 6.14 ± 0. 67 2.59 ±0.12 42 0. 050 ± 0. 015 0. 0566 ± 0. 0030

.36 2.90 ±0.36 3.39 ±0.33 2.49 ±0.32 1.76 ±0.27 2.63 ±0.19 1.01 ±0.17 27. 8 ± 2.1 30. 6 ± 2. 9 18,2 ±1.9 16.9 ±2.5 14.1 ±1.0 10.0 ±1.6 05 i' 39 13.7 ±1.1 16.9 ±1.6 9.02 ±0.95 9. 50 ± l. 42 5.95 ±0.43 5. 71 ± 0. 94 42 0. 110 ± 0. 017 0.49 to. 05 0. 112 ± 0. 016 0.198 - 0.030 0. 048 ± 0. 005 0.140 ±0.028

36 1.75 ±0.23 1. 93 ± 0. 14 1.37 ±0,18 1.30 -0.14 2.09 i 0, 15 1.06 ±0.14 24.0 38 16.6 ±1.5 18.1 ±1.3 9. 83 ± 1. 29 11.7 ±1.29 10.6 ±0.7 9.51 ±1.23 39 8. 65 ± 0. 87 10. 4 ± 0. 8 4. 97 ± 0. 65 6. 52 - 0. 72 4. 46 ± 0. 32 5.41 ±0.70 42 0. 089 ± 0. 012 0.38 ± 0. 03 0. 084 - 0. 012 0.216 ±0.063 0. 0464 ± 0. 0038 0.147 ± 0. 019

Table 2

Cross sections in mb for Ar production in various targets 80

T—I I l( II | i III "T

? asymptote between 5 and 10 GeV

THIS WORK

o FOR 71

SCH 59

BIE 62

— o — GOE 64 (arbitrary line)

Excitation Function ^ 73

a more probable excitation function.

j t 1 1 1 111 _1 L t I I I I 1 10 Ep(GeV) Figure 1 Experimental and calculated cross sections for ^(Ar + CI) production in Fe + p

THIS WORK 24GeV o HUS 73 29'GeV! 3< a /( * AAr \) * t

SIL 73 FORMULA (E=EJ

,36 , a( aAr) •x—x

45 50 55 60 A- 6>6W0Ofg4 95

CROSS-SECTIONS FOR PRODUCTION OF BORON ISOTOPES IN CARBON SPALLATION i PROPAGATION OF TEE LIGHT COSMIC RAY NUCLEI Pierre FONTES Laboratoire Rene Bernas du C.S.N.S.M./ 91406 ORSAY, France. ^ _ The cross-sections for and production In carbon spallation by 40 MeV to 25 GeV protons and 100-160 MeV a-particles have been measured by mass spectrometry. The chemical abundances of the light L cosmic ray elements and their variations as a function of the energy are accounted for by propagation calculations based mainly on experimental cross-section values. The calculated values of the boron and lithium isotopic radios in cosmic rays are found to be independent, of the energy from 1 to 100 GeV per nucleon.

I - Introduction It is generally admitted that the formation of the light (L) cosmic ray nuclei can be explained by the spallation reactions induced by the interaction of the cosmic radiation with the interstellar gas, most of the lithium, beryllium and. boron isotopes are then produced by spallation of carbon, nitrogen and oxygen nuclei, and more than one half of the L nuclei comes from carbon spallation. The isotope excitation functions for lithium and beryllium production in carbon and oxygen spallation are experimentally known (Fontes et al., 1971 j Yiou et al.f 1973 ; Lindstrom et al., 1975). The last important excitation functions required for the study of the light element production in cosmic rays were those for boron isotopes in carbon spallation. Proton excitation functions for boron isotope production in carbon spallation will be presented here as well as production cross-sections by 100 to 160 MeV a-particles and implications of these measurements on light cosmic ray nuclei propagation. II - Experimental The and cumulative cross-sections in carbon spallation have been measured by mass spectrometry and by means of a method especially developed for that purpose. Irradiations wetfe performed in the internal beam of the following accelerators i Orsay synchrocyclotron (a-particles and up to 150 MeV protons), CERN synchrocyclotron (600 MeV protons) arid CERN synchrotron (25 GeV protons). The whole experimental- method is described in details elsewhere (Fontes, 1975). Measurements are made in two steps : 1) The isotopic spallation ratio A1B/iUB is first determined by the analysis of the spallative boron ex- tracted from an irradiated carbon target. 2) The absolute cross-section values are then obtained from an irradiated target where a known quantity of a boron isotope has been introduced by m^ans of an isotope separator used as an ion-im- plantor. An isotope dilution-like method is thus carried out in solid phase.

III Results a - Isotopic cross-section ratios The 11B/1°B spallation ratio is directly obtained by mass analysis of boron from an irradiated target and corrected for isotopic discrimination of 96 the mass spectrometer. Uncertainties are about 5 % on boron cross-section ratios. The isotopic ratio of boron produced in carbon spallation by protons ranging from 40 MeV to 25 GeV is shown in fig. 1, it is found to be constant above a few hundred MeV.

Figure 1 Boron isotopic ratio produced by proton spallation of carbon. Solid circles are from this work. 11 Triangles are from Davids et al. (1970)y and squares from Lindstrom et al. (1975).

10* K>' *>' ENERGY (MeV)

b - Absolute cross-section values

The cross-section values 0ioB and CnB for production of boron isotopes in carbon spallation (including and contributions) are given in Table 1, as is the monitor cross-section °7Be (used for the determination of the flux of incident partitles).

E MeV *S 10B mb 0 nB mb mb M protons a

HI 15.,8t 3 98.. 5 + 20 21.5 + 3.S

49 22.. 5 + 4.3 98 20 23.3 + 3.5

150 19 + 3.4 63 + 13 12.2 £ 1-Z

600 25 + 4.5 75 £ 15 11 £ 1'1

25000 20 +_ 3,2 59 + 12 9.1 + 0-4

alpha particles 7 100 - 160 38 ± 114 £ 17 30 £. 4 Table 1 - -Boron isotope cros3-section values in carbon spallation, (a) Adopted value of the monitor cross-section (compilation, see Fontes, 1975). The uncertainties calculated as standard errors, including the uncertainty on the monitor cross-section value are about 20 rate 10B and 11b 97 excitation functions in carbon spallation- by protons are shown in figure 2 and figure 3. For the study of the propagation of the light cosmic ray nuclei, as discussed hereafter, it is of great interest to note that these functions are almost energy independent above a few hundred MeV as are those for lithium and beryllium production.

1 r - , CC.P-nB HI •1 -

1 llj ^ I • 1I1 ENERGV (M-V)

. i i i - —— 107' »' so" Figure 2 - B production cross- ENERGY (MeV) section in carbon spallation by protons. Solid circles are from this work. Figure 2 - ^B production cross-section Triangles- are from Davids et al. in carbon spallation by protons. (1970) (mass 10 measwemsnts helow Solid circles are from this work. the threshold for l^Be production) Triangles are from Daoids et al. (1970), and squares from Lindstrom et al. Crosses from Roche et al. (1976)3 and (1975). squares from Lindstrom et al. (1975),

IV - Discussion The production of the L isotopes in cosmic rays by interaction between the primary nuclei and the interstellar medium was studied using the pres.' it results and all previous experimental values of light nuclei production cross sections. The calculations were performed using the " leaky box " model, for energies ranging from .1 to 100 GeV per nucleon and by means of an improved version of the computer program of cosmic ray nuclei propagation elaborated by Comstock (1969, and unpublished) . The production of tertiary and higher order nuclei are taken into account as well as the ionization energy losses. The propagation was assumed to occur in a pure hydrogen medium, ~C, l^N, ^O, 20fje,

'•^Mg, 2Beji. and were considered the only species present at the source whose chemical composition, assumed as energy independent, was fitted in order to reproduce element abundances around 1 GeV per nucleon.

The overwhelming contribution to L element production is due to ^O an(j mostly for which spallation excitation functions are now well known. For instance, more than 60 % of boron is produced from carbon spallation (Fontes, 1977). For unmeasured crost. sections, the values calculated by the semi-empirical formulas of Silberberg and Tsao (1973) were adopted, but the L nuclei production through reactions with unmeasured cross-sections does not exceed 20 and the propagation calculations are thus mainly based on experimental nuclear data..

The spallation excitation functions for light element production are constant at high energy, so the decrease of the lithium, beryllium and boron Abundances at high ener^-y (see for instance Smith et al., 1973 and Juliusson, 1974) cannot be explained by cross section variation effects, but can ba discussed for instance in terras of tin energy dependence of the leakage mean 98 path length A. As shown by Fontes et al. (this Conference, paper OG.170), the " best " ratio to be considered for the study of the light secondaries is the (Li + Be + B)/(C + 0) ratio which is well accounted for by a leakage mean path length varying as a power law in rigidity : A = AR~S (with S ^ .3 to .4). With the same A variations, we have calculated B/C + 0, ratio of a pure secondary to the most abundant primary species and major progenitors of boron (this latter being a significant fraction of the L elements, about 50 %).

Fig. 4 compares calculated abundances with experimental data, all corrected in the same way for interactions in the atmosphere using corrections from Meyer et al. (1977). The calculated values are interstellar, so that the experimental points have to be shifted towards higher energies because of solar modulation. The lower and upper envelopes for the L/C + O ratio are shown in fig. 4, as well as calculations with an energy independent A. Some experimental values are slightly above this upper envelope and the B/C + O ratio seems rather.underestimated by these calculations. However, as well as for L/C + O, one can distinguish two energy regions, the first one below 5 GeV per nucleon, the second one above 20 GeV per nucleon, for each region the data seem consistent with a constant A value : in, the range 5.5 to 7 g cm" 2 at low energy, --nd about 1.7 g cm-2 at high energy

ENERGY (GeV/n) Figure 4 - Calculated insterstellar B/(C+0) ratio in cosmic rays compared with experimental values. Curves show results of calculations for different leakage mean path length A. "Power law rigidity dependent A are shown as well as energy independent value (A = S.S g em~2). The source spectrum is a power law function in total energy. Experimental data corrections for atmospheric production are from Meyer et al. (1S77).

On the other hand, while the chemical abundances are dependent on the propagation assumptions, as well as on the source parameters (composition and energy spectra), the calculated isotopic ratios and ^Li/^Li are found to be independent of these parameters as seen for the boron isotopic ratio in fig. 5 where dashed area includes large variations in these parameters. The calculated value of these ratios in cosmic rays depend essentially on the spallation cross-section ratios (which are the quantities directly determined by our method with a good precision) , and especially those from 12c and targets. As seen in fig. 1, these ratios are almost energy independent above 99

Figure 5 - Calculated interstellar boron isotopic ratio in cosmic- rays compared with experimental values. The dashed area includes variation effects in source composition in spectrum shape, 10B and in leakage mean path length. Experimental points are from : + Webber et al. (1973) , • Webber , Lezniak (1974) , x Garcia-Munoz et al. (1975) 3 v Eagen et al. (1975) , A Mc Donald et al. (1975) , w1 »' • Preszler et al. (1975) . ENERGY (MeV/n) 11 m 100 MeV, so the ratio (as well as the ^Li/^Li ratio) is energy independent in a wide energy range.

V - Conclusion We have presented excitation functions for boron isotope production in carbon spallation and implications of the cross section ratios and of the absolute cross section measurements to cosmic ray propagation. With propagation calculations taking into account the L/C + O variations in cosmic rays, the B/C + O ratio is found to be rather underestimated. The calculated boron isotopic ratio is found to be independent of the propagation parameters as well as of the source composition, its value (about 2.) is energy independent from 1 to 100 GeV per nucleon.

Acknowledgments I am indebted to the teams of the accelerators used, for their assistance in performing irradiations, especially to C. Steinbach and R. Deltenre (C.G.R.N.} , to R.W. Mc Ilroy (Harwell) . I wish to thank C. Carle for her technical assistance, G.M. Comstock for tha use of the computer code and J.P. Meyer and C. Perron for useful discussions.

References Casse, M., Koch, L,, Lund, N., Meyer, J.P., Peters, B., Soutoul, A. and Tandon, S.N., 1971, 12th International Cosmic Ray Conference, Hobart, 241. Cartwright, B.G., Garcia-Munoz, M., and Simpson, J.A., 1971, 12th International • Cosmic Ray Conference, Hobart, 215. Comstock, G.M., 1969, Astrophys. J., 155, 619, and (unpublished). Davids, C.N., Laumer, H. and Austin, S.M., 1970, Phys. Rev. Cl, 270. Fontes, P., Perron, C., Lestringuez, J.., Yiou, F., and Bernas, R., 1971, Nucl. Phys., A165, 405. Fontes, P., 1975, Ph.D. Thesis, Orsay, (unpublished). Fontes, P., Phys. Rev. C, 1977, May issue. Fontes, P., Meyer,J.P., Perron, C. f 1977, this Conference paper OG.170. Garcia-Munoz, M., Mason, G.M., and Simpson, J.A., 1975, 14th International Cosmic Ray Conference, Munich, J_, 325. Garcia-Munoz, M., Mason, G.M., and Simpson, J.A., 1975, Astrophys. J., 201, L145. Hagen, F.A., Fisher, A.J., Ormes, J.F., and^Arens, J.F., 1975, 14th international Cosmic Ray Conference, Munich, 1, 361. 100

Juliusson, E., 1974, Astrophys. J., 191, 331. Juliusson, E. , Meyer, P., 1975, 14th International Cosmic Ray Conference, Munich, JU 256, and private communication. Julliot, C., Koch, L., and Petrou, N-, 1975, 14th International Cosmic Ray Conference,. Murn'ch, _12, 4118. Lindstrom, P.J., Greiner, D.E., Heckman, H.H., Cork, B., Bieser, F.S., .1975, preprint, L.B.L.-3650, (unpublished). Lund, N., Rasmussen, I.L., Peters, B., and Westergaard, N.J., 1975, 14th International Cosmic Ray Conference, Munich, 1, 257. Mc Donald, F.B., Lai, N., Teegaxden, B. J., Trainor, J.H., and Webber, W.R., 1975, 14th International Cosmic Ray Conference, Munich, _1_, 318. Meyer, J.P., Casse, M., and Goret, P., 1977, this Conference paper OG.166. Ormes, J.K., Fisher, A., Hagen, F., Maehl, R., and Arens, J.F., 1975, 14th International Cosmic Ray Conference, Munich, _1_, 245. Preszler, A.M., Kish, J.C., Lezniak, J.A., Simpson, G., and Webber, W.R., 1975, M1^1 International Cosmic Ray Conference, Munich, 12, 4096. Roche, C.T., Clark, R.G., Mathews, G.J., and Viola Jr., V.E., 1976, Phys. Rev. C, 14, 410. Silberberg, R. and Tsao, C.H., 1973, Astrophys. J. Suppl., 220, 315. Smith, L.H., Buffington, A., Smoot, G.F., Alvarez, L.W. and Wahlig, W.A., 1973, Astrophys. J-, 180, 987. Webber, W.R., Damle, S.V. and Kish, J., 1972, Astrophys. and Space Sci., 15, 245.

Webber, W.R., Lezniak, J.A.r Kish, J., and Damle, S.V., 1973, Astrophys. and Space Sci.f 24, 17. Webber, W.R., Lesniak, J.A., 1974, Conference on Cosmic Ray Isotopic Composi- tion, Durham. Yiou, F., Raisbeck, G.M., Perron, C. and Fontes, P., 1973, 13 International Cosmic Ray Conference, Denver, 512. 115

44 CROSS SECTIONS FOR SPALLATION PRODUCTION OF *4Ti APPLICATION TO DETERMINING COSMIC RAY ACCELERATION TINE G.M. Raisbeck and F. Yio^u Laboratoire Rene Bernas du Centre de Spe^trometrie Nucleaire et de Spectrometri'e de Masse, 9140b Orsay, France.

Fheoretical Pj Experimental j j Both

Experimental cross sections for s/allation production of Ti in targets of Fe and Ni have been measured With protons of 0.6 to 25 GeV and alpha particles of 0.5 to 4.6 GeV. Propagation calculations using these and electron attachment cross sections/Seduced from recent measurements are presented. The results are discussed in connection with the suggested use of this nuclide for determining t^ne time between cosmic ray nucleosynthesis and acceleration.

Coordinates: /OG 1.8.3. (Implications of the composition of cosmic ray i y

Mailing address:/ G.M. RAISBECK Laboratoire Rene Bernas - Bat 108 Faculte des Sciences •B.P. n° 1 91406 ORSAY France 116

26 CROSS SECTIONS FOR THE PRODUCTION OF Al FROM TARGETS OF Si, Al, AND Fe IRRADIATED BY PROTONS OF 600 MeV G.M. Raisbeck Laboratoire Rene Bernas du CSNSM, 91406 ORSAY, Freuice C. Menninga Department of Physics, Calvin College, GRAND RAPIDS, Mich. 49506, USA

R. Brodzinski and N. Wogman Battelle Pacific Northwest Laboratories, RICHLAND, Wash. 99352, USA

Cross sections have been determined for the production of 26a1 from targets of Si, Al and Fe irradiated by protons of 600 MeV. The result for Si, which is the most important progenitor for this potential cosmic ray chronometer isotope, is in significant disagreement with an earlier measurement, and with semi-empirica. estimates.

1. Introduction In another contribution to this conference (CG.164), the question of the nuclear cross section data relevant to the use of as a cosmic ray " chronometer " have been discussed. There are several other long lived radionuclides such as 2®A1, 3®C1 and 54Mn (assuming that its decay branch could be reliably established) which have been considered at various times in this same role. Although, for various reasons, none of these otners is as favourable as ^Be, therlr$i»lid reasons for examining their possibilities. For one thing, it would permit one to " date " different components of the cosmic rays. (As we will show below, 2®A1 would essentially date 28Si) . At various times, and particularly since the reported differences ir\ energy spectra for different primary components, serious consideration has been given to the idea that different components of the cos iic rays might have different origins. A measure of their respective propagation times might give important information on this question. Secondly, use of two separate nuclides, having different half-lives, can sometimes help avoid ambiguities regarding the interpretation of the decay times. For example Ginzburg and Ptuskin (1) have pointed out this possibility in models where the diffusion time out of the galactic disk might be comparable to the radioactive half-lives.

Now thatj^as discussed in 0G.164, the cross section data is fairly complete for Be, we felt it was worthwhile to give some attention to similar data for 2®A1. This nuclide presents an interesting nuclear physics aspect because it has a- 6.4 sec isomer which decays directly to 2^Mg. Thus predictions for its cross section are particularly difficult because they necessitate estimating how much of the spallation yield is formed or passes through this state, and thus does not end up as 2^a1. For the same reason this reaction is an example of a cross section which cannot be measured by the Berkeley heavy ion technique (2) since, at least in its present configuration, that method would also include the isomer yield as part of the 26A1 yield.

For the most important cosmic ray progenitor, 28si, there are\published cross sections (3) both at 600 MeV and 24 GeV. However, based on sAne earlier work, we had some reservation about those results. \ 117

2. Experimental procedure

The experimental procedure will be described in detail elsewhere. Briefly," targets of Si, Al and Fe were irradiated with 600 MeV protons at the CE^N synchrocyclotron. After being counted-for their 22Na content, they were dissolved, together with a known quantity of Al carrier solution, and che- mically treated to recover the Al in a purified form. The chemical yields were determined by irradiating the final samples and a sample of the carrier solution in a reactor, and then measuring the 2®A1 activity with a Ge(Li) detector. The 2®Al counting was carried out in a large multidimensional Nal system having an efficiency of 14 % and a background of 0.022 cpm in the y-y mode (.511 - 1.810 MeV) which uniquely identifies 2^A1. From the 2^A1 and original 22Na activities the 2®A1 cross sections can be directly related to known 22Na cross sections.

3. Results The results are given in Table 1. These should be considered preliminary at the present time because the chemical yields are' currently being remeasured by another technique. We are particularly bothered by the difference in the two Si results (made on two portions of the same target) which is considerably outside the expected statistical errors. For the moment we take the average of these two results., and assign an uncertainty of 20 %. This result is found to be considerably larger than the previous measurement of Regnier et al. (3) at the same energy. As shown in Table 1 it is also about 60 % higher than the predictions of the Silberberg-Tsao formula (4). Interestingly enough two other (p, 2pn) reactions which have recently been measured, 22Na from Mg (5) and 54Mn from 56Fe (6) showed similarly large deviations from the semi-empirical formula. It was in fact our surprise that the 2®A1 cross section in Si could be so much different than 22Na in Mg (thus possibly related to the isomer question discussed above) that first aroused our doubts concerning the earlier measurement of Regnier et al. The observation that the present cross section is close to that for Mg(p,x)22Na in fact suggests that relatively little of the 2^A1 reaction proceeds through the isomer. Regnier et al. have also reported a cross section of 6.4 mb for this reaction at 24 GeV. We feel that it is most unlikely that the cross section can decrease in this manner, and further experiments are under way to check this point.

The cross section measured here in Fe is in good agreement with that of ref.(3). There are, to our knowledge, no other comparable measurements in Al, which is the second most important progenitor for the cosmic ray question.

4. Propagation calculations Using as a basis the cross sections measured here at 600 MeV, we have(Fig.1) carried out t. propagation calculation to estimate the abundance of 2^A1 in the cosmic rays, both without decay, and assuming average propagation densities of 1.0 and 0.2 atom/cm^. The propagation program and the parameters adopted are the same as those described in QG.164. All elements between Al and Fe were included in the calculation with source abundances being taken from Shapiro et al. (7). we note in passing that the " effective " half-life of 26A1 in cosmic rays is 15 % larger than its laboratory value because this fraction proceeds by orbital electron capture, a decay mode not available to the cosmic species except at low energies. For production from 28Si we assumed an excitation function similar to that for Mg(p,2pn)22Na. For reactions where no experimental data existed we adopted the estimates of the semi-empirical formula (4). A recent measurement of 2(>Al in Ar (8) shows good agreement with 118 those estimates for progenitors in that region of the periodic table. In any event, these other reactions are of minor importance because, by setting all other cross sections to zero, we find at 600 MeV that contributes about 75 % to the total production. When the contribution from Al is included, this fraction becomes 86 %. Thus, with just these two cross sections, a larger fraction of the calculated 26A1 abundance is based on experimental data than for *°Be with all available measurements ! (It will be important, of course, to have similar measurements over a larger energy range, and work in'that direction is presently underway). Thus the situation is particularly favourable from a nuclear physics point of view, and the 2^A1/Si ratio calculated here should be quite reliable, at least at energies of around 600 MeV. It is also evident that dates essentially the Si component of the cosmic rays and thus offers an interesting comparison to ^Be, which dates mainly the CNO group.

It will, of course, be necessary to have isotopic separation to use this isotope because, even if the 27Al cross sections were known, there is calculated to be a substantial " primary " abundance of 27AI at the cosmic ray source. While isotopic separation in this region requires better resolution than for 10Be, the larger stopping power for 26A1 means that dE/dx-E techniques can be utilized effectively to higher energies. The calculated abundance without decay is also quite comparable to that for ^Be.

5. Conclusions Experimental cross sections and propagation calculations have been presented which show that 26ai is a. very promising cosmic ray " chronometer ". The secondary production at 600 MeV is considerably larger than predicted on the basis of previous experimental or calculated cross sections, and quite comparable to Further cross section measurements at.other energies would be very worthwhile.

TABLE 1 26 Cross sections for the production of Al in targets of Si, Al and Fe irradiated with 600 MeV protons

a26Al/CT22Na adopted a26Al a 26A1 a Al target (mb) 22 Als work a Na work ^ 3) 4)

Si 1.51 17 }28.5+5.7 12.6+1.9 17.2 1.84

Al 1.78 15 26.7+5.3 — 32.7 Fe 1.05 .31 .33+.07 0.4+ .1 .45 119

References 1 - V.L. Ginzburg and V.S. Ptuskin, 14th Int. Cosmic Ray Conf. Munich (1975), 2, 695. 2 - P.J. Lindstrom, D.E. Greiner, H.H. Heckraan, B. Cork, and F.S. Bieser, Lawrence Berkeley Laboratory, report LBL-3650 (1975) (unpublished). 3 - S. Regnier, M. Lagarde, G.N. Simonoff and Y. Yokoyama, Earth. Plan. Sci. Lett. 18^, 9 (1973). 4 - R. Silberberg and C.H. Tsao, Ap. J. Suppl. 220 25, 315 (1973). 5 - G.M. Raisbeck and F. Yiou, Phys. Rev. C 12^, 915 (1975). 6 - C.J. Orth, H.A. O'Brien, M.E. Shillaci, B.J. Dropesky, J.E. Cline, E.B. Nieschmidt and R.L. Brodzinski, J. inorg. Nucl. Chem., J38, 13 (1976) and C. Perron, Phys. Rev. C _14, 1108 (1976). 7 - M.M. Shapiro, R. Silberberg and C.H. Tsao, 14th Int. Cosmic Ray Conf., Munich (1975) vol. 2, p. 502. 8 - J.L. Reyss, Universite de Paris-Sud, Thesis (1977).

E (GeV /n)

Figure 1 - Calculated ratio of Al/Si in cosmic rays as a function of energy for average propagation densities of 0.2, 1, and 00 atoms/cm3. Calculation is for 5 g/cm2 exponential pathlength. 120

A TWO-ZONE COSMIC RAY PROPAGATION MODEL AND ITS IMPLICATION OF THE SURVIVING FRACTION OF RADIOACTIVE COSMIC RAY ISOTOPES M. Simon University of Siegen, Physics Department, 59 Siegen Vest-Germany R. Scherzer, V. Enge Institut fUr Kernphysik, University of Kiel Vest-Germany

In cosmic ray propagation calculations one can usually assume a homogeneous distribution of interstellar matter. The crucial astrophysical parameters in these models are: The path length distribution, the age of the cosmic ray particles and the interstellar matter density. These values are interrelated. The surviving fraction of radioactive cosmic ray isotopes is often used to determine a mean matter density of that region, where the cosmic ray particles may mainly reside. Using a Monte Carlo Propag- ation Program we calculated the change in the surviving fraction quantitively assuming a region around the sources with higher matter density.

1. Introduction. While the electromagnetic radiation from the stars comes on straight lines to the earth cosmic ray particles travel from their source scattered by diffusion by interstellar magnetic field variations. Thus cosmic ray can give answers to the structure of interstellar space when their process of propagation in these regions has been understood more in detail. Continuing the work (1-7) which has been done on this subject in the past in this paper a two-zone propagation model using a Monte Carlo program is presented. It is the temporal aspect which can be obtained from long live secondary radioactive cosmic ray isotopes, called radioactive clocks, like 1°Be,'it>Al and 36ci and which can be studied adequate only by an inhomogeneous model like a two-zone model that led us to develop the earlier proposed two-zone models further (8-11). The number of stable secondary cosmic ray isotopes produced by fragmentations on their way from their source through interstellar space is only influenced by the total amount of interstellar matter, the number of instable radioactive secondary isotopes, however, is in addition strong„ly effected ^y the distribution of the interstellar matter. 2. The two-zone model and the Monte Carlo propagation program Supernovae - considered here as cosmic ray sources (12-15) - are surrounded by an envelope indicating that cosmic ray particles may penetrate a certain amount of matter with high density shortly after their injection from the source before they reach the interstellar space which is of much lower density. We developed a Monte Carlo program to be able to follow the individual particle through the source region and through the interstellar space by varying the densities and the mean path 121 lengths in both regions. Thus this two-zone model has five parameters: 1) the mean path length inpthe source region 2 x1[g/cm ] and 2) in the galaxy x2 [g/cnr] , 3) the number density 5 n1 of H-atoms per cm in the source region and 4) in the galaxy ni and 5) the kinetic energy of the particle. Table I shows seven selected cases for which the calculations were performed. Assuming an energy independent exponential path length distribution in both regions one has the situation of a "double leaky box"-model. In the Monte Carlo program one starts with a great number (e.g. 50000) of iron nuclei, the heaviest primary element and steps with all these iron nuclei individually through some random generators simulating on the average the path length distribution in the different regions. The interactions with the interstellar matter and the fragmentation characteristics are determined by the cross sections concerned using the semi empirical formulae (6) and experimental data, if available. The surviving primary iron nuclei and all the fragmentation products were stored for further evaluations. This was also done for all the other primary source nuclei taking the source composition given in (7). The loss of radioactive isotopes in this procedure could be due to interactions or to decay. The increase of their life time due to relativistic velocities at high energies has been considered, while no energy loss was taken into account.

3. Results. The figures 1, 2 and 3 show the resulting ratios of the calculation for the seven cases of Tab.I. In Table II in addition the surviving fraction <£ - i.e. the ratio of the at the earth surviving secondary radioactive isotopes to all produced secondary radioactive isotopes of the same kind - at four different primary energies and the mean travelling time T are listed. T is defined by T = (x-i +x2)/(( -/3-C ) where (x-j+xp) is the total ngth length. + J is the toial mean density (o = 1.67* 10"2^-n jg/cm-3] ) aild fh*c is the velocity of the particle. 4. Discussion. As can be seen from Tab.II, in case 3, 4 and 5 about the same percentage of 1oBe/Be derived for different combinations of the densities in the two zones belong to mean times which differ by a factor 100, i.e. between these model cases cannot be distinguished even with very accurate measurements . It is too early to decide from presently available measurements which one of the seven cases is given in nature. The "°Be measurements - sumarized in (16) to be 1oBe/^Be + ^Be )= 5±§ % at 100 MeV/Nuc - are spread over the whole set of curves 7 Because no solar modulation was included in our calculations this measurement should be applied at about 300 MeV/nuc in the calculated curves. When future measurements achieve results which are accurate enough the cases 1, 2, 7 and may be 6 at higher energies could be discriminated (see fig. 1,2,3). The cases 3, 4 and 5, however, cannot be discriminated by this method. For 2°A1/A1 and 1oBe/Be the situation allover is a little bit better than for ^bCl/Cl, thus future Al-isotope measurements in continuation 122 of prasently available very preliminary ones (17-19) look very promising Judging from our calculations. Acknowledgement. The authors R.S. and W.E. are grateful to Prof. Dr. E. Bagge and to Prof. Dr. G. Wibberenz for their support of this work. The financial support of the Deutsche Forschungsgemeinschaft is gratefully acknowledged. R.S. thanks for the financial support of the Graduiertenforderung.

References ( 1) Daniel R.R., Stephens S.A., Propagation of Cosmic Rays in the Galaxy, Techn.Rep.No. 75-028, Univ. of Maryland, (1975) 2) Kulsrud, R., Rapp.Paper, 14th CRC MUnchen, S.3753,(1975) 3) Peters B., Vol.Is "Prog.in Cosmic Ray Phys.n, North Holland Publish Company, (1952) 4) KaplonM.F., Noon J.H., Racette G.W., Phys.Rev. 96, 1408 (1954) 5) Shapiro M.M., Silberberg R., Ann.Rev.Nucl.Science, 20, 323 (1970) 6) Silberberg R., Tsao C.H., Ap. J. Suppl. 220, 315 (1973) 7) Shapiro M.M.. Silberberg R., Tsao C.H., 14th CRC Miinchen, S.532, (1975) 8) Lindstam S., techn. rep.: LUIP-CR-74-04, Lund, Schweden, (1974) 9) Meyer P., Phil.Trans.Roy.Soc. London A 277, 349 (1976) 10) Simon M., Scherzer R., Enge W., (Ex 68), DPG-Friihjahrs- tagung, Freiburg, (1976) 11) Cowsik R., and L.W. Wilson, 13th CRC Denver 1, 500 (1973) 12) Scott J.S., Chevalier R.A., Ap.J.Letters 197, L5 (1975) 13) Hainebach K.L., Norman E.B., Schramm D.N., Ap.J. 203. 245 (1976) 14) Kristiansson K., Astrophys. Space Sci. ^0, 417 (1974) 15) Cass6 M., Goret P., Cesarsky C.J., 14th CRC Munchen, S. 646, (1975) 16) Meyer J.P., Rapp.Paper, 14th CRC Miinchen, S.3698, (1975) 17) Webber W.R., Lezniak J.A., Kish J., Ap.J. 183, L81 (1973) 18) Beaujean R., Enge W., 13th CRC Denver, S.111, (1973) 19) Fisher A.J., Hagen F.A., Maehl R., Ormes J.F., 14th CRC Miinchen, S. 373, (1975) 123

case source region gala ctic region path length nuaber density path length nuataer density x1 [g/cm ] 3 g/c 2 n2[ca~3] n1(ca~ j *2 ! " l

1 4.5 103 0.5 1

2 2.5 103 2.5 1 3 0.5 103 A.5 1

2.5 1 2.5 1

5 0.5 10-3 4.5 1

6 2.5 10-3 2.5 1

7 4.5 10-3 0.5 1

•attar density j [g/oa3] - n (ca"3] •1.67-10-24 [gj 10 26 2 Tab. II Surviving fraction t£ and ratio Rftor B«, AI and ^Cl in % tor 5 g/ca

daneity graph 0.3 Oa V/Huc I 0.6 0« V/Nuc 1 o«v /Nuc 2 0«V /Hue cast sourca cart]\ 10B. *ci J 10B. 26AI *C1 10B. 26A1 ^Cl 10B. 26A1 ^Cl

83 79 30 I 91 86 63 93 89 93 78 1 -V/ V 'V \ R * 12 18 21 i 16 15 23 16 16 27 I 16 16 28 * 4.4-105 a 1 3.7-105a 3.3-105a 8 <£ 54 42 17 65 23 70 60 30 79 72 59 W/. ' 14 12 15 14 I 18 15 16 1 2 R 9 13 13 15 ,2 T 2.4*10 a 2*10 a 1.8-10ba 1.7*11 € 34 sr 9 51 35 15 59 43 19 70 57 It> R 11! 9 11 11 12 11 15 14 y 3 3 13 1 .17 •/,

Da'lnitioiwi e.g. for B«

A TWO-ZONE C%SMIC RAY PROPAGATION-MODEL AND ITS IMPLICATION OF THE SOURCE COMPOSITION AND OF THE ENERGY DEPENDENT ABUNDANCE OF COSMIC RAY NUCLEI _>_

"M. SIMON UNIVERSITY OF SIEGEN, PHYSICS DEPARTMENT, W-GERMANY 59 SIEGEN, ADOLF-REICHWEIN-STRASSE. 3

Abstract In this paper a Monte Carlo Propagation Proqram is used to follow the individual particles through space by varying the boundary conditions between a containment region around the source with higher density and the interstellar space. Assuming an exponential pathlength distribution in both regions this two-zone-model leads to a general enhancement of heavy primary source nuclei. With an energy dependent dwelling time in the source confinement region this model also offers an explanation for the observed energy dependent abundance of cosmic ray nuclei. 126

Introduction Observations show that at energies above several GeV/nucl. the nuclear composition of the cosmic radiation changes. This is confirmed by the different experimental qroups (1 to 7). Some results are displayed in the figures 1,2 and 3. One might conclude from these data, however, that the decrease in the ratios levels out at higher energies and above about 30 GeV/nucl. the ratios are probably constant aga.in. There are some models proposed in order to explain these changes which either use propagation effects (8) or even invoke different source mechanisms (9). Here, another approach will be offered picking up the idea of a confinement region around the cosmic ray sources with higher matter density and with an energy dependent ability to hold the cosmic ray particles before they enter the less dense interstellar space. This picture of a "double leaky box"-configuration is already proposed by Cowsik and Wilson (lo,ll) and Simon et.al. (12). It can be shown that such a two zone configuration can explain consistently the changes in the chemical composition due to the energy dependent leakage from ;he source region and which is important due to a chanae of the source composition a further consequence of this model.

T—i innn T—i i iiiiij r The effective path length distribution in a "double 0.5 o SMITH et al m leaky box" model a WEBBER. DAMLE-K/SH (l*) In order to calculate the OA • WEBBER et al 11 > source composition the • BALASUBRAHMAN-ORMES ('>pat h length distribution is Z0.3 one of the crutial quantities which has to be con- 0.2 sidered. Due to the existence of heavy nuclei in the cosmic radiation one at usually accepts an exponential path length distri- I Mill JL I IJL. 1-1,1. i., i 11111 i bution, which offers a ar r io 100 sizable portion of short ENERGY (GeV I NUCLEON I path lengths. This distri- Fig.l: The measured abundance of the L/M-ratio at bution is described by the different energies. The dashed curve:"single-leaky picture of a leaky galaxy box-configuration with an energy dependent mean (box). If one accepts the leakage path length y in the galaxy and a source "double leaky box"-confi- composition which is listed in column 4 of table I. guration, one obtains a The solid curve:"double leaky box"-configuration real change in the overall with an energy dependent mean leakage path length path length distribution. x in the source region and an energy independent For instance, if fx{x) = mean leakage path length in the galaxy. The source a-exp(-a-x) is the distri- composition is that of column 5 in table I. Values bution in the source re- for x and y are given in table IV and III. gion and fy(y) = 6-exp (-fl-y) that in the galaxy : the overall effective path length distribution fz(z^ x+y) is given by a convolution: z

fz(Z) = fx(x)-fy(Z-x)dx

thus J'S-a'8 -a f exP(-«-Z)"exP(-P-z)j ff t a fz(z) = 2 a Z • exp (-fi'Z) B = a 127

Fig.4 shows the result of such a convolution. Since the mean nuclear interaction lengths of the heavy nuclei are short and since the number of short path lengths is depleted in fz(z), the heavy nuclei will be more destroyed on the average during their path through space than in a "single leaky box"-model. Itn I II' Hl'l '•• • B*LASUB»*t*fAf(r*M • #IBB€**<* (•» ., The source composition assum- C*vfS *»» • JULIUSSON »l * i' » o CaiTaPiZhT ml all it ing a "double leaky box"-con- • MUhiO< OffO^jP ( - figuratioi n To investigate the implications of the source composition due to this convoluted effective path length distribution a Monte Carlo Propagation Program was developed, which is able to follow the fate of every individual primary nucleus and of all the stable and radioactive fragmentation products through esewr ig»v i huci e on) space by varying different parameters. The fragmentation cross Fig.2: The abundance of C and 0 relative to sections were calculated from the elements in.the iron-group. See caption the semi-empirical formula (13) under Fig. 1 ancf the experimental cross sections if available were add- • HIKlCH GBOVP ( 1 ed. It was further assumed that • AJUUSSCN(2) just hydrogen accounts for the interstellar matter and no energy loss by ionization was considered. Choosing in this program just one region with an exponential path length distribution and a homogeneous distribution of the interstellar hydrogen one veryfies the "single leaky box"-model. With a mean leakage path length of y=5.33("g/cm2) and - 10 DO the source composition (15) of £XMOr tOtvtHUCLCCMI column 4 in table I one verifies Fig.3: The abundance of nuclei with charges Z the abundance of the cosmic ray between 17 ^ z 23 relative to elements with nuclei observed on top of the atmosphere (see column 2 and 4 charges Z >_ 24. See caption under Fig. 1 of table II). The proper calculations of the source composition under the assumption of a "double leaky box"-configuration requires the knowledge of the mean path lengths in both regions. Since this model is postulated to explain the measured composition of cosmic ray nuclei as a function of energy, a fit to the existing data Iras been done in order to settle these parameters. The value of the galaxy has to account for the probably constant secondary/primary ratio at high energies and it was found to be y = 1.67 (g/cm?). At lower energies the additional contribution from the source region has to account for the observed higher production of secondary fragments. Due to the change in the overall path length distribution, however, this process is accompanied by an increase of heavy nuclei in the source abundance in order to explain the measured abundance of the cosmic radiation. With the source composition of column 5 in table I and a mean path length in the source region of x = 2.5(g/cm7) one calculates the arriv- ing composition, which is listed in column 3 of table II. Good agreement with the observed abundance can be seen. The new source composition is this "double 128 leaky box"-configuration shows an enhancement of heavy nuclei, which is more than 20% for the most abundant heavy nuclei.

Fig.4:

fx(x) and fy(y) are two exponential path length distribution with a mean path length of X=2.5(a/ cm2) and Y=1.67 (q/ cm2)resp.fz(z) is the convolution of both with a mean path length of Z=4.17(g/cm2). fx(x) represents the condition in the source •region and fy(y) in the galaxy. fz(z) is the overall path length distribution in a "double leaky box"-configuration.

Table X

Cosmic ray source i mpositions taken from the literature and compared to a cora^. jition, which la deduced under the assumption Of a "double leaky-box"-conflguratlon.

The numbers are relative to carbon C - 100

charge ele- Webber (141 Shapiro C151 "double leaky difference difference in (») to in (») to S ment "single leaky "single lea- box"-conflgu- box"-configu- cy box"-con- ration Webber C141 Shapiro (151 ration figuration

( C 100 100 100 0 0

• 7 N I0.9i1.55 11 1 2 0 0

1 0 106.2 107± 2 107 +0.7 o

10 Me 16.8 16 t 2 19 +13 +18.8

12 ttfl ti. 3 23 ± 2 26 4-12 +13.0

13 Al 2.12*0.43 2 1 1 3 +41,5 +50.0

14 Si 17.3 20.4t3 22 +27.2 + 9.8

1< S 3.410.48 3i0.6 4 +17.6 +33.3

30 Ca 2.510.39 2.210.8 3 +20.0 +36.4

37 Fe 19.4 20.513 +29.0 +22.0 129 Table II

The calculated and measured abundance of cosmic ray nuclol on top of the atmosphere, assuming a single and a double "leaky-box"-mode with the different source compositions listed In Table I

The numbers are relative to carbon C • 100.

Element ^single leaky box" "double leaky box" Messurementii Y-5.33 (g/cnr ) source region: 115J Source Composition: X-2.5 (q^cm1) Rigidity _> 4 OV Column 4,Table I galaxy: Y-1.67 g/cm1 Source Composition: Column 5, Table I

Li 17.6 17.9 16.5 1 2 Be 10.8 10.9 10.5 ± 1 -B 25.1 26.3 * 28 ± 1 C 100 100 ioo i M 24 27.4 25 t 2 0 89.7 89.3 91 t 2 Ne 15.2 18.0 16 i 2 Mg 17.5 19.9 19 t 1 Al 2.5 3.0 2.8 t 1 Si 13.8 13.9 14 t 2 P 0.28 0.36 0.6 t 0.2 s 3.7 3.5 3 i 0.4 cl 0.53 0.76 0.5 t 0.2 Ar 1.35 1.45 1.5 t 0.7 K 0.61 0.78 O.ft t 0.2 Ca 2.02 2.6 2.2 t O. 5 Sc 0.29 0.39 0.4 t 0.2 Tl 1.89 2.5 1.7 t 0.3 V 0.57 0.84 0.7 t 0.3 Cr 0.88 1.3 1.5 t 0.4 Mn 0.62 0.89 0.9 ± 0.2 re 9.5 10.2 10.8 1 1.4

The energy dependent abundance of Cosmic Ray Nuclei If one takes the source composition of column 4 in table I and assumes a "single leaky Box"-configuration with an energy dependent mean path length in a way that one fits the L/M-ratio dashed curve in Fig. 1, one cannot find a proper and constistent fit to the ratios shown in the figures 2 and 3. Parti- cularly, the.measured iron abundance is higher at high energies than one is able to explain with a "single leaky box"-model assuming just an energy dependent escape from the galaxy. Values for the energy dependent mean path length y(g/cm2) at different energies necessary to fit the dashed curve in Fig.l are listed in table III. A "double leaky box" configuration, however, with the changed source composition leads to the solid curves. The decrease in the ratios is achieved by putting the energy dependent mean leakage path length into the source region. These values x(g/cm2) at different energies are fisted in table IV . In this calculation there remains a constant mean path length y of 1.67 (g/cm2) in the galaxy independent of the energy. 130

Table III: The energy dependent mean leakage path length y (g/cm2) in a "single leaky box"-model, necessary to fit the L/M-ratio (dashed curve) in Fig. 1

E (GeV/nucl.) 1 2 4 8 14 2o 3o 5o y (g/cm2) 5.33 4.87 4 2.86 2.22 1.82 1.43 1.11

Table IV: The energy dependent mean path leakage length x (g/cm2) in the source region, necessary to fit the L/M-ratio (solid curve) in Fig.1 . The energy independent mean path lenqth y (g/cm2 in the galaxy is y = 1.67 (g/cm2)

E (GeV/nucl.) 1 1.5 4 6 *12 16 30 x (g/cm2) 2.56 2.5 1.43 1.0 0.4 0.2 0

Conclusion The combination between the energy dependent leakage from the source region and the energy independent mean path length of 1.67 (a/cm2) in the galaxy leads to the decrease of the ratios and also to constant values at hiaher energies, where the trapping mechanism in the source region becomes inefficient. This is assumed to be around about 30 GeV/nucl. At higher enerny the galaxy remains as the dominant confinement region with an enerny independent exponential path length distribution. It is important to note, that the consistent fit in all three figures - also in the C+0/Fe-group-fioure - is attained by the cbancie of the source composition, which is also a consequence of the "double leaky box"- confiquration. This enhancement of heavy nuclei supports even more the idea that the basic sources of the cosmic radiation are in the nucleosynthesis highly involved massive stars. This two zone model necessarily leads to a constant ratio in the fiaures 1, 'I and 3 at high energies. The accuracy of the available data, however, !s not sufficient enough at the present and measurements at energies in the renion of hundred GeV/nucleon are also missing. This makes it difficult to check unambi- geousl.y on this consequence. But these calculations indicate that it may be still feasable to explain the observed changes in the abundance of the cosmic ray nuclei by invokinn just propagation effects. References: 1) Balasubrahmanyan, V.K., Ormes, J.F., Ap.J.186, 109 (1973) 2) Smith, L.H., Buffinqton A., Smoot, G.F., Alvarez, L.W. and Vahllg, H.A. Ap.J.180, 987 (1973) 3) Jullusson, E., Meyer, P. and MUller, D., Phys. Rev. Letters 29, 445 (1972) 4) Schmidt, W.K.M., Atallah, K., Cleghorn. T.F., Jones, W.V., Simon. H., Astron. and Astrophys. 46, 49, 1976 5) Cartwright, G.B., Garcia-Munoz, M. and Simpson, J.A. Proc.12. Int.Conf.Cosnr.c Rays, Tasmania 1, 215 (1971) 6) Webber, W.R., Lezniak, J.A., K1sh, J.C. and Damle, S.V. Nature Physical Science, Vol. 241, 96 (1973) 7) Jullusson, E., Ap.J.191. 331 (1974) 8) Audouze, J. and Cesarsky, C.J., Nature Phys.Science 241, 98 (1973) 9) Ramaty, R., Balasubrahmanyan, V.K.\ Ormes, J.F., science 180, 731 (1973) 10) Cowsik, R. and Wilson, l.W.Proc. 13th Int.Conf. on Cosmic Rays, Denver I, 500 (1973) 11) Cowsik, R. and Wilson, L.W., ICRC Munich 1975, Vol. 2, 659, 1975 12) Simon, M., Enge, W. and Scherzer, R., Annual Spring Meeting of the German Physical Society, Freiburg, Germany 8-10 March, EX 68 (1976) 13) Silberberg, R. and Tsao, C.H., Ap.J. Sup.No. 220, Vol 25, 315 (1973 14) Webber, W.R., Damle, S.V. and Kish, J., Astrophys. Sp. Sci. 15, 245 (1972) 15) Shapiro, M.M., Silberberg, R.t Phil.Trans.R.Soc. London 277, 319 (1974) 131

SILICON, SULPHUR, ARGON, CALCIUM : PUZZLING THOUGHTS ON A KEY QUARTET * M. Cass£ and J. P. Meyer

Service d1 Electronique Physique, Centre d'Etudes Nucl^aires de Saclay (France) * Present address : California Institute of Technology, Pasadena, USA

We show that : (i) the cosmic fay source abundances of the quartet cannot be explained by explosive Si burning, and (ii) that no one Sulphur abundance in the galaxy is consistent with present views on both nucleosynthesis and production of the cosmic ray source composition.

1. INTRODUCTION. This paper starts from a reanalysis of galactic abundances. Those of Si and Ca are very well determined, and need no discussion. Ar is discussed in the foot notes of Table 1 of Meyer and Reeves (1977). S is discussed below.

2. THE SULPHUR ABUNDANCE IN THE GALAXY 2. 1 Sulphur in meteorites . In meteorites Sulphur behaves as an ordinary volatile element following nicely the traditional fractionation pattern of volatile elements between CI, C2 and C3 carbonaceous chondrites (Mason 1971, Anders 1972). In the scale Si-=100 the CI mean abundance is S = 50 (range qf observations from 43 to 56), the C2 abundance S = 23 (range from 19 to 36). Hence our adopted meteoritic abundance, S = 38 ± 20 fully takes into account the lower C2 abundances,including their spread. Note further that the E4 enstatit e abundance is S = 30 (range from 29 to 32) (Suess and Zeh 1973, Cameron 1973, Reeves and Meyer 1977). 2.2 Sulphur in the phctosphere. The photospheric abundance of Sul- phur is based on two indications : - the_ £ermittjed_gj_lines_: a careful recent reassessment is due to Holweger (1976, 1977). It is based on 14 weak unblended lines. They are chosen as to involve only unperturbed atomic levels, for which Holweger estimates that the f-values can be reliably calculated to better than ^15%. This accuracy is confirmed by the small spread of the abundances deduced from the 14 lines considered (standard deviation = 18%), since errors on the calculated f-values are not expected to affect the abundances deduced from the various lines in the same way. For these weak lines with high excitation energies, non-LTE effects are negligible. The dependence of the abundances on the solar model is also weak, especially when abundance ratios are considered. Holweger gets S/Ca = 6. 8 ± 1. 0. With Ca = 5. 7 ± 1. 0 (Meyer and Reeves 1977) we get 3 = 39 ± 14 (standard deviation CT of the 132

spread of the abundances derived from the various lines : a = 7). - the J[orbidden_ _SI_ _lines_: forbidden lines always provide abundance determinations which are quite independent of the solar model used and free from non-LTE effects. Two lines are available. One of them, very heavily blended, yields S=31, the other, much more reliable, yields S = 47.

The convergence of the permitted and forbidden lines photospheric abundances is good. Based on an independent reanalysis of all the data, Lambert (1976) proposes S - 44 as a best-value, in good agreement with the value deduced from Holweger (1976, 1977)'s work : S = 39 ± 14. 2. 3 Sulphur in the corona . - The EUVj7range : two studies by Dupree (1972) and Malinovsky and Heroux (1973) in different ranges of wavelengths have yielded S = 58 and S = 14 respectively i.e. differing by a factor of four. The latter value is lower than the Sulphur abundances found in all other meteori- tive, photospheric and coronal studies, and more similar to the cosmic ray source value. It therefore deserves a closer study. The source of the discrepancy cannot lie in Malinovsky and Heroux1 s observations, which are of very first quality. On the other hand we note that Sulphur does not follow the beautiful self consistent pattern of repartition of the ions among the various degrees of ionization provided by the other six elements studied. It appears as if the Sulphur ions were found at a lower temperature than expected. In any case something is not understood in the behaviour of Sulphur and at present no one Sulphur abundance can be found consistent with the l-'nes of all its six observed stages of ionization. Jordan (1976 and private communication) has reanalized the data of Dupree (1972) and of Malinovsky and Heroux (1973), with her own set of atomic parameters. She finds that both nets of observations are consistent, and yield both S 29, within a factor of 2 resulting from the uncertainties on the atomic parameters. In an independent reassessment of the EUV data Withbroe (1976) has recommended S=35. We thus feel justified in stating that the coronal EUV Sulphur abun-

-v dance, though accurate to only a factor of ^2, agrees well with the photospheric and meteoritic abundances, and does not suggest a low Sulphur abundance as found in the cosmic ray sources. - Tl^_X-£ay_range_ : Walker et al. (1974) get S = 26, in good agreement with Jordan's (1976) reanalysis of the EUV data. Parkinson (1976) has not included Sulphur in his recent reanalysis of Walker et al. 1 s data. 2.4 Adopted Sulphur abundance in the galaxy. In view of the convergence of the abundances from the various sources „(fig. 1), we feel the adopted abundance S = 39 ± 14 an the scale Si = 100 is quite conservative. 133

3. THE SULPHUR ABUNDANCE IN COSMIC RAY SOURCES AND IN SOLAR COSMIC RAYS. Fig. 1 summarises the S/Si ratios observed at Earth. Taking into account the (small) spread of the observations, a 40% error on the S formation cross-section and ± 1 gcm"2 error on the escape length of cosmic rays (6 ± 1 gcm"2 below 5 GeV/n, « 2. 5 gcm"^ at 45 GeV/n), we get a source ratio S/Si = 0. 14 ± 0. 03. A comparably low abundance is often observed in solar cosmic rays above ^15 MeV/n (see e.g. Crawford et al. 1975, Webber 1975, Bertsch and Reames 1976), although this point requires closer consideration. We conclude that S is underabundant with respect to Si in galactic cosmic ray sources by a factor of 1.5 to 5, but most likely close to ^ 3 0.71 1—I i | l • 111 1—i i | l iii| 1—ri | it— ADOPTED EUvV 6/SI C1 SI * iCsQ

04 C2 E4 03 A»6.gcnrl 2S gem- L PHOTOSPH. METEOR. 0-1 SOLAR CR SOURCES SYSTEM • • '••••' • •»••••!, E [Gev/_l I nI 1I I III .1 1. 10. 100. Fig. 1. Left : S/Si ratio observed in the solar system. Right : S/Si ratio as observed in cosmic rays and calculated with escape lengths of 6 and 2. 5 gem"2 , based on the CRS abundance S/Si = 0.14. Satellite observations : Oc^rtwright (1973) ; • Julliot (1976). Balloon observations : Jg Cass6 et al. (19"1) ; •Webber et al. (1972) ; VBenegas et al. (1975) ; • Ormes et al. (1975) ; ® Lund et al..(1975) ; • Juliusson and Meyer (1975). 4. DISCUSSION Abundance pecularities of galactic cosmic rays are usually discussed in terms of either (i) specific nucleosynthetic processes more Or less directly associated with the acceleration (supernova hypothesis, see e.g. Hainebach et al. 1976, Scott and Chevalier 1975, Chevalier et al. 1976), or (ii) selection effects associated with the ability of atoms to get ionized in a globally neutral medium of ordinary composition (and in which Ca, Al. . . are not locked in grains) where an electro-magnetic process accelerates only ions (Havnes 1973 ; Kristiansson 1971, 1972, 1974 , Casse et al. 1973, 1975 ; Cass£ 1976). If the Sulphur deficiency of solar cosmic rays is confirmed, it will strongly point towards the second hypothesis. We new discuss in turn the case of S in both hypothesis.

4. 1 Nucleosynthetic hypothesis. In both explosive oxygen and silicon burning, the equilibration of a-capture by photodesintegration leads to a quasi-equilibrium of o<-particle nuclei, reminiscent of the a-process described by Burbidge et al. (1957). The abundant a-particle nuclei are 134 linked by the chain 21 32 si + Of S + y 32 36 s + Of Ar+Y

36 4 Ar + a °Ca + Y As shown by Woosley et al. (1973), a large fraction of solar system abundances in the mass range 28 < A < 62 can be produced by explosive silicon burning alone (Bodansky et al, 1968 ; Michaud and Fowler 1972) or by the combination of explosive oxygen burning (28 < A < 45) and e-process (46 < A < 66). a-particle nuclei reach a qua si-equilibrium abundances in the very early stage of the explosion. The subsequent freeze out of nuclear reactions occuring at this early stage does not affect appreciably their distribution (Woosley et al. 1973). The quasi - equilibrium distribution is therefore expected to give a good approximation to final abundances between silicon and iron (if iron peak nuclei are not largely produced in different conditions). The relative abundances of a-particle nuclei (or their stable P-decay product) are related by Saha-like equations. Bodansky et al. (1968) have shown that, if qua si-equilibrium prevails, the expression 2/3 A 28 (¥) - ' J / < " ) = f(A,Z)+ logf-i^Zll/ (A-28) A cu(A, Z) n(Si^°) n(Si28) is for any temperature a linear function of the binding eaergy per nucleon added to Si2® B(A,Z) - B(Si28) j /(A-28) (where to = nuclear partition functions ; n = abundances ; B = binding energies ; f(A,Z) describes only the intrinsic properties of the nucleus (A, Z). The slope of the correlation depends only on temperature. The fit of the relevant solar system abundances between Si and Fe has been the main achievement of the theory. Fig. 2 shows an attempt to fit the recent solar sytem abundances (Mayer and Reeve s 1977) with this quasi-equilibrium theory. Clearly, not all species can be fitted by the same straight line: iron peak nuclei (A>44) have got to be largely produced in complete nuclear statistical equilibrium (e-proces,-.. Hainebach et al. 56 48 44 1974). If Fe , Cr52) Ti and Ca are excluded from the correlation, we are left with three points, two of which being poorly determi- 4 ned : S32, Ar36f Ca ®. The correlation becomes very loose The range of possible straight line fits is shown in fig. 2. Note that any correlation of this type (and hence the qua si-equilibrium theory of a- particle nuclei abundances in the mass range A = 28 to 40) can be valid only if the real S and Ar abundances are in the upper part of their error bars (i. e. close to the CI carbonaceous chondrites for S and consistent with the solar wind and coronal values but not with the interstellar value for Ar, see Meyer and Reeves 1977). Note however that according to Hainebach et al. (1974) Ca44 and Ti4° are not produced in adequate amounts by the e-process. Hence they may have to be 135

a SOLAR SYSTEM Fe .CRS/SS o C.R. SOURCES 1 -

Na 0.15 O.t — I, CRS/SS N

cosmic ray source abundance of the four nuclei Si^®, S^^, Ar36; Ca^" (which are believed to be generally produced by quasi equilibrium Si burning) cannot be understood in terms of this process, whatever the temperature chosen. 4.2. Selection according to atomic properties. The astrophysical applica- bility of the three current models of selective ionization (non thermal non equilibrium model, pbotoionization, coronal equilibrium)has been discussed by Casse et al(1975)and Casse(1976). The three models yield s-imilar abundance patterns. The following discussion will consider the coronal ionization model, but is valid for the three models. Fig. 3 shows the classical correlation between the first ionization potential I and the CRS overabundances with respect to the solar system SS(or galactic) abundances, normalized to Si(abundances after Shapiro et al 1975 and Meyer and Reeves 1977 , both with uncertainties). The elements with ionization potential 9 eV have normal abundances, while these with I>9eV are progressively more and more depleted. Also shown is the ionized fraction of each element calculated for a temperature distribution ^ (T)oC exp(-T/To), where 4 3 4o To = 10 °K and 10

CRS/SS ratio, although T0 should be adjusted to a slightly lower value to get the observed depletion of elements with large I. The CRS Sulphur abundance is marginally accounted for. There is still a serious problem if the SS Sulphur abundance is close to its higher bound(i. e. CI abundance), but everything is all right if it is close to its lower bound(C2 abundance; in which case the quasi equilibrium Si burning theory has problems! ). 136

Possible charge exchange effects are unlikely to modify this situation after integration over the temperature distribution (Casse 1976).Within its large error bar, Ar is all right. Ne makes problems. Is our adopted uncertainty on its galactic abundance too tight? Hydrogen (taken at a given rigidity, see Webber and Lezniak 1974) does not work at all. Apossible way out has been proposed by Casse et al (1975). 5. CONCLUSION • • ••• •— - • 11 v. The quartet formed by the elements Si, S, Ar, Ca is of crucial importance for both the theory of nucleosynthesis and the origin of cosmic rays. In the galaxy, only the abundances of Si and Ca are very accurately known. The nucleosynthesis of the quartet can be under-

stood int terms of a qua si-equilibrium under exchange of a-particles such as that prevailing in explosive Si-burning (Bodansky et al. 1968) only if the actual galactic abundances of both S and Ar are "high" (on the scale Si s 100, say S >45, i, e. near the CI carbonaceous chondritic value, and Ar >9. i.e. consistent with coronal and solar wind observations, but conflicting with interstellar values). In the cosmic ray sources (CRS) Si, S ancT'Ca are rather well determined, and the upper limit is totally reliable for Ar. In any case the low abundances of Ar and S in the CRS definitely rule out the view that the CRS composition could reflect the quasi-equilibrium of explosive Si-burning whatever its temperature. Simple minded electromagnetic selection effects operating in a medium of normal galactic composition can account for the poorly known abundance of Ar in the CRS whatever its abundance in the galaxy. As for the Sulphur abundance in the CRS, it is well accounted for if S is low in the galaxy (S ^ 25), but remains obscure if its galactic abundance lies around S = 50 as required by the qua si-equilibrium theory. So, Sulphur makes problems, either with nucleosynthesis, or with cosmic ray sources. The Devil is around . . . ACKNOWLEDGMENTS .We acknowledge helpful discussions with Suzy Collin-Souffrin, Edith Mllller, Hartmut Holwegei, Carole Jordan, Maryvorm?. Ledournevif, Monique Malinovsky and Claude Zeipen on the atomic parameters and abundance of Sulphur . REFERENCES Anders, E, 1972, in "l'origine du syBteme solaire",Nice 1972, Juliusson, E. et al. 1975, 1 1974, Ap.J. 193. 157. Shapiro, M. M. et al. 1975 14thlCCR, Munich, 2, 532. Hamebach, K.L. et al. 1976, Ap.J. 203, 245. Suess, H. E. et al. 1973, Sp. Sci. 231, 173. Havnes.O. 1973, Astr.Ap.24 ,435. Walker, A. B. C. ct al. 197t. Ap.J. 188, 423. Holweger, H. 1976, tAU Colloquium n"39. Lyon 1976. Webber, W.R. 1975, 14th ICCR, Munich, 5, 1597. Holweger, H. 1977, Earth Plant. Sci. Letters, in press. Webber, W. R. et al. 1972, Ap. Sp. Sci. J_5. 245. Jordan, C. 1976, Grenoble IAU Meeting, Report of Com. Webber, W.R. et al. 1974, Ap.Sp.Sci.30 .361. 12 (Solar atmosphere) Withbroe, G.L. 1976, To appear in Solar Phys. Woosley, S. E. et al. 1973, Ap.J.Supply 231. REALISTIC UNCERTAINTIES ON GALACTIC ABUNDANCES AND SIGNIFICANCE OF THE COSMIC RAY SOURCE COMPOSITION

J. P. Meyer and H. Reeves Service Electronique Physique, Centre d'Etudes Nucleaires de Saclay, France We present a critical study of the galactic abundances. We show that the N/O and Pb/Pt ratios are not necessarily abnormal in the cosmic rays sources, but that S is definitely seriously depleted. 1. INTRODUCTION We propose in table 1 a critically evaluated set of solar system or "galactic" abundances, with a realistic estimate of errors. It should help in interpreting the solar and galactic cosmic ray source compositions, and in deciding which deviations from the galactic abundances are significant, and which are not. In this context we of course systematically avoid using solar cosmic rays as a source of solar system abundances. 2. ABUNDANCES FROM VARIOUS MEDIA 2. 1. Meteoritic abundances: Contrary to Cameron (1973), we consider that whether CI or C2 carbonaceous chondrites are more representative of the primitive material is still an open question due to possible enrich- ments of CI chondrites in volatile elements (Goles 1969, Schmitt et al 1972, Urey 1972, Suess and Zeh 1973, Reeves and Meyer 1977; see however in favour of CI chondrites Anders 1971 -a, b, 1972, Cameron 1973, Holweger 1976, 1977). The C2 abundances of volatile elements is usually about half its CI abundance. Our error bars include the CI and the C2 abundances, and the spread of the observations, based on the references given by Cameron(l973) (in particular Mason 1971, Krahenbdhl et al 1973, Case jt al 1972, Schmitt et al 1972)complemented by Nichiporuk and Moore (1974), Eisentraut et al (197 1)« , Quandt and Herr(1974)and Weller et al(l976). 2.2. Photo spheric abundances: We have critically evaluated them in view of the various sources of errors (quality of the observations, i. e^ number of lines, background correction and blends;uncertainty on f-values and on dissociation constant for molecules; non-LTE effects; dependance on solar model). The difficult cases have been discussed with specialists. Tie sources are those quoted in the recent reviews by Trimble(l975), Ross and Aller(1976), Hauge and Engvold(1977), Holweger(l976) and Grenoble(l 976), complemented by more recent papers when available (see footnotes in table l). 2. 3. Coronal abundances: We have not used the abundances from optical forbidden lines, which are very unreliable because (i) the upper sub-level is largely populated by cascades from higher levels which cannot be accurately calculated duo to resonances, and (ii) radiative excitation is important and a good knowledge of the radiation field is therefore required (see e.g. de Boer et al 1972). This is no longer the case for the resonance transitions recently observed in the EUV and X-ray ranges, which are directly and purely collisionally excited. See the sources in the footnotes of table 1. The abundances are typically good to within a factor of 2 . We get crucial information on Ne and Ar. The sulfur abundance in the corona has also been a subject of controversy (see Casse and Meyer 1977). 138

2. 4. Solar wind abundances: Except for He which is on the average low by a factor si2. 5 and highly variable, the solar wind abundances of major elements are within a factor of 2 of their photospheric abundance. This behaviour can possibly be explained in terms of the drag exerted by the expanding proton gas on the heavier species (Geiss et al 1970), although this simple theory does not account for the all observed features (Hirshbex-g 1975). Our data are based on Bochsler and Geiss's(l976) review. The important points are Ne and Ar, which are discussed in the footnotes of table 1. 2. 5 Interstellar and stellar abundances: They are determined with the same intrinsic errors as the solar abundances, plus other ones. Since theu do not show significant deviations from solar abundances, we considei- them only for those elements where the latter are insufficient. See footnotes of table 1. 3. ADOPTED "GALACTIC "ABUNDANCES They are synthesis of the above ones. The agreement between meteoritic and photospheric is generally impressive. The error is still large on the crucial elements N, Ar, Pb, but the S value is reliable and Ne is reasonably well known. 4. COMPARISON WITH COSMIC RAY SOURCE ABUNDANCES The best estimate of the N/O ratio is 0.11, but it may lie anywhere between 0. 06 and 0. 24. The cosmic ray source value lying somewhere between 0.04 and 0.09 (Meyer 1975) there is no significant indication of a depletion of N with respect to O in galactic cosmic ray sources. Note however that the N/O ratio in the present interstellar gas might be higher that at the time of the birth of the sun by a factor within the range 1 to 2 ( Vigroux et al 197 6). The Pb/Pt ratio: Pt is rather well determined, but not Pb. Tlfle "Pb group" (Bi, Pb, Tl, half of Hg) to "Pt group" (half of Hg, Au, Pt, Ir, Os) ratio has a "best value" of 0. 80, but could lie anywhere between 0. 35 and 1.80. Hence Pb/Pt may be

ACKNOWLEDGMENTS We wish to acknowledge very helpful discussions with Jbhannes Geiss on meteoritic abundances, with Roger Cayrel, Giusa Cayrel de Strobel, Nicolas Grevesse, Hartmut Holweger, Edith* Muller and Fran^oise Praderie on photospheric abundances, Maryvonne Ledourneuf, Monique and Francois Querci, and Claude Zeipen on atomic parameters, and Carole Jordan and Monique Malinovsky on coronal abundances. ^Si s 100 METEORITES Rem. PHOTOSPHERE Rem. CORONA Rem. *Si s 106

H „ 0 2. 5 106 k He - 0 - e Li* 55 ± 10. t - t Be* 0 90 ± 0. 30 t 0. 35 (1.6) t B* 37 ± (2.) t 5. 0 (2. ) t C - 0 1200. ± 3 00. 6 700. (2) UQf N - 0 240 (1.6) 6 200. ± 80. ux O - 0 2100. ± 500. 6 1200. (2) UXzP F 0 30 ± 0. 20 V 0. 10 (5. ) a, f, 1, m - Ne - 0 _ g 150. ± 70. uxp Na 4. 6 ± 1.8 V 5.2 ± 0. 8 6. (1.6) ux Mg 106. + 3. r 93. ± 25. 100. ± 30. uxp Al 8. 4 ± 0. 3 r 6. 3 (3 ) f. l.» 7. (2) uxa Si s 100. + 3. rak =1 00. ± 25. k s 100. uxk P 0. 95 ± 0. 30 V 0. 7 (3 ) f.l S 38. + 20. vet 39. + 14. t 30. (2) uxt CI 0. 37 ± 0.20 v 0.60 (3 ) s, £, m Ar - o - g 17. (3) XOY K 0. 30 ± 0. 12 V 0. 36 + 0. 12 1 Ca 7. 2 ± 1. 0 r 5. 7 + 1. 0 Sc 0,00J3± 0. 0008 r 0. 0028 ± 0. 0006 - Ti 0. 27 ± 0. 05 r 0. 24 ± 0. 10 q V 0. 026± 0. 003 r 0. 030 ± 0. 015 f,h Cr 1. 25 ± 0. 12 r ( 1. 25 ± 0. 30 « Mn ' 0. 82 ± 0. 22 v / 0. 63 (2.5) f, h, n Fe 86. 2 8. r c 89. ± 35. 100. ± 40. uxP Co 0. 21 ± 0. 04 r 0. 23 (3 ) f.l Ni 4. 6 ± 0. 5 r c 4. 8 + 1.2 5- (1.6) ux Os* 0. 74 ± 0. 08 r 0. 13 (6 ) f, l.b ITr * 0. 72 ± 0. 12 r 0. 18 (6 ) f, l.b Pt* 1. 3 ± 0. 3 r 1.4 (2.5) f. l,b Au* 0. 19 ± 0. 05 r 0. 14 (2.5) f, l.b Hg* - dc < 8. TI* 0. 15 ± 0. 07 v£ 0. 20 (2.5) s, 1, b + 2. 0 PbH*U 3. 2. VCp (2) l.b Bi 0. 12 ± 0. 05 vc <0.16 TABLE 1 a Th* 0. 050± 0. 013 r e 0. 050 < 0. 030 e.l , b U* 0. 027± 0. 008 r e < 0.270 e - 100 SOLAR INT KRS'l' KL. ADOPTED Cf l H ' * II I 6 Rem Rem Rem. II I W N " 1 o WIND ' STELLAR GALACTIC

H = 2.5. I 06 k s 2. 5. 106 k 2. 5 106 P 5 He (1±0. 25). 105 w (2. 7±0. 5). 105 i (2. 7±0. 5) . 10 I Li" - 25'. (2) t 25. (2) I Be* - 0.33 (1.6, t 0. 35 (1.6) PI B* - 3.7 (2.) t 5. (2) PI C - - 1200, ±300 P N - - 240. (1.6) P O 1300. (3) - 2100. ±500. P + F - - 0. 30 0. 20 M Ne 190. ± 60. w 180. (1.6) j • 170. ± 70. CWI + Na - - 5. 2 0. 8 MP + Mg - - 106. 3. MPC Al - - 8.4 ± 0. 3 M Si 190. (3) k - H 100. 3. MP + P - - 0. 95 0. 30 M + •t* S - - 39. 14. MPC o CI - - 0. 37 + 0. 20 M Ar 4. 6± 2. 3 w 1. (3) y 5. (3) CWI K - - 0. 33 ± 0. 1 0 MP Ca - - 6. 5 ± 0. 4 MP + 1 Sc - - 0. 0030 0. 0005 MP * + Ti - - 0. 27 ' 0. 05 MP + V - - 0. 026 0. 003 MP + Cr - - 1. 25 0. 12 MP + Mn - - 0. 82 0. 22 M + Fe 125. (2) - 86. 8. MPC + Co - - 0. 21 0. 04 M Ni - - 4. 6 + 0. 5 MPC + Os* - - 0. 74 0. 08 M + ; - 0. 72 0. 12 M pt - 1.3 -f 0. 3 M Au * - - 0. 19 ± 0. 05 M - - 0.4 (3) d x ± Tl - - 0. 15 0. 07 M Pb* - - 2. 0 (2) MP - - 0. 12 ± 0. 05 TABLE 1b Bi * M Th* - 0. 050 ± 0. 013 MPe

U * - - 0. 027 ± 0. 008 Me 141

FOOTNOTES TO TABLE 1 ( numbers in parathesis indicate factors of error) a: Si=reference element. Error based on the spread of the Si weight content between meteorites of a given type, b: Essential lines severely blended c: Chalcophile element-According to Ure^(1972) chalcophile elements might possibly be enhanced in CI chondrites, d: The highly variable Hg abundances observed in carbonaceous chondrites are almost certainly all too high due, either to genuine enrichment in the parent body, or to terrestrial contamination (Hg is extremely volatile, like Boron). Following Cameron (1973) we adopt an abundance based on theoretical estimates in terms of r and s process'nucleosynthesis, anchored on the abundance of neighbouring elements: Hg-0.4. This value is close to that found in E4 enstatite chondrites, which often give quite reasonable, abundances (Suess and Zeh 1973, Cameron 1973, Reeves and Meyer 1971). e: Th, U: abundances at the birth of the solar system, corrected for decay since then after Cameron (1973). f: f-values (oscillator stengths) poorly known. g: Noble gases do not appear in the photosphere, whose temperature is too low. h: Problems with hyperfine structure. i: The abundance based on galactic and extra-galactic HII regions observations yielding He/H= 0.11 +0.02 (Aller 1972, Churchwell et al 1974, Peimbert 1975), in agreement with hot stars observations (Auer and Mihalas 1972, 1973a). A possible increase of the He abundance from a pre-galactic abundance He/H —0. 08 (observed in metal poor regions) possibly up to = 0. 13 in very metal rich regions is being controversed (Churchwell et al 1974, Peimbert 1975, Smith 1975, Trimble 1975, Perrin et al 1977). j: Ne: based on hot stars (Auer and Mihalas 1973b, Peters 1976) and HLL regions (Peimbert and Costero 1969, Aitken and Jonesl974) observations, k: To go over from the meteoi-itic and coronal scales (reference element= Si, hydrogen being not observed) to the photospheric, solar wind, stellar and interstellar scales, (reference element=H), we take Si/H= 4. 0 x 105, or Si= 7. 60 on the scale log H=i2. This conversion factor can be considered good within si 15% in view of the agreement it provides between the well measured meteoritic and photospheric abundances of Na, Mg, Si, S, K, Ca, Sc, Ti, V, Cr, Fe, Ni. On the scale Si= 100 one gets then H= (2. 5 + 0.4). 106. 1: Few lines available m:Molecular lines, difficult to interpret n: Serious non-LTE problems o: Meteorites do not provide any information of the abundance. Volatile element, which could not be effectively trapped in meteorites ( either noble gas; or very abundant species (H, C, N, O) for which only a small fraction of the atoms could find a partner to combine into a molecule capable of forming stony material), p: Pb: only very few measurements, with a large spread: one CI, giving an abundance of 4.0; three C2's, giving abundance of 1.0, 1. 6 and 4. 8 (Mason 1971). q: Ti: based mainly on Whaling et al (1977), who provide new high quality measurements of oscillator strengths. See also Ellis (1976). r: Refractory element. The CI and C2 abundances are about equal, s: Abundance observed in sunspots. Very sensitive to the sunspot model, t: See detailed discussion in text, and in Reeves and Meyer (1977) for Li,Be B, and in Casse and Meyer (1977) for S. u: Based on EUV data (Dupree 1972; Malinovsky and Heroux 1973; Withbroe 1975; Flower and Nussbaumer 1975; critical reviews by Jordan 1976 and Withbroe 1976). v: Volatile element - A fractionation effect is observed between CI and C2 carbonaceous chondrites (the C2 abundance is usually about half the CI abundance). Our error bar includes thetl and tlye C2 abundances, w: He is clearly deficient in the average solar wind by a factor 2 to 3. If this deficiency is understood in terms of the drag factor theory, Ne is expected to be possibly slightly high in the solar wind, and Ar to be somewhat low, by a factor up to 2. Including the measurement error, this leads us to a solar Ar abundance anywhere between 2. 3 and 14. x: Based on X-ray data (Walker et al 1974 a, b, c; Rugge and Walker 1976; Acton. 1975; Parkinson 1976). y: Based on the Copernicus satellite observations of HI gas (Morton 1974, 1975; Gomez-Gonzalez and Lequeux 1975). See also Peters (1976) for aLTE analysis of a hot star. z: Oxygen is poorly determined in EUV studies. a: Few measurements only. p: Several measurements in different wavelength ranges. The error is partly based on the spread of the various abundances determinations. y. Based on a single X-ray observation by Walker et al (1974a). The error is difficult to assign. 6: See the excellent review by Lambert (1977). The C abundance is now very reliably determined by the forbidden [ClJ, the CH A-X and the C2 lines. The permitted CI, CH B-X, CH C-X and CO lines, though less reliable, also give consistent abundances. Mount et al (1973), Mount and Linsky (1974 a, b, 1975a, b) and Curtis et al (1976) have recently proposed a C abundance lower by a factor of 2. None of their arguments stands on solid ground: their determinations are based",either on molecules whose dissociation constant is highly controversed^or on "bandhead" observations where many lines are lumped together, or on obsolete equivalent width observations and solar models. The error given includes possible non-LTE and macroturbulence effects. The O abundance is also reliably determined by the two forbidden [01J lines. The less reliable permitted OI , OH and CO lines yield consistant results. The N abundance is not accurately known since the available permitted NI lines are quite sensitive to possible non-LTE effects, and the dissociation constants of the observed molecules NH and CN are highly controversial. C: Adopted abundance based on Corona. 1: Adopted abundance based on Interstellar medium or stars •M: Adopted abundance based on meteorites. P: Adopted abundance based on Photosphere. W: Adopted abundance based on solar wind.

REFERENCES

Acton. L.W.et al. , 1 975, Ap. J. Letters 195, L 93. Mason, B. 1 971, Handbook of Elemental Abundances in ~ — , .. „ . . <- Meteorites (Gordon and Breach) Aitken, D. K. et al., 1 974, Mon. Not. Roy. Astr. Soc.J_67, 1 . ' . . , Mever. J. P. . 1975. 14tht. G. G. R. (Munich). 11, 369B. ... ; „ . . . c . . Morton,D.C., 1974, Ap.J. Letters, 193. L35. Aller, L. H., 1972, Ann . MN . vY. Acad. Sci._1_94,45 1Q . , . J r- r f \ . -c. c,i Morton, D.C. , 1975, Ap. J. 197. 85. Anders, E., 1971a, Geochim. Cosmochim. Act* j5, 516. ; —— • j r, . . a n i — Mount, G. H. et al., 1974a. Solar Phys. 35. 259. Anders, E., 1971b, Ann. Rev. Astr. Ap. 9, 1. , _ . T7 . . ~ , • r. "S „ , . ,, Mount, G.H. et al., 1974b, Solar Phys. 36,287. Anders, E., 1972, in"L'Ongme au Systeme Solaire", _ ,„,, _ ' Tr ., ... ., _ . „ . ; Mount, G.H.et al. , 1975a, Solar Phys. 41,17. Nice, H.Reeves ed. (CNRS, Paris), p. 179. .. . _ „ . , ,„,.. . , i .. — ,„, , „ , , . . _ . ,, .„, Mount, G. H. et al., 1975b, Ap. J. Letters 202. L51. Auer, L. H. et al.,l972,Ap. J. Suppl. 24,193. ,„,, _ , ,, - t u . . ,.„ a r c T Mount, G. H. et al., 1973, Solar Phys. 32. 13. Auer,L.H.ct al. ,1973a, Ap. J. Suppl. 25,433. , . , . _ — , . . ' ,, , . . 7TT Nicluporuk, W. et al., 1974, Geochim. Cosmochim. Acta Auer. L.H. et al.. 1973b. Ap. J. 184, 151. 38 1691 Bochsler, P. et al., 1976, Grenoble IAU Meeting, Report —" ' ,, ... , _ ' . , , , or Parkinson, J. H., 1976, Astr. Ap., in press, of Com. 12 (solaT atmosphere). _ . .„,, . „ ., .., ^ . ^ im-. ^ e • o ic i,i Peimbert, M. , 1975, Ann.Rev. AstT. Ap._13, 113. Caemron, A. G. W., 1973, Sp. Sci. Rev. 15,121. _ . 1 ' , .„,„ , ^T ^ „ ' , ' „ ' —' . . ,, ,„ Peimbert, M. et al., 1969 . nBol. Observ. Torrantai in Case, D. R. et al. , 1973, Geochim. Cosmochim. Acta 37,19, ' ' ' r- r %m . i mh .i.- r rif \~7Z »a Tacuvaya, 5, 3 , Quoted by Aller 1972. Cagsl, M. et al., 1977, this conference, paper OG-146. . ' — • " . . ' ^ ,,„ ; ,, _ . , .„,. . . . ,, Perrin, H. N. et al. , 1977, Astr. Ap. 54, 779. Churchwell, E. et al., 1974, Astr. Ap. 32,283. _ ' , . _ . —, _ .. , . a. , . TZ im Peters,G. J., 1976, Ap.J T. Suppl. 30, 551. Curtis, L. ct al., 1976, Pliys . cScripta 13,270. • ' ; , , .. _ ^ _ • . ',„,' . , r. -rr AM Quandt, U. et al., 1974, Earth Planet.Sci. Letters 24,53. De Boer.K.S.et al., 1972, Astr. Ap. 16,417. _ .... r , n « v io-7^> A T MO — Reeves, H. et al. , 1977, this conference, paper OG-129. Dupreo, A. K.,1972, Ap.J. 178, 527. ' , ,„,, .. ,„. ,,,, t- . . J , 1 i « ,, Ross, J.E. et al. , 1976, Nature, 191.1223. Eisentraut, K. J. et al.. Anal. Chem. 43,2003. ' ' ——- ,,,„ _„ V, ' .„_, ^ . —/, Rugge, H. E. et al., 1976, Ap. J. Letters, 203. LI 39. Ellis, R.S. ,1976, Solar Phys. 50. 261. _ " ' . \ ... _ — . _ '' . . ' .—,„ Schmitt, R. A. et al. ,1972, Meteoriti 7, 131. Flower, D. R. et al., 197a, Astr. Ap. 39,295. _ ., ,, _ ,„,_ , , „„ ce _ . ; . . . ' rr-co Smith, H.E.,1975, Ap.J r . 199, 591. Geiss.J.et al., 1970 , cSolar Phys. 12,458. „ ,, , ' —_ _ . ,, /-I ^ „ ,„,„ . „ .. . . 7T . . . „ „ Suess, H. E. et al. . 1973, Astr. Sp. Sci. 23, 173. Goles, G.G,, 1969, in Handbook of Geochemistry, K. H. _ . ' ,, ' ,, , —, . . ,,, Trimble, V., 1975, Rev. Mod. Phys. 47,877. r/edepohl eo., Springer, vol. I, p. 116. _ ' „ „ ' — . „. ,c Gomez-Gonxalez, jfet al., 1975, Astr. Ap. 38, 29. "f'"-^ ''"f* fn". N Y Acad. Sc.. 194, 35. Grenoble 1976, IAU Meeting, Report of Com. 12 = V / f t ,« „„ , . . , 6 Walker, A. B. C. et al. ,1974a, Ap.J. 188. 423. (solar atmosphere) ... „ . „ „ . . » . , „r ; . n IT ^ .• I . nn t . » TL. 1 A . t Walker, A. B. C. et al., 1974b, Ap.J. 192, 169. Hauge, O. et al., 1977, Inst, of Theoretical ABtrophys., ' _ _ ^ , , . _—r„, , q . " r ' Walker, A. B. C. et al., 1974c, Ap.J. 194. 471. u- » e ,, , en Weller.M.R.et al., 1976, preprint Cal. Tech.OAP-467. Hirshbe-g, J. , 1975, Rev. Geophys. Space Phys. 13,1059n . „„ .. V . ' __ Holweger, H. 1976, IAU Colloq uium n -39, Lyon ^t '"®' A 'r ^ . P'c ,n, Holweger.H., 1977, Earth Planet.Sci. Lett4T», in pre... f°Ur V^. 301 Wl,hbr0e G L 1976 t0 in SoUr Jordan, C. f 1976, Grenoble XAU Meeting, report o£ Com. ' " " ' W" 12(solar atmosphere) Krahenbahl, U. et al., 1973,Geochim.Cosmochim. Acta 31.1353. Lambert, D. L„1977,to be publi.h.d inM.N.R.A.S. M»Jinov«ky, M. et al. , 1973, Ap.J. 181. 1009. 143 k^mofif

MASS COMPOSITION OF PRIMARY COSMIC RAYS ABOVE 1013eV

J. Olejniczak and J. Wdowczyk, Institute of Nuclear Research, Lodz, Poland

and

A.W. Wolfendale Physics Department, University of Durham, England.

The mass composition of high energy primaries has relevance to both Astrophysics and High Energy Nuclear Physics. The available evidence is assessed.

1. Introduction. Analysis of EAS data shows that the results are inconsistent with the primaries being protons and the Scaling model being applicable for proton - air nucleus interactions. Analysis of any one set of EAS data (e.g. Wdowczyk and Wolfendale, 1972; Gaisser and Maurer, 1972 and later publications) shows that Seating can be restored if the primaries become progressively more massive as the energy increases. We contend elsewhere (Olejniczak et al., 1977 a,b) that it is difficult, to choose a primary composition that will satisfy all the data mu retain Scaling but, as is pointed out, the conclusion is not firm; JiLect measurement of the various primary mass spectra would be extremely useful.

2. Direct Measurements of Primary Composition. Figure 1. summarises the present data, with particular emphasis on the spectrum of the iron group. The earlier measurement of Balasubrahmanyan and Ormes (1973) gave a rather flat spectrum which, when extrapolated, made iron the predominant primary at energies above lOl^eV. It is of note that the intensity at several times 10^ is close to what we have estimated from EAS data (denoted P.W. - present work - in the Figure).

However, the very flat iron spectum is not universally accepted and other workers have found steeper spectra. Specifically, the other measurements shown in the Figure have been made and the best line through these intensities, and its extrapolation, is also shown. This new extrapolation gives an iron intensity at 3 x lO^eV lower than the BO value by a factor of 10.

Despite being lower than the BO intensity the extrapolated line from Schmidt et al. and Matsubayashi et al. may still be too high for reasons of propagation in the interstellar medium. The point is that iron will fragment considerably in the I.S.M. and insofar as the mean path length * in the I.S.M. appears to fall with increasing energy (X a e.g. Lachieze-Rey and Cesarsky, 1975) the measured iron spectum will be too flat. The effect will be biggest for iron in view of its shortest interaction length. 144

£4J(C) (eV* W)

io*

jJI iz 13 Hh IS ,J<° 10 E (ev /nucltH,) 10

Figure 1. Energy Spectrum of primary cosmic rays. The data are derived from: Ryan.et al. (1972): P,o£. Schmidt et al. (1976): CNO, LH(10 £ Z $ 16), MH (17 £ Z < 23) and 'Fe1 (Z > 23). The 'Fe' points are denoted X, a typical error is shown. The lines beyond lO^eV are all extrapolations. Matsubayashi et al., 1975: 'Fe', denoted ©with a typical error. The iron spectrum of Balasubrahmanian and Ormes (1973) extrapolates along the line marked BO. Present work: P.W. The lower limit from the analysis of de B.eer et al. (1969) and Hillas (1972) is shown as 111111. The summed intensitis of Ryan et al. (1972) and Schmidt et al. and their extrapolations is denoted by Z. 145

E\j(0 (eVm-W)

Figure 2. Energy spectra of the major components. The spectra are composite from the results of different workers. J: Juliusson (1974, 1975) R: Ryan et al. (1972) M: Matsubayashi et al. (1975) S: Schmidt et al. (1976) The experimental errors (not shown) become large at high energies. The dotted lines represent our estimate of the/source spectra allowing for fragmentation in the I.S.M. 146

Figure 2 shows the measured spectra and corrections applied by us (see I for details) to allow for the fragmentation. It is interesting to note that the corrected spectra for both the CNO group and for iron have exponents of.^ 2.6 below lOHeV and this is the exponent of the source spectrum in this region. Now the spectrum of the proton component is not very different from this (Ryan et al., 1972} give 2.75 but many workers prefer a value nearer 2.6) so that if all production spectra can be extrapolated with unchanged exponent the spectra at the top of the earth's atmosphere will be virtually parallel above about 10 eV and protons will continue to dominate.

If the proton spectrum were indeed to have an exponent of 2.6 above 10 eV then, using our arguments.- the ratio of iron to protons at 1013eV and above would be MD.25. At 1013eV CNO/P and a/P would also be ^0.25 with LH/P ^0.15 and MH/P %0.09. The total intensity (E of Figure 1) would move up to a value close to P.W. of Figure 1 at 10-^eV but still a little below at 1015eV.

3. Indirect measurements of the Primary Spectrum. Many studies of EAS fluctuations have been made which indicate the presence of at least some protons in the primary beam. The analysis at the end of §2 indicates protons constituting very approximately 50% of the total (in the range 1013 - 1015eV). Watson and Wilson (1974; and private communication) estimate that at least 40% of the primaries are protons in the range 10" - lO^eV a result that would call for a significantly higher fraction below the kink in the primary spectrum at ^4 x 10 eV. Many experiments indicate a 'normal composition', i.e. as at ^lO^-OeV at EAS energies,but the uncertainties are large. In this field we set store on a future comparison of fluctuations at sea level and at mountain altitude, the point being that for a particular ratio of protons to heavy nuclei in the primary beam there will be a big difference in relative numbers at two levels in the atmosphere for showers of the same size.

Acknowledgements.

The authors are grateful to E.Juliusson, W. Schmidt and R. Silberberg for helpful correspondence.

References.

Balasubrahmanyan V.K. and Ormes J.F., 1973, Ap. J. 185, 109-22.

de Beer, J., 1969, J. Phys. A. Gen. Phys. 2, 354-64.

Gaisser, T.K. and Maurer, R.H., 1972, Phys. Lett. 42B, 444.

Hillas, A.M., 1972, Cosmic Rays (Oxford: Pergamon).

Juliusson, E., 1974, Ap. J., 191, 331-48, 1975, Proc. 14th Int. Conf. on Cosmic Rays, Munich, 2689-49.

Lachieze-Rey, M. and Cesarsky, C.J., 1975, Proc. 14th Int.Conf. on Cosmic Rays, Munich, 489-94. 147

Matsubayashi, T. et al.,1975, Proc. 14ch Int. Conf. on Cosmic Ray Munich, 489-94.

Olejniczak, J., Wdowczyk, J. and Wolfendale, A.W., 1977a, J. Phys (in the press), 1977b, These Proceedings (OG 148).

Ryan, M.J. et al., 1972, Phs. Rev. Lett., 28, 985-8.

Schmidt, W.K.H., et al., 1976, Astron. Astrophys. 46, 49-59.

Watson, A.A. and Wilson, J;G., 1974, J. Phys. A. Math. Nucl. Gen. 7, .199-212.

Wdowczyk, J. and Wolfendale, A.W., 1972, Nature, 236, 29-30. 148 £>Q?900(%&

COMMENTS REGARDING HIERARCHICAL MODELS OP COSMIC RAY ORIGIN.

K. Sitte Faculty of Physics, University of Freiburg, Freiburg i.Br.

Predictions of the leaky-box theory, the closed-galaxy theory, and the mixed-origin two-component model at various energies are compared. In the low-energy range they do not differ signifi- 1 cantly. Around 10 4eV, as well as in the EAS region, distinctive effective masses of the primaries are expected. Since GAS primaries originate in comparatively nearby sources, their composition ist not strongly modulated in propagation. This throws doubt on the validity of assumptions of a high-energy extragalactic heavy-primary radiation.

I. Introduction. Three recently discovered features of the primary intensities have necessitated a thorough re-thinking concerning the theories of cosmic ray origin. Two of them are firmly established: the variation of the spectral indices of the primary components -or expressed in different terms, the energy dependence of the^abundance ratios, and the presence with undiminished flux rates of GAS of energies around 102®eV, perhaps even with a flattening energy distribution. The third, the possible existence of a "bulge" in the energy spectrum between about lO^eV and 10^-5eV, is still disputed. It may well be a direct consequence of the differences in the spectra of protons and of heavy primary nuclei (HPN). If this is so, one must expect a rising abundance, possibly a dominance, of HPN in the bulge region. In any case the question must be asked whether particulars of the propagation alone can account for the data oberserved at low and medium energies, or the cause should be sought in distinctive origin of the components. Regarding the GAS data, there can be little doubt that they demand the assumption of extragalactic origin of the primaries. Even if one did postulate the existence of extremely powerful sources, unknown and perhaps hidden in the galactic centre, one would find it hard to explain the absence of a corresponding radio emission. •Thi s, in brief, is the case for a "hierarchical" theory of cosmic ray origin in which a variety of sources -in the simplest version and as a first approximation a "two-component" model with a galactic and a extragalactic part- is assumed. But the crucial argument ist that once the dominance of extragalactic particles at the highest energies is admitted, the traditional view that cosmic rays of galactic origin previal at lower energies should be questioned without prejudice. Consistency of the predictions and plausibility of the suppositions will have to serve as arbiter. In the following some recently suggested models will be tested accordingly.

II.The Low-Energy Range. If the low-energy particles are of galactic origin, the energy dependence of the abundance ratios finds a natural explanation in terms of the "leaky-box" model of Cowsick and Wilson(l) in which the confinement time in the source region can be a function of the particle energy. But alternative interpretations have been offered as well. There is the closed-galaxy model of Peters and his colla- borators' 2' in which the particles originate in galactic sources 149

and diffuse out of the disk in a comparatively short period but have an unrestricted life time in the halo. (Thus the model has "leaky-box" character, with the galactic disk representing the confinement region. It can also he classified as hierarchical theory because it leads to the development of two quite distinct components). Moreover, a "mixed" two-component modelwJ ascribing different composition and different energy spectra to the galactic and the extragalactic radiation yields very similar results. In all cases one finds a satisfactory agreement between the calculated abundance ratios and the experimental data. It seems that at present none of these versions can be ruled out from available evidence, but none can claim complete success. The proponents of the leaky-box theory owe us a plausible model of the trapping region providing the appropriate energy dependence of the escape time. It is highly probale that for a galactic cosmic radiation a leaky-box effect does exist; it remains to be proved that it is fully responsible for the observed energy dependence of the abundance ratios. In both other cases it has been shown that an approxi- mate evaluation can adequately reproduce the observed trends; it remains to be shown that an exact calculation gives convincing fits. The open tasks appear formidable, but until they have been tackled no unbiassed verdict can be rendered.

III. Medium Energies ; The "Bulge". As stated above, a model of pure galactic-disk origin and propagation can produce the "bulge" in the energy distribution if the flatter spectra of the HPN continue up to the highest energies. In the closed-galaxy theory it appears as a consequence of the flatter energy spectra of the (mostly secondary) lighter components, especially H and He, above 1013 ^o lO-'-^eV. The "mixed" two-component model ascri- bes it to the dominance of the pulsar-generated galactic component at medium energies (extragalactic particles, mostly protons, are assumed to prevail at both ends of the spectrum). It is evident that here we find, at least in principle, a handier criterion for acceptance or rejection of the rival theories. The galactic-disk theory predicts a steadily rising abundance of the heavier constituents, since a possible contribution from extra-galactic sour- 1 ces, needed to account for the GAS events (and perhaps richer in protons) is still quite negligible in this energy range. In contrast, one expects in both other models that the increase in the abundance of the heaviest components comes to an end at a certain energy (around 10-'-5eV), and beyond it the lightest, H and He, begin to take over. Hence the effective mass of the primaries of small EAS, and to a lesser extent also details of the spectrum and the charge ratio of muons, can provide the needed evidence. Concerning the observations on muons, recall that several authors (ref.(4-6)) have already noted that the interpretation of the experimental data seems to demand the assumption of a,rising contribution of neutron interactions. A more systematic investigation of the problem, taking into account the stepwise fragmentation of the primaries, will be reported elsewhere in this Conference (7). Regarding the effective mass of the EAS primaries, estimates can be obtained "by two comparatively simple experimental methods. One is the determination of the muon/electron ratio as a function of the primary energy which for nucleon-nucleon collisions can be calculated with only moderate extrapolation from ISR parameters. Doubts have been cast on the "traditional" results by a recent investigation^ in 150 which, unlike in previous work, the variation of the lateral distribution of the muons with the shower size was considered. Indeed it was found that the experimental results could he fitted most satis- factorily by calculations assuming a higher fraction of muons -that is, a larger fraction of HPN parents- in showers of less than about 10° electrons. The experiment was continued; further results will be given in another session'9), However, a word of caution is in order concerning these results. They are inevitably tentative because the calculations have to be based on parameters derived from experiments in which -erroneously as we believe- a constant muon lateral distribution had been used for the evaluation of the shower size. 'While it is unlikely that after due corrections for which we lacked the required information our conclusions will be completely upset, reliable quantitative evidence cannot be given at this stage. Also for this reason a study of the height of the shower maxima at energies between, say, 10^4 to 10^ 'eV appears well worth while. Experimental data are in part available, in part easily obtainable. A systematic theoretical treatment has not yet been carried out but offers no serious difficulty. Summing up the evidence of the medium-energy range it seem fair to say that support is found for the existence of a "bulge", ^rd indications of support for a bulge made up of particles with a larger effective mass than at lower and at higher energies. This :.s a slight argument against a disk leaky-box model but not one disproving it beyond reasonable doubt. The evidence holds no clue for a discrimination between the closed-galaxy theory and the two-component model of mixed origin.

IV. The Hiph-Energy Region 1016 to 1018eV. Apart from the steadily rising effective mass, the leaky-box theory predicts no peculiarities of medium-sized EAS. But a very distinctive feature is expected under the assumptions of the closed-galaxy theory: the presence of a substantial fraction of EAS of electromagnetic origin. Recall that in this theory the bulk of the energetic protons -at 10 'eV amounting to more than 25 of the total flux- derives from fragmentation of HPN in nuclear interactions. All the pions created in these collisions will contribute to a high-energy electromagnetic component. The size spectrum of the EAS resulting from the atmospheric interactions of these photons and electrons, evaluated with the parameters used in MN 4 and with NKG approximations, is compared with the size spectrum of all EAS in Fig.l. Since the calculation invol- ves extrapolations of dubious accuracy, only the order of magnitude of the data should be credited: about 1 ^ of the total at N = 104, increasing to roughly 10 $ at N - 10*7. Moreover, the showers of electromagnetic origin

should show a marked n Fig. 1 Size spectrum of all showers (EA5) and of electromagnetic cascades (y,e) 151 anisotropy because most of their primaries come from the halo. It is tempting to see a confirmation of this prediction in the observation of muon-poor showers reported by Hochart et However, before accepting this conclusion one must await their results on the angular distribution of the events. Besides, these .nuon-poor showers still contain about 20-50 c/o of the average rate of penetrating particles. This is a very large fraction if the particles are due to photcnuclear interactions; it is -perhaps fortuitous- ly- rather close to the ratio one would expect if the bulk of the showers originated in HPN collisions, and the muon-poor events in proton interactions. An explanation in these terms, and under the assumptions of the mixed-origin two-component model, would demand that the presence of muon-poor showers be restricted to events of sizes not exceeding a few 105 particles, gradually fading out with increasing shower size.

V. Very High Energies ; The GAS. All models ascribing extra-galactic origin only to the GAS primaries and galactic origin to particles of energies below about 10^®eV face the difficult problem of explaining why not only the intensities of the two components match so closely at the "cross-over" energy, but also the slopes of their spectra. Recall that for the galactic component this slope is determined by the escape time, and for the extragalactic particles by the attenuation on their passage from the source region. This difficulty is avoided only if the galactic component extends to about 10l9eV -but at the cost of more serious trouble concerning the sources. As to the extragalactic primaries, it is in- structive to define an "effective distance" of the sources as a function of the particle energies. This was done using the procedures developed by Tkaczyk et al. (ref. (ll)) but adopting the fractional rate of energy loss of ffdowczyk and Wolfendale, with a constant spectrum S(E) of uniformly distributed sources. Writing B(E,r) for the modulation factors, the effective radius is simply the ratio of the contributions S(E)/B(E,r) integrated up to the Hubble radius R^, to the unmodulated intensities. In Fig. 2 the results are reproduced for the case of a purs proton primary radiation (a), and for that of Fe primaries (b). Regarding the saGOnd case the fraction of surviving Fe nuclei is presented by (c). One notes the expected, and in part well- known, results. Whatever the nature of the primordial particles, GAS primaries reach us only from very moderate distances. Their anisotropy is £ natural consequence of Fig. 2 that fact, and not Effective source distance of necessarily due to particular proton primaries (a), sources of confinement condi- and of Fe primaries (b). tions. More essentially, the source composition i9 not 152 drastically altered in propagation even at the highest energies -unless, of cource, the particles are contained in the source region for a period comparable with the Hubble time, and even then the ensuing strong attenuation of the captured protons enhances the flux of the HPN component. Hence it is concluded that the effective mass of the GAS primaries reflects rather fairly the primordial composition. If, as it seems likely, protons are abundant among them, they must have been present at the sources in a comparable ratio.

References ( l) R. Cowsick and L.W. Wilson, Proc. 13th ICRC, Denver, 1_, 500 (1973) I. Lundgaard Rasmussen and B. Peters, Nature 2581 412 (1975); B. Peters and N.J. Westergaard, preprint 1976 K. Sitte, Nuovo Cimento ^OA, 195 (1975) H. Kasha, R. Kellogg, B. Higgs, L. Leipuner and R. Larsen, Proc. 14th ICRC, Munich, 6., 1868 (1975) A.A. Petrukhin and V.I. Yumatov, Proc. 14th ICRC, Munich, 6, 1937 (1975) A. D. Erlykin, L.K. Ng and A.W. Wolfendale, Proc. 14th ICRC, Munich, j6, 2003 (1975) S. Alessio, M. Dardo and K. Sitte, paper MN 4 L. Bergamasco, C. Castagnoli, M. Dardo, B.D1 Ettorre Piazzoli, G. Mannocchi, P. Picchi, R. Visentin and K. Sitte, Nuovo Cimento 54A, 613 (1976) B. D'Ettorre Piazzoli, G. Mannocchi, P. Picchi, R. Visentin and K. Sitte, papers MN46, 47- J.P. Hochart, R. Maze, G. Milleret, A. Zawadzki, J. Gawin and J. Wdowczyk, Proc. 14th ICRC, Munich, 8., 2822 (1975) W. Tkaczyk, J. Wdowczyk and A. W. Wolfendale, J.Phys. A8, I5I8 (1975) J. Wdowczyk and A.W. Wolfendale, Nature 258, 217 (1975) TIME VARIATION OF SMALL SH<

C. Aguirre, R. Anda, D.. Instituto de Investigacic Universidad Mayor de La Raz - Bolivia/

Theoretical Both • An army of 12 detectors of 1 m2 is being set up at Mt. Chacaltaya in order to study the time variation of. showers in the energy range 1012 lO1** eV.

By this array it is possible e air showers for the study of high energy cosmic ray modulation. The of the detector (5200 m.a.s.l.) makes it an ideal location to stud1 'S of snail sizes.

In this paper a desca?iptio67a(f the array will be made and also the first preliminary data will be T3r//ented.

Coordinates: MG 6.9 (others)

Mailing addrei Prof. Carlos Aguirre B., Director Instituto.de Investigaciones Fisicas Universidad Mayor de San Arrires La Paz, Eolivia. mrnm 154 0

Sidereal Anisotropy of Small Air Showers Observed at Mt. Norikura.

K. Nagashima, S. Sakakibara, K. Fuiimoto, Z. Fujii, H. Ueno and I. Kondo*.

Cosmic Ray Research Laboratory, Nagoya University, Nagoya, Japan. *Cosmic Ray Laboratory, University of Tokyo, Tanashi, Tokyo, Japan.

Abstract Observation of small air showers has been continued from August 1970, using a part of the multidirectional cosmic, ray telescope at Mt, Norikura. Most significant result obtained from this observation was a sidereal diurnal anisotropy of amplitude 0.051 + 0.004 % with maximum at 1.0 + 0.5 h, which showed a persistent trend over six years. Based on the results of the observation together with those obtained by Gombosi et al and Fenton et al., a tentative model of sidereal anisotropics is presented. Summation Dial of Sidereal 1st and 2nd Harmonics

of NORIKURA 3F-AS 1. Observed Results ("0 Ist Harmonic Observatiox of small air showers 03 % were continued from August 1970, uti- It-.' lizing a part of the multidirectional 2nd Harmonic cosmic ray telescope at Mt. Norikura 0" 0.1 % (2770 m, A=36°N, =137.5°E)} This observation was carried out in order to derive information about the anisotropy of primary cosmic ray intensity in the energy region of 1012 - 10llf eV. Most remarkable result obtained from the observation 18"- over six years, was a sidereal diurnal anisotropy having an amplitude of 0.051 + 0.004 % with time of maximum Fig. 1. at 1.0+0.5 h sidereal time. As seen from the summation dial shown in Fig. la, this anisotropy showed a persistent trend over 6 years. A sidereal semi-diurnal anisotropy showing similar persistent trend in the same period as shown in Fig. lb is also obtained. It has an amplitude of 0.026 + 0.004 % and time of maximum at 5.5 + 0.3 h. Two independent results about the sidereal anisotropy in the same energy region were reported. One from air shower observation at Peak Musala 155

by Gombosi et3 al , and another from underground observation at Poatina by Fenton et.al . Together with two other results of 4F air showers and the directional air showers at Mt. Norikura, all the results are consistent with each other as shown in Fig. 2.

2. Compton-Getting Effect and Galactic Loss-Cone Model

The observed

results described in the Sidereal Anisotropy of High Energy Cosmic Rays

previous section strongly tst Harmonic 2nd Harmonic suggest the existence of sidereal anisotropy in 1012 - 101** eV region. 0.04 % Especially the constancy of the sidereal vectors for 3F observation through one half of a solar cycle indicates no A Dir ' 3F 4F influence of solar o Mu modulation on these obser- 6h Fig. 2. vations. Further, the

fact that the observed phase of the anisotropy is ~1 hr. sidereal time suggests that this is not due to the sidereal anisotropy of solar origin which has the eigen phase of 6 or 18 hr. There are two kinds of relative motion of the solar system in the Galaxy which might produce the Compton-Getting effect. One is the proper motion of the solar system relative to the local stars in the direction of 18 hr. right ascension, with speed of ~20 km/sec. Another is the motion of the solar system relative to the intersteller gaseous matter which consti- tutes the spiral arm in the direction of 4.0~4.7 hr. right ascension with speed of 20~30 km/sec. (Fujimoto^, Roberts"*, cf. Table I). Cosmic ray anisotropies produced by these two relative motions are estimated and the observed vectors are corrected for the Compton-Getting effects as shown in Fig. 3 by A and 0 respectively. Since cosmic ray particles are spiralling around the intersteller magnetic field frozen in the gaseous matter, it is more likely that the observer in the solar system observes the Compton-Getting effect due to the second relative motion. Then the true galactic anisotropy has maximum in the direction 23.5 hr. for 3F showers. The fact that the 1st and 2nd 156

Table 1. Direction Magnitude Compton-Getting Effect SLC) M°) 6„(°) a«,(°) n (%) i

Due to the proper motion 44 25 20 17.9 0.031 of solar system (20 km/s)

Due to the relative motion 0.047 150-160 ^ 0 52-43 4.-4.7 of solar system to the -0.031 Orion arm (20-30 km/s)

harmonic vectors are 1st Harmonic 2nd Harmonic different in phase by 0h 6 hours from each other, suggests that they might -Clco»8Clco«8^ M •>_ ^ be produced by the loss- V P 0.04* 6 cone type anisotropy . In order to estimate the I*- / direction of the reference axis and the opening angle of the loss-cone, the following 6" facts are utilized. Fig. 3. As there is only a small difference in the observed diurnal vectors in the northern (Norikura and Musala) and southern (Poatina) hemispheres, the north-south asymmetry (a^) in the 1st harmonics is not so large. Using

the difference between Norikura and Poatina-+2 , a^ is derived as -0.010 while the 2nd space harmonic component a is derived from the average of 12 2nd harmonics at Norikura and Poatina as~0.014 %. The ratio of a^/a^ is used to obtain the declination <5„ of the reference axis by the following relation , a 1 /a 2 = 2' 2 4 * I tanS • tan&0 | ,

where 6 is the declination of average viewing direction of the telescopes.

Then this gives the direction of anisotropy as S0-12° and right ascension «o~0 hr., which corresponds to the galactic latitude of b~-50° and longitude of 8-115°. This direction is not exactly coincides with the general direction of the Orion arm as shown in Fig. 4, but it may represent the true direction of the magnetic line of force in the vicinity of the solar system. 157

COHPTON-GETTING EFFECT SIDEREAL HARMONICS

LST 2ND a-* ~5h i •l.c 0h Orion Arm * Spiral r— Out - In 18 '

Solar System ! I Galactic Center

GALACTIC LOSS-CONE EFFECT

6 9

aj <«*>) o Solar System it

_ ,«.lts". b— H- I Oh , S- 12'

Loss Cone a2,f(S<0' 0

Out 18-

Fig. 4

The half opening angle x °f the loss-cone is estimated from the ratio 2 1 6 8 a^/a^ as ~71° by the following equations ' .

a1 = n P1, (sin 5 ) P^ (sin 8) 'I I Q J2 a2 = n2 (sin 80) P2 (sin 6)

n = -3/4 (sin2 X ) Aj/j„ 7I c n- = -5/4 (sin2 x COS X ) Al/I i c c 0 where P is the semi-normalized associated Legendre function, J is the n 0 averaged directional intensity in interstellar space and AJ is the decrement of the intensity from the direction in the loss cone. These facts suggest that the observed sidereal anisotropy is produced by the diffusion of cosmic ray particles along the galactic magnetic field with some loss mechanisms in the region of the spiral-out direction from the •solar system. 158

3. Discussions The sidereal anisotropies derived from the small air shower experiments at Mt. No'-ikura together with the results from Peak Musala and Poatina, showed the existence of galactic anisotropies. Two possible origins of the observed anisotropies are discussed and the amount and the direction of these anisotropics ' derived. One of them may be due to the motion of the solar s> ;- ar \ to the interstellar gaseous matter, and has an amplitude of -0.019 % ^nd time of maximum in ~4.4 hr. sidereal time at Mt. Norikura. Another source of tbe sidereal variation may be due to the ioss-cone-type anisotropy of the cosmic ray intensity around the galactic magnetic field, the direction of which is estimated as

References 1. Nagashima, K., H. Ueno, K. Fujimoto, Z. Fuiii, S. Sakakibara and I. Kondo; Proc. Int. Cosmic Ray Conf. Munich, 4_, 1503 (1975).

2. Gombosi, T., J. Kota, A.J. Somogyi, A. Varga, B. Betev, L. Katsarski, £. Kavlakov and I. Khirov; Proc. Int. Cosmic Ray Conf. Munich, 2.. 586 (1975). 3. Fenton, A.G. and K.B. Fenton; Proc. Int. Cosmic Ray Conf. Munich, 1482 (1975). Fenton, A.G. and K.B. Fenton; Proc. Int. Cosmic Ray Symposium on High Energy Modulation, 313 (1976) 4. Fujimoto, M; Non Stable Phenomena in Galaxies, IAU Symp. No. 29, Ed. M. Arakeljan (Acad. Sci. Armenia USSR), 453 (1967). 5. Roberts, W.W.; Ap. J. 48, 1 (1969). 6. Fujii, Z.; Rep. Ionos. Space Res. Japan, 25, 242 (1971). 7. Jacklyn, R.M.; Proc. Int. Cosmic Ray Conf. London, 1, 141 (1965). Jacklyn, R.M.; ANARE Scientific Reports, . Series C(ll) Cosmic Rays, Pub. No. 114 (1973). 8. Nagashima, K.; Rep. Ionos. Space Res. Japan, 25, 189 (1971). 9. Somogyij A.J.; • Proc. Int. Cosmic Ray Symposium on High Energy Modulation, 142 (1976). 160 b^S 00-190

YEAR TO YEAR VARIATION OP SIDEREAL ANISOTROPY OF COSMIC RAYS M. Ichinose Department of Physics, Fucalty of Liberal Arts, Shinshu University, Matsumoto, Japan Abstract. Year to year variation of sidereal anisotropy of cosmic rays (ft'1011eV) has been observed for 1948-76, in the data from meson telescopes at underground and sea level and from ion chamber. The phases of sidereal diurnal variation in this energy region showed a drastic change for the year of 1968-69 and 1974-75; the former time of which corresponds to the epoch of the polarity reversal of the sun's polar magnetic field and latter to solar activity minimum. The maximum time of sidereal diurnal variation is nearly in the direction towards midnight after being corrected for anti-sidereal vector which is produced from loss-cone effect of solar origin. This fact may suggest that even in the energy region of~10^eV could be observed the galactic anisotropy of cosmic rays. 1. Introduction. A significant change in phase of sidereal diurnal variation has been reported by Cini-Castagnoli et al.(1975) and Swinson (1976). This significant change in phase occurred in 1968-69, at the time which corresponds to the epoch of the polarity reversal of the sun's polar magnetic field. It has been pointed out by Ichinose et al. (1976) , however, that the sidereal diurnal variation in the northern hemisphere has a remarkable shift in phase, not only at the reversal of the sun's polar magnetic field but also at solar activity minimum. This result may indicate that a remarkable shift in phase of sidereal diurnal variation can not be produced only by corresponding to inversion of the sun's polar magnetic field, but could be attributed to the year to year vari- ability of sidereal diurnal variation due to some physical changes in interplanetary space. This version has also been discussed by Kota (1976) and Swinson (1976). The synthetical interpretation has beer, given by Nagashima et al., (1976), using data in a wide energy range of 1011 - 1014eV. 161

In the present work, year to year change in sidereal diurnal variations has been examined, and also it will be shown that even in the energy region of^l011eV the galactic anisotropy of cosmic rays could be observed. 2. Analysis of data. Observed amplitudes and phases of the first and second harmonics in solar, sidereal and anti-sidereal time at Misato (Mori et al.,1975.1976) are summarized in Table 1. First Harmonics Solar Sidereal Anti-Sideral Year Amplitude Phase Amplitude Phase Amplitude Phase (%) (°) (%) (°) (%) (°) 1974 0.10440.004 191.8 0.013±0.004 251.1 0.03110.004 308.4 1975 0.079±0.003 144.3 0.027+0.003 306.5 0.013+0.003 45.6 1976 0.064+0.003 110.9 0.021+0.003 326.2 0.009+0.003 24.9 Second Harmonics 1974 Ct069+0.004 41.5 0.012±0.004 229.6 0.020±0.004 337.3 1975 0.047±0.003 5.3 0.016±0.003 245.3 0.006±0.003 104.6 1976 0.026*0.003 354.0 0.01110.003 309.8 0.006*0.003 24.1 Table 1. Observed amplitudes and phases of the first and second harmonics of vertical component at Misato. Errors are derived from counting rate.

The averaged vectors over three years are also shown in Fig. 1, not corrected for the deflection in the geomagnetic field. As seen in Table 1, the amplitudes and phases of the solar diurnal and semi-diurnal variations change year to year, and this varia- bility is discribed in the accompanying paper (Mori et al., in this issue). One can notice.in Fig. 1 that the phases of sidereal and anti-sidereal diurnal variations are 18 hour local sidereal time (LST) and about 0 hour anti-sidereal time, respectively. By following the idea advocated by Nagashima (private communication and 1976), we regard Misato (35°N in latitude, median energy 145Gev) and Hobart (40°S in latitude, median energy 175GeV) (Fenton,1976) and also Misato and Mawson (67°S in latitude, median energy 162GeV) (Jacklyn, private communication) as the conjugate pair stations, by neglecting the differences in their latitudes and median energies. The north-south symmetric a} and asymmetric 1 1 sidereal first harmonic can be derived by the observed sidereal 162 diurnal variations for conjugate stations. Fig. 2 shows these a^" and ai for 1974-7S. It was obtained that the phases of l l vectors a^ and a^ are about 2 hour and 19 hour LST, respectively. These results are in good agreement with the results already

reported FIRSbTy HARMONINagashimC SECOHD HARMONIa Ce t al. (1976) . Oh M15AT0-H0BART

MISATO-MAWSON ( WT1-SIDEBEAL) Q^ *

It )

Fig.1. Averaged vectors over Fig . 2 . Harmonics of north-south three years. of meson, telescope symmetric and asymmetric sidereal at Misato,not corrected,for the 1st harmonics a) and a^ derived geomagnetic field;Vertical(V), from two pairs of conjugate* North(N),South(S),East(E).West stations: Misato-Hobart and (W).Errors are derived froia Misato-Mawson. eountin? rate. 4. Discussions. According to the loss-cone model of solar origin (Nagashima et al.,1971,1972), the solar anisotropy re- ponsible for the solar semi-diurnal variation with a phases of 3 hour solar local time produces the sidereal and anti-sidereal variation with same amplitude and with the phase difference in 90°, the former of which is 18 hour LST and latter 0 hour anti- sidereal time in the northern hemisphere. Then, sidereal vector due to solar loss-cone effect can be eliminated from observed sidereal vector by utilizing, the anti-sidereal vector due to solar loss-cone by shifting the anti-sidereal vector counterclockwise by 90°. As seen in Table 1, the phases of anti-sidereal vectors are 0 hour anti-sidereal time, suggesting the observed diurnal vector can be attributed to the loss-cone effect of solar origin. Then, we have made correction of observed sidereal vector for this anti- sidereal vector. The results thus derived year to year are shown in Fig. 3 (a), where SI, C.S and AS denote the observed sidereal 163 vector, the corrected sidereal vector and the observed anti- sidereal vector, respectively. The summation dial of this corrected vector is also shown in Fig. 3 (b) by solid line. Futhermore, comparing the anti-sidereal diurnal vector in Fig. 1 with Fig 2 (c), we found these vectors almost coincide with each other. Similar results to the above were also obtained by using data from the ion chambers at Cheltenham and Christchurch for the period of 1937-58 (Nagashima et al.,1976), "if we take the average over one solar cycle; 1937-47 and 1948-58. . By assuming that this relation may hold for other time-periods, the correction of sidereal diurnal vector has been made, using data from ion chamber at Itabashi and from underground meson telescopes at .Takeyama and Misato._ The summation dials thus corrected are shown in Fig. 3 (b) (dashed line) and in Fig. 4. It is found that the directions of summation vectors are towards midnight. This, result is in good agreement with the results already reported by Sakakibara (1976) 12 14 and Fenton (1976) for higher energy region of 10 - 10 eV. Above fact may suggest that even in the energy region of ^lO^^eV the galactic anisotropy of cosmic rays could be observed. MISATO (34m.w.e.) Year to year variations of the sidereal diurnal variation have been also analyzed, using data from underground meson telescopes at Takeyama (54 m.w.e. in depth) for 1968-75 and at Misato (34 m.w.e. in depth) for 1974-76 and from Nagaya (sea level) IO{ITAHA5HIN CHAMBE) R (TAXCYMUtMESON TEl£SC0PU nLMtJE)

Fxg . 3 . (a);Correction for loss cone effect of solar origin on the observed sidereal vector.Si, C.S and AS denote observed sidereal, corrected sidereal and anti-sidereal, (b);Summation daials of cor- Summation dials of corrected vector,using anti- rected sidereal diurnal vectors sidereal derived from every for anti-sidereal which are aver- year(Solid line) and average age over one solar cycle;1948-58, over three years(Dashed line) 1959-69 and 1970-75. 164

for 1971-7 5, and ion chamber at Itabashi (sea level) for 1948- TIME SERIES OF PHASE OF SIDEREAL IST HARMONIC 75 and Cheltenham (sea level) for 1958-68. Time series of their phases are shown in Fig. 5 without correcting for deflections in the geomagnetic field, together with the sunspot number R and the polarity of the sun. In the figure, the phases are classified conventionally into the morning (0-12h) and the evening (12-24h) Fig.5. Time series of phase of sides. It is clearly seen the sidereal 1st harmonics.Solid circle:Morning side (0-12h), phases change from the evening Open circle:Evening side (12- side to morning side occur in 24h) . 1968-69, and come back to the evening side 1974 afterwards, and no evidence for such drastic change in phase probably happ ms in the period of 1948-68.

4 . Conclusions. By using the data from underground meson telescopes at Takeyama for 1968-75 and Misato for 1974-76 and from Nagoya for 1971-75, and ion chamber at Itabashi for 1948-75 and at Cheltenham for 1958-68, we have analyzed the diurnal variation in sidereal time. From above results and discussions, we can concluded that the phase of sidereal diurnal variation in the energy region of ^vl011eV showed drastic change for the years of 1968-69 and 1974-75, at the former time period which corresponds to the epoch of the polarity reversal of sun's polar magnetic field and the latter period corresponds to solar activity minimum. Even in the region of *vlO eV the galactic anisotropy of cosmic rays could be observed.

Acknowledgements. The author expresses his sincere appreciation to Prof. K. Nagashima for his constant encouregement for the present work, and also indebted to Prof. S. Mori for his stimulating discussions with him. We are grateful to Dr. M. Wada and also all the menberrfor kindly providing valuable data of Takeyama, Nagoya and Hisato stations.. Mawson data were supplied through Antarctic 165

Division, Department of Science, Melbourne,Australia. The calculations were made in part by using a computer at Computer Center of University of Tokyo and the Remorte Station of Shinshu Uni- versity, and some were also performed at Nagoya University Computation Center.

References. Cini-Castagnoli, G., D. Maroch, H. Elliot, R. G. Marsden and T. Thambyahpillai., Proc. 14th Inter. Cosmic Ray Conf., Munich, 4, 1453,1975. Fenton, A. G.,and K. B.Fenton, 2nd Inter. Cosmic Ray Sympo., Tokyo, p313,1976 . Fenton, A. G.,2nd Inter. Cosmic Ray Sympo., Tokyo, p308, 1976. Ichinose, M. and K. Murakami, 2nd Intr. Cosmic Ray Sympo., Tokyo, p291, 1976. Mori, S., S. Yasue, M. Ichinose and S. Akahane, Proc. 14th Inter. Cosmic Ray Conf., Munich,1469, 1975. Mori, S., S. Yasue, M. Ichinose, S. Sagisaka, S. Akahane and K. Chino, 2nd Inter. Cosmic Ray Sympo., Tokyo, p78, 1976. Nagashima, K. and H. Ueno,. Rep. of Ionosphere and Space Res., in Japan,25, 212, 1971. .Nagashima, K., K. Fujimoto, Z. Fujii, H. Ueno and K. Kondo, Rep. of Ionosphere and Space Res., in Japan, 26_, 31, 1972. Nagashima, K. and S. Mori, 2nd Inter. Cosmic Ray Sympo., Tokyo, p326, 1976. Sakakibara, s., K. Fujimoto, Z. Fujii, H. Ueno I. Kondo and K. Nagashima, 2nd Inter, cosmic Ray Sympo.,Tokyo,p316,1976. Swinson, D. B., J. Geophys. Res., 81, 2075, 1976. Swinson, D. B., 2nd Inter. Cosmic Ray Sympo., Tokyo, p291,1976. 166 ^

SOME THOUGHTS ON KUSALA MISOTRC2PY; PITCH ANGIiE DISTRIBUTION OR WHAT /ELSE ?

u . Ko-ta and A.J. Somoflyi Department of Cosmic Rays, Central Research Institute of Physic; Budapest, Hungary/ Theoretical • Experimental Q Both [x]

Based on the first and second harmonics obtained in the Musala experiment and in other galactic anisotropy measurements, an attempt is made to explore the tftree-dimensional structure 12 l1! / of the anisotropy in the 10 -10 ^eV range. /1/ It is investigated whether observations can he recon- ciled with the theoretically favoured assumption of.pitch angle distribution. / /ii/ Assuming that the am.sotropy consists of vector and tensor anisotropics only and, furthermore, the principal axes of the tensor anisotropy point along known, physically reasonable directions, the two kinas of anisotropics can he separated and all their components, except for one component of the vector anisotropy /]|callel to the Earth's axis/, can he reconstructed. The theoretical background of the assumption made, the physical implications of she results obtained and possible origins of the significant second harmonic are discussed.

Coordinates:os /Sidereal Variations of Cosmic Rays/

Mailing address: A.J. aomogyi Department of Cosmic Rays Central Research Institute of Physics H-1525 Budapest P.O.B. 49, Hungary 169

MEASUREMENT OF VARIATIONS OF EAS WIT# FEW NU?T3kH OF PARTICLES

V.V.Alexeyenko, A-Tg.Chn^nTrmY, I.M.^ogai, A.R.Mikhelev, N.S.Miranova Institute for Nuclear Research., ^cademy of Sciences, USSR

Experimental

For EAS registration experiment array is used containing scin- tillatorsof total area 200 m2, .ch is situated at the altitu?- de of 1700 m above sea level. >unting rate of fold coinei- 2 ir second and corresponds to pri- dence 4 x 50 m is 50 pulses resuits of six monthss period mazy energies ev. Preliii of observations are present*

Coordinates* MG 6.5. ition

Mailing addresss Professor A.E.Chudakov, Institute for Nuclear Research at tb* USSR Academy of Scoeaces,

>fsoyusaaya» 7av Moscow ¥-117312, USSR

\ 170 &OWM94 0 INVESTIGATION OF THE SIDEREAL ANISOTRQFY OF HIGH ENERGY MUONS V.V.Borog, V.G.Kirillov-Ugiyumav, H.P.Kokoulin, A.A.Petrukhin, V.V.Shestakov, and Yu.A.Stepanov Moscow Physical Engineering Institute Moscow 115409, USSR

The results of an analysis of muon generated cascade shower arrival directions are presented. Cascade showers with energies more than 0.2 TeV at zenith angles 60° ^ 83° have been, registered by means of an ionization calorimeter. The declination range 32°S to 56°N lias been scanned, The evidence for the possible narrow angle anisotropy near the right ascension oC = 156° and declination 8 = - 6° is found. No global anisotropy is detected.

1. Introduction. Study of sidereal anisotropy of primary cosmic rays can give an information about the galaxy magnetic field structure and the role of local cosmic ray sources. At energies more than TeV primary cosmic ray directions are copied by sea level muon arrival directions, fiecen t investigations - (see Table 1) do not give reliable evidence for the existence 2 of the sidereal anisotropy at muon energies 10 to 10 TeV. The detected anisotropics are not confirmed by the independent experiments. But there are at least two reasons for such descrepancy. firstly, various ranges of declinations S have been scanned in different time periods (see the diagram in £ig3) and the time dependent anisotropy [[6,93 could be not observed in subsequent experiments. Secondly, the studied muon energy Intervals differed in these investigations more than a decade. Thus any pair of measurements have not been made in close conditions. The new data accumulation should be desirable for a more definite conclusion about the existence of arrival directions anisotropies. in this paper the results of a search of sidereal anisotropy of muons with energies more than ** 0.4 TeV are presented. 171

Tablel. Group fief. Energy, TeV Number Bin size ttuons Primaries of events Ao6° 3 Utah (1969) [1] 100 2.5x10 Utah (1971) L2] >0.75 ~ 25 1.2X105 10X10 6 Utah (1976) [71 * 1.1 ~ 7 ~ 10 10x10 4 Manitoba £3] -0.15 - 10 4x30 6 Kiel [4] > 0,002 ~ 10 2x2 5 Kiel-DESX [5] >0.003 0.1-5 6x10 6x6 0 Mont-Blanc [6] > 0.2 ~ 1.5 8x10' 5x5 Present work >0.4 ~ 4 2575 8x <2 -1 DUMAND project [8] Z 2 ** 20 ^lO^ear" 1x1

196B 1970 1972 1974 YEAR

tfig.1. Diagram of reported union arrival directions investigations. Figures in the diagram from 1 to 7 correspond to the reference numbers.

2. Experimental, Mvion generated cascade showers were registered by means of the ionization calorimeter described earlier Qiol . The accuracy of zenith and azimuth angle measurements with the G.« n. counter ho&oscope was 2° and 6° respectively. The arrival time was fixed to about 3 minutes. The data collected during two runs from October 1968 to May 1969 and from September 1970 to May 1971 are analyzed. The total running time exceeds 9x10^ hours. The number of cascade sho- 172 wers with energies E, more than 0.2 TeV in zenith angle interval from 60° to 88° is 2575. The average man energy is 0«4 TeV , which corresponds to primary energies of about 4 TeV. About 90% of the events have a nealy uniform distribution in the declination range -20° £ 5 6 44°. The nonunif oraity of the exposure time during sidereal day does not exceed 10%. Jfuan arrival directions are classified into cells AS x Aol = 2°x3°. Then these cells have been grouped into bins 8°x120, which corresponds to the approximately double measurement error, the total number of bins was 240. The number of muons IX in a bin is compared with the average number per a bin for the given declination band (fit). Four bins with the anomalously high deviations were found} these are listed In the Table 2. Mean numbers of bins F with deviations equal to or more than observed ones were evaluated as Poisson probability S($ n,m) multiplied by 240 (the total number of bins). But this evaluation is not q,uite well, since the data were regrouped to maximize deviations. Table 2. Center Grouping of 2°x3<9 cells into Continuous coordinates 8°x12° bins displacement oC s ft ITl (n-m)/VE? P H n H 156 -10 26 11.0 +4.5 0.02 0.26 28 0.20 156 - 2 0 11.0 -3.3 0.004 0.06 228 +24 23 10.2 +4.0 0.09 1.12 334 +12 1 11.4 -3.1 0.03 0.43

A more appropriate method in the case of a parallel displacement of the rectangular grid was suggested by Hillas £11 ] . The corresponding values of the mean number H of "large" deviations are given in the Table 2. Thus, even about 4b deviation is not significant in our case. Only the bins with the center coordinates («6, S) = (156°,-10°) and (156°,-2°) might be considered as "candidates" for a narrow angle anisotropy. The continuous displacement of the first of these bins gives maximum n = 28 events, which corresponds to the accidental probability«• 0.20 (according to Hillas). 173

3* Discussion. The energy spectrum and the time variation for the (156°,-10°) bin were analyzed. The ratio of the number of muons in this bin to the average one for the corresponding declination baud is plotted in Fig.2 as a function of the cascade shower energy. Fig.2 shows the abnoxmaly high count at energies near 0.4- TeV. The time dependence of the ratio mentioned above is presented in Fig. 3. The number of muons din the anomalous bin exceeds the average value through all the experiment.

n (A£)/m(A£) n(AT)/m (AT)

0 i.2 03 0.5 6, TeV 1968 1969 1970 T.YEAR Fig.2. H.g.3. .

It should be noted that the maximum "negative" deviation (156° ,-2°) lies in the neighbouring band of declination and these anomalies may be interconnected. But we were unable to find any apparatus effect which would not be spread over sidereal time. So| despite the low statistical confidency of these "anisotropies" their mutual location and energy spectrum indicate same anomaly in this part of the .sidereal sky. The ratio of the cosmic ray fluxes from two galaxy hemispheres evaluated using cascade showers with energies more than 0.2 TeV is equal to 0.96 + 0.05 (center/anti-center). The comparison of the cosmic ray intensity from the galaxy plane to the halo flux gives the ratio 0.97 + 0.04. Thus, aiy global anisotropy has not been detected in our experiment, and new investigations are required. Fran this view-point the DU1LABD 174 project [8] is of great interest. Its characteristics are listed in the Table 1 and in the Flg.1. Some possibilities of this project for mnon registration are discussed in the paper [12].

References 1. Porter L.G., Stenerson R.O., J.Pbys., Ag, 374 (1969) 2. Davis K.H., Fall S.M., Ingebretsen R.B., Stenarson R.O., Phys.Rev., D4, 607 (1971) 3. Hicks R.B., Flint R.W., Standil S., Oanad. J.Phys. , 2079 (1971)

4. Uhr R.C., Fahnders E., Koseck K., et al.t Proc. XIV ICCR, Miinchen, 2, 575 (1975) 5. Jokisch H., Carstensen X., Proc. XIV ICCR, Miinchen, 2, 578 (1975) 6. Bazer-Bachi A.R., Vedrenne G., Sheldon W.R., Benbrook J.R., Proc. XIV ICCR, Munchen, 12 , 4151 (1975) 7. Barrowes S.C., Bergeson H.E., Phys.Rev., 554- (1976) 8. Proc. 1976 DUHAND Summer Workshop, Honolulu, Hawaii (1976) 9. Sekido I., Yoshida S., Kamiya Y., Phys .Rev., 11^, 1108 (1959) 10. Borog V.V., Cheroyatin V.K., Kirillov-Ugryumov V.G., et al., Proc. XII ICCR, Hobart, 6, 2428 (1971) 11. Hillas A.M., Proc. XIV ICCR, Munchen, % 3439 (1975) 12* Borog V.V., Kokoulin R.P., Petrukhin A.A. , Shestakov V.V., Yumatov V.I., This conference, MET-76 Mmom 197

COSMIC RAY INTENSITY ANNUAL VARIATIONS FOR THE LAST SEVERAL CENTURIES V. A. Dergachev, G.E.Kocharov, S.Kh.Tleugaliev

,.?. Icffe Physical-Technical Institute, Academy of Sciences of the USSR, 194021, Leningrad, USSR

The problem of differential intensity of cosniic rays in the past is considered, by using the time variation of cosmogenic isotope '4c concentration in the Earth's atmosphere * and solar activity changes for the last several centuries are analysed. The cyclic variations of cosmic ray intensity with duration of 11 and 80 years are revealed. The rate of 14c formation caused by changes of incident cosmic rav fluxes is obtai- • ned usjng the variations of »%! content in the Earth's atmosphere. Spectral analysis of available data on '^C content and solar spot numbers is carried out. The autospectra, functions of coherence and phase difference are obtained.The correlation functions of these values are calculated. On the basis of investigations performed by measuring the 14c concentration in samples of known age it is possible to reestablish the annual variation of cosmic ray intensity for the ~50 000 years.

The problems and possibilities of investigation of the Sun by content determination in annual tree-ring samples are formulated in a number of papers (Konstantinov and Kocharov, 1965, 1967; Kocharov et al,,1974, a, b, c; Dergachev, Sanadze, 1974; Dergachev, Kocharov, 1977 etc,). The concrete experimental data have been obtained already and the availability of ge- netical connection between cyclic activity of the Sun and 14C contents in terrestrial reservoir is shown (Kocharov et al. 1976, a, b, c ; Alexeev et al, 1974; Arslanov et al,, 1977 ; Dergachev et al,, 1977). The connection between the Sun and 14c content in the Earth's atmosphere has two modifications : A, Sun -•solar cosmic rays variation of 14c concentration , B, Sun -*• galactic cosmic ray intensity modulation -*- radiocarbon content variation. The aim of this work is to study the second possibility, namely, to determine the annual variation of cosmic ray intensity by analysis of available experimental data on 14c concentration in annual tree-ring samples during last several hundred years. We use experimental data fulfilled both by us (Kocharov et al,, 1974» a, b; Dergachev and Sanadze, 1974; Ars- lanov et al.. 1977; Dergachev and Povinec, 1977; Alexeev V.B, et al., 1977) and other authors (Cowan et al., 1965; Stuiver, 1969; Lerman et al., 1970; Baxter et al., 1970; Damon et al., 1973). For the purpose of receiving the information about variations of radiocarbon concentration for the most large time-intervals, the experimental data of different authors were incorporated to one unified generalized line, covering the 198 period from 1688 up to 1951 y. (Dergachev et al., 1976 ). The studv of relationship betwfeen solar activity and radiocarbon content may be carried out due to mutual spcctral analysis of weli known series of solar spot numbers W (regular observations of solar ^pots are carried on from 1749, there are indirect evaluations of solar activity variation UD to 648 year B.C. (Schove, 1955)) and. generalized line of data on '^C concentration in the Sarth's atmosphere. ... The generalized line of data on '^C abundance variations for the last 250 y. is shown in fig.1 (with due regard for corrections on Suess effect),

(S^C), ar V ~to 2 - i ii 'iHl 4 ,

I 1 111 I If Hi? 0 ll.i i 1 I 1 TT t j III -I

i l l i 1 i i i i 1 III. 1700 1750 1800

" ^ .''UHIUII/1 'A'xj 11 i ii 11 r

1 1 1 1 i ! 1 1 1 1 1 1 1 1 1820 1850 1900 Years 1950 Fig.1, Generalized line of radiocarbon data.

According to de Vries (1958) atmosphere's reservoir may be imagined like some filter, then the solar activity maybe considered in the input of such system with the concentration in the output. The character of filter transformation may be understood, if some values are to be calculated; a) covariant and mutual covariating functions of solar spot numbers and generali- 199 r.,.d line a C (& C); b) spectra of these data; c) phase *s differs no? si?ectr;.; a) coherence spectra between investigated data ; e ) enhancement function of such system. Calculated spectra point ;C bO and 11 j'ears periodicity at both sets (Dergachev et al., the amplitude of 80-years harmonics, which is the most significant in radiocarbon data being about 3 times larger than 11-vcarrs oscillation for this line. At the same time 11-years periodicity amplitude typical for solar spots W is twice as large as the amplitude for the secular cycle data. Coherence spectrum shows the correlation between two investigated sets at the frequencies, corresponding to secular cycle. But the correlation rate for other frequencies is not Buffici- high, that msty be associated with experimental errors of £ '^C measurements, the influencies of different local factors ...e place of specimen growing and the procedure of integration of short tiire data or in one generalized line (Der- r^hev et al., 1977), The calculation of phase difference spectrum has shown that the shift of phases of A^C ( <5"l4c) relative to ¥/ timber, for 11-year's harmonics is equal to 5+2 years, for 80-year*s - 20+8 years, which is in accordance witE theoretical estimates. It is necessary to pay attention to one peculiarity: phase shift is not constant in time; it is connected with the time of 14c transfer from one part of reservoir to another. This time-interval may have been changed in the past depending on geophysical and cos- iaophysical factors. Such peculiarity on the one hand complicates analysis and on the other hand open3 the possibilities to study 1he character of dynamical peculiarities of terrestrial system in the past. At the whole the character of enhancement function of this system is found to be rather complicated. Specifically,the enhancement of system at the frequencies, according to 11-year cycling is found to be smaller, than at lower frequencies. It confirms that Earth's atmosphere smoothes off the high-frequency oscillations of 14c levels, which may be caused by for example, short- -time cyclic variation of solar activity. Using the experimental data on 14c concentration for the period from 1744 up to 1884 (fig,2a) we consider the possible variations in '4c production's rate in the past. Pig.2a shows too, the approximating curve, calculated from the experimental d 3. * S*C(t) ^(Ci + CLiCQStoit +eisintOit), (1 ) I where C^ - some constant level, with reference to which we consider the oscillations £14c, = 2k/1i - frequency,Coefficients cL, aL, bj, are defined by the method of least squares. The period used Ti = 2x/U)i is defined by choosing the periods from 2 to 100 years, with step of 1 year. A number of optimal harmonics necessary for 0 14c data approximation is defined on the basis of following consideration. If removing the individual harmonic of frequency o){ from the initial row, the quantity

1i< 2 F(u)i) =Z[£ CU*) - Ci - cueosiod -SiSincoU] ( 2 } 1< 200

1750 1780 1810 1840 1870 Years

Pig,2. Time variation of Wolf numbers W , relative abundance of 14C (a), relative production rate of 14c (b). 201

is decreasing. Decreasing of ?(o>i,) with growing i is found to be slower and finally to be practically constant-. Prom these considerations 12 harmonics were revealed. For investigated row the sinusoid with .67 year's period put the most contribuLion and then one with 12 year's period. Its amplitudes, correspondingly, are equal to 0,45lj% and 0,328$. Accepting the 14c/12C concentration ratio to be equal for atmospheric and tree-rings ratios for the same moment it is not difficult to receive the following expression for variation of ^^C rate production:

SQlt)^t-(a'iC05£Oit*6'isin^it*cl)9 ( 3 )

Qc = -~f> al = a; +6iO)jT, b[=bi-aiU)Lt, ( 4 )

where Kc - ^C concentration at the period before A-bomb tests; T - average time of radiocarbon stay in the Earth's atmosphere. As it is clear from (3) the amplitude of 14c rate production CLi')2 •+ (gi)2" depends on the time-interval vjnich may be received on the basis of '4c specific activity distribution in the exchange reservoir. The calculation of this value includes two possibilities: from the equilibrium state and from reservoir change due to burning of fossil fuel or the explosion of atomic installations. (Dergachev and Stupneva, 1975). Here v;e use the value X - 3 years. Calculated dependence o Q, (t) for the time-interval 1744-1884 is represented in fig.2b, where dependence of £P4C and V,'olfs numbers from time are shown, too. As seen from fig.2, the'amplitude of variations Q (t) reaches (10- -12)^, which is confirmed by theoretical estimates (Lingenfelter and Ramaty, 1970; Dorman, 1977). The khow ledge of time-dependence for 14(j production rate gives us the possibility to determine the annual variations of REFERENCEcosmic raSy intensity.

1. Alexeev V.A., Lavrukhina A.K., Milnikova Z.K., 1974, Proc. Y All-Union Conf., "Astrophysical Phenomena and Radiocarbon", (ed.G.E. Kocharov, V.A.Dergachev,Univ. Tbilisi Press,1974), p.39 2. Alexeev V.B., Vasiljev V.A., Dergachev V.A., Nasyrov R.Kh., Sementsov A.A,, 1977. Proc.YI All-Union Conf., "Astrophysical Phenomena and Radiocarbon", Tbilisi, in press. 3. Arslanov Kh.A., Dergachev V.A., Kocharov G.E.. Chernov S.B. , 1977, ibid. 4. Baxter M.S., Parmer J.G., Walton A,, 1973, Earth and Planet, Sci,Lett., 20, 307. 5. Cowan C., Atluri C.R., Libby W.P., 1965, Nature, 206, 861. 6. Damon P.E., Long A. , Wallick E.I., 1973, Earth and Planet, Sci,Lett., 20, 300. 202

7. Dergachev V.A., Sanadze A.A., 1974, Proc.7 All-Union Conf., "Astrophysic&l Phenomena and Radiocarbon" (ed,0,2.Kocharov and V.A.Dergachev. Univ.Tbilisi Press, Tbilisi,1974),p.103 . 8* Dergachev V.A., Stupneva A.V., 1975, Preprint of A.P.Ioffe Physical-Technical Institute, Academy of Sciences, USSR Leningrad, W.431. 9. Dergachev V.A., Tleugaliev S.Kh., Zih.it or chuk Ju.V,, 1 9 7 6, ibid, K.511. 10. Dergachev V.A., Kocharov G.E., 1977, Izv.AII 53SR. ser. fiz. 41, 422.

11. Dergachev V.A. , Povinec P., 1977, ?roc4 YZ All-Unicn Conf., ,lAstr jn'r-ysi ?r:onv?ena end. .

17. Konstantinov B.P.f Kocharov G.E. , 1965, Dokladi AN SSSR, 165, 63. 18. Konstantinov 3*P., Kocharov G.E,. , 1967, Preprint of A.F.Iof- fe Physical-Technical Institute, Academy 01 Sciences, USSR, Leningrad, N.064. 19. Lerman L.C., Hook W.G,, Vogel J.C., 1970, In Radiocarbon Va- riations and Absolute Chronology, New York, p.275. 20. Lingenfelter R.E., Raraaty R,, 1970, ibid, p.513. 21. Schove D.I., 1955, J.Geophys.Res, , 60, 127. 22. Stuiver M. , '1969, Radiocarbon, jH, 545, 23. de Vries H,, 1958, Koninki.Ned. Acad.Wetenschap,, Proc.B.61. 94. THE 10Be PROBLEM REVISITED G.M. Raisbeck and F. Yiou Laboratoire Rene Bernas du C.S.N.S.M., 91406 ORSAY, France.

Propagation calculations are presented using the most recent experimental cross sections available, including new measurements for Be isotope production in Si and Mg targets at 0.6 and 25 GeV, and revised data for production from 0 at 0.6 GeV. It is demonstrated that, contrary to current opinion, the use of 10Be as a cosmic ray chronometer is not seriously restricted at low energies because of solar modulation effects.

1. Introduction Four years ago at this Conference (1), we treated the problem of determining the cosmic ray " age " by means of the *°Be nuclide. We concluded at that time that the available nuclear cross section data did not justify the then prevailing opinion that the Be/B ratio showed that " most of the Be survived "(2a), thus indicating a mean propagation density of ^ 1 atom/cm^. While severely criticized in some quarters (2b), that cautionary note appears, in retrospect, to have been justified.

Since that time significant progress has been made toward the goal of having complete isotopic separation of the Be isotopes (3,4,5). At the same time there has been an increasing tendency to feel that, at low energies (where all the isotopic measurements have thus far been concentrated), uncertainties associated yith solar modulation might seriously limit any information that the l^Be abundance could reveal.

The objectives of the present paper are twofold, (a) To give results of our latest propagation calculations on the expected distribution of Be isotopes, including effects of some new cross section measurements, (b) To show that uncertainties in the " age " determination introduced by solar modulation effects can be significantly reduced by using the 10Be/5 Be ratio as the relevant parameter.

2. Cross sections As we pointed out in a recent review (6), experimental cross section information on Be production is now rather extensive, at least for those progenitors most important to the cosmic ray question. It was also noted in ref.6 that, while the recent Berkeley heavy ion experiments (7) had confirmed most of the earlier Orsay high energy measurements on ^C and ^O, there was a serious discrepancy regarding *®Be production from oxygen. It was felt important to find out whether this represented an error in one of the measurements, or an energy effect (the two results being at 600 and 2000 MeV respectively). An experiment was therefore carried out to remeasure by mass spectrometry this cross section at 600 MeV (8). The experimental technique was basically the same as described earlier (9), except improvements in accelerator technology during the past ten years permitted a significantly larger quantity of product nuclei to be formed in the H2O target, and thus available for analysis. The results, shown in Table 1, are now in good agreement with the higher energy Berkeley results, and it seems likely that they also represent the asymptotic high energy values. At lower energies an important question remains as to whether the sharp decrease implied by the earlier Orsay measurement at 135 MeV 204 is real or not (the 135 MeV result, being based on a larger quantity of product nuclei, is less likely to be in error than the previous high energy results). After the " M " group of elements, and the next most important progenitors for Be production are the group Ne, Mg and Si. We have previously reported 7Be and 1®Be cross sections from Mg and Si, using radioactivity techniques (10). However, as we try to show below, it is the Be/ 3e ratio which is most useful to the " age " question. We have therefore made mass spectrometric measurements of the Be produc'ed in Mg and Si by 600 MeV and 25 GeV protons (11). The experimental technique for separating the Be was the thermochromatographic procedure used earlier for Fe target measurements, as described by Perron (12) . For Mg it was found necessary to pre-oxidize the irradiated target before separation. Preliminary results are shown in Tabls: 1. For Mg at 25 GeV we have only a single measurement and therefore prefer to quote only a ^Be/7Be ratio (the ^Be being suceptible to possible contamination and/or interference by 27A1). The luBe cross sections at 600 MeV are in good agreement with our previous isotope separator results. Along with the results summarized in refs(6), there are thus now experimental results which allow a reasonably reliable estimate of the ^Be/^Be production ratio in targets over the entire range of interest to the cosmic ray ptoblem.

3. Propagation calculations Our propagation calculations have been carried out using an improved version (13) of the computer code developed by Comstock (14). As " standard " parameters we used a 5 g/cm^ (H equivalent) exponential path length and power law source spectra in total energy, (although the relative abundance of Be isotopes produced are not at all sensitive to these choices). Source abundances were taken from Shapiro et al. (15) . In addition to those noted above, the experimental cross section information used has been summarized in refs(6). For those reactions where no experimental data exist, we have used predictions based on the semi-empirical formulae of Silberberg and Tsao (16), or our own interpretation of nuclear systematics. We have also included a-induced reactions in these calculations, assuming a 10 % abundance of He in the interstellar medium (thus the 5 g/cra^ H equivalent cited above, represents actually 6.5 g/cm^). While, in the energy range of interest, there are still very few experimental a induced cross sections for reactions directly applicable to the cosmic ray problem, our results on radioactive products (17) has enabled us to make estimates of the trends of the a cross sections compared to the corresponding proton ones.

The results are shown in Fig. 1. These results do not differ appreciably from those given in refs(6), nor even from the values calculated in a much cruder fashion in refs(l) . In fact, we are now at the point where we can forsee no new nuclear information that will modify the results in Fig. 1 to any significant degree. (Unlike the Be/B ratio, even a 20 % change in these calculated abundances would not dramatically alter any conclusions based on their application to the ^Be " age " question).

4. Effects of solar modulation

In parallel with the improved prospects for having reliable isotopic" measurements of the Be isotopes, there has been an increasing scepticism on the possibility of interpreting any low energy data, because of modulation effects (4, 5, 18). One reason for this uneasiness is evident in Fig. 1, where it can be seen that the calculated Be isotope abundances vary considerably in the region of a few hundred MeV/n, which is just the region where present 205

isotopic measurements have been reported. This would seem to indicate that *»any interpretation of the fraction of 10Be surviving will be very sensitive to the solar modulation model adopted. However, most of this uncertainty can be avoided by choosing 10Be/9Be as the appropriate parameter to calculate the survival fraction. 10 9 To demonstrate this we show in Fig. 2 (a) the ratio Be/ Be both without any solar modulation and with modulation corresponding to a solar maximum, as calculated in a manner described earlier (19) using the model and parameters of Urch and Gleeson (20) for 1970. The two curves, which probably represent the extremes that can be expected, are seen to never vary at any energy by more than ^ 30 %. This is in strong contrast to similar curves, for the two other parameters ^Be/C and ^Be/Be which have been most often used to evaluate ^Be survival* (3, 4, 5). These are plotted in Fig. 2 (b) and (c), and are seen to involve differences of a factor of 2 to 3 between modulation and no modulation at 100 MeV/n.

Thus, from the nuclear physics point of view, at least, the use of the iOse/^Be ratio can avoid most of the difficulties associated with variable cross sections. There remains, of course, the effect of the uncertainty in the velocity of the ^Be giving rise to a corresponding uncertainty in the " age " deduced from the amount of decay.

Conclusions The nuclear data, including cross sections reported here, are now at a stage where fairly firm predictions can be made on the expected distribution of cosmic ray Be isotopes. By using the ratio ^Be/^Be, uncertainties associated with the variation of cross sections in the low energy region can be largely avoided, and thus difficulties due to solar modulation effects minimized. The final resolution of the ^Be problem now would seem to reside in the hands of the cosmic ray observer.

TABLE 1 Cross sections for the production of Be isotopes in targets of 0, Si and Mg bombarded by high energy protons.

10„ 7 9 10 Target Energy a !0TB,e a Be a Be a ~Be a Be (GeV) 9 (mb) (mb) (mb) 0 Be a 7Be

0 0.6 0 .40+ .04 0. 20+.03 9.5+1.1 4.85+.73 1.94+.36 Si 0.6 0 .33+ .03 0. 16+.03 5.3+1.2+ 2.49+.62 0.82+.15 23 0 .43+ .04 0. 19+.04 10.7+0.9+ 4.72+.81 2.03+.44 Mg 0.6 0 .33+ .03 0. 20+.04 6.5+1.5+ 3.95+.*99 1.27+.33 23 0. 24+.05 9.9+0.9+ 2.38+.53 — —

+ taken from ref.(6) 206

E(GeV/n)

Figure 1 - Calculated abundance of Be isotopes in cosmic rays relative to C (assuming complete survival of ^Be and *®Be) using parameters described in text.

100 1000 E (MeV/n)

Figure 2 - Calculated Be abundance (assuming complete survival) relative to (a) 9Be, (b) Be, (c) C. Solid line is for interstellar ratio and dashed line is an example of the possible effect of solar modulation calculated using parameters of Urch and Gleeson (20) for 1970. 207

References 1 ttl I - G.M. Raisbeck and F. Yiou, 13 Int. Cosmic Ray Conf., Denver (1973),

vol. 1, p. 494. th 2a- F.W. O'Dell, M.M. Shapiro, R. Silberberg and C.H. Tsao, 13 Int. Cosmic Ray Conf., Denver (1973), vol. 1, p. 490. 2b- M.M. Shapiro, 13th int. Cosmic Ray Conf., Denver (1973) Rapporteur talk (unpublished). 3 - M. Garcia-Munoz, G.M. Mason and J. Simpson, Ap.J., 201 L, 145 and 201, L141. 4 - W.R. Webber, J.A. Lezniak, J.C. Kish and G.A. Simpson, preprint (1977) . 5 - F.A. Hagen, A.J. Fisher and J.F. Ormes, Ap.J., 212, 262 (1977). 6 - G.M. Raisbeck and F. Yiou in " Spallation Nuclear Reactions and their Applications " ed. by B.S.P. Shen and M. Merker, D. Reidel, Dordrecht, Holland (1976). 7 - P.J. Lindstrom, D.E. Greiner, H.H..Heckman, B. Cork and F.S. Bieser, Lawrence Berkeley Laboratory report LBL-3650 (1975) (unpublished). 8 - S. Salaiin and G.M. Raisbeck (to be published). 9 - F. Yiou, Ann. Phys. (Paris) 169 (1968). 10 - G.M. Raisbeck and F. Yiou, Phys. Rev. C, 1385 (1974). II - G.M. Raisbeck, J. Lestringuez and F. Yiou, (to be published). 12 - C. Perron, Phys. Rev. C, 14, 1108 (1976). 13 - G- Corostock, G.M. Raisbeck and F. Yiou (unpublished work). 14 - G. Comstock, Ap.J., 155, 619 (1969).

15 - M.M. Shapiro, R. Silberberg and C.H. Tsao, 14 Int. Cosmic Ray Conf.r Munich, (1975) vol. 2, p. 532. 1-. - R. Silberberg and C.K. Tsao, Ap. J., supp. 220, 25, 315 (1973). i? - G F. .M. Raisbeck and Yiou, 14th Int. Cosmic Ray Conf., Munich (1975), vol. 2, p. 502 and (to be published) . 1£ - J.P. Meyer, 14th Int. Cosmic Ray Conf., Munich (1975) Rapporteur paper vol. 11, p. 3698. 19 - G.M. Raisbeck, G. Comstock, C. Perron and F. Yiou, 14 Int. Cosmic Ray Conf., Munich (1975) vol. 3, p. 937. J2j0 - I.H. Urch and L.J. Gleeson, Astrophys. and Space Sci., 17, 426 (1972). In a preprint (M. Garcia-Munoz, G.M. Mason and J.A. Simpson - preprint Match 1377) received after this paper was first drafted, the i®Be/9Be ratio has been more explicitely emphasized by the Chicago group. Similar conclusions regarding the relative insensitivity of the decay interpretation to modulation effects have also been reached. 208

LIFETIMES OF COSMIC RAYS IN THE ENERGY RANGE 5-50 Gev/n

frangoise LE GUET Observatoire de Nice, BP 252, 06007 NICE Cedex, France

II N.(E,r,z) r dr dz

ABSTRACT The lifetimes of cosmic rays, are calculated for different types of II S^(E,r,z) r dr dz nuclei in the energy range 5-50 Gev/n. Use is made of a galactic non-hoitiogeneous diffusive model in which the source composition is energy independent and the decrease of the ratio L/M with energy is a/propagational effect. We find that primary heavy nuclei have a shorter lifetime than light ones and that their lifetime energy dependence is flatter. We deduce also an age or time of escape from the galaxy of the cosmic rays. We give the energy dependence of this age and we show that, at a given energy, the age can depend on the Wpe of nuclei considered and on the distribution of the primary qtid secondary sources of cosmic rays in the galaxy.

I. INTRODUCTION

The problem of the determination/of the age of CR has not yet been solved. While Ginzburg and Ptuskin (197yb) think that CR are confined within a large / 8 halo and have a lifetime of -J \0 years, Garcia-Munoz et al. (1975) deduce a "clock" lifetime of = 2*1(Y years from Be1^ satellite measurements and Hagen et al. (1977) obtain ^fti "age" of 5(+6,-3) xlO6 years from Be10 balloon measurements. With the propagation models currently used (exponential distribution of the escape length), the determination of the age x of CR from Be'^ measurements

depends very much on tlye mean escape length Xg deduced from the relative abundances of the light secondary nuclei Li, Be and B because (i) T ^ and (ii) n , the meai/y density of the interstellar gas traversed by CR > is

proportional to (I+ l/ABe10) , ABe10 being the path length against nuclear destruction (see Hagen et al. (1977) for example). Since is probably energy dependent down to a few hundred Mev/n (Webber et al. 1973), it is/therefore important, when evaluating and comparing different estimations of the CR age, to take into account the energies at which the X / 10 e determinations and the Be measurements have been made. In what follm/s we shall use a non-homogeneous energy dependent propagation model in oraer to evaluate the importance of this energy dependence upon the CR age. At the same time we shall show by means of a simple example how geometrical effects^which are ignored in homogeneous models (e.g. spatial STABILITY OF HORIZONTAL EQUILIBRIA

OF THE GALACTIC GASEOUS DISK

M. Lachieee - Rey1, E. Asseo2'3, C.J. Cesarsky1and R. Pellat3

1. Service Electronique Physique, CEN Saclay (France) 2. Observatoire de Meudon, Meudon (France) 3. Centre de Physique Theorique, Ecole Polytechnique, Palaiseau (France)

We give a stability criterium for horizontal equilibria of the interstellar gas - magnetic field - cosmic ray system, applicable when the ratio of gas to magnetic fiel'd and cosmic ray pressure varies with height. Using this criterium, we show that the equilibria considered by Badhwar and Stephens (1977) are all unstable in times 10® years.

1. Introduction - In a series of clasical papers, Parker (1966, 1S69) has considered the problem of the equilibrium of the diffuse part of the galactic disk, consisting of three components (gas, magnetic field and cosmic rays), held together by the gravitational attraction of the stars. The equilibrium equation becomes particularly simple when the lines of force of the magnetic field are assumed to be parallel to the galactic plane. Parker has solved this equation.for the case where the pressures of the gas, of the magnetic field and of the cosmic rays vary with height z above the galactic plane in the same way, and studied the stability of the resulting static equilibrium. He found that such a system is unstable, if the adiabatic index y of the gas is larger than some critical value yc- For values of the intervening parameters that he considers appropriate for the solar neighborhood, Yc ^ 2.5, while he estimates that y Thus, he concludes that the instability must have occured, i/ith a grov/tli rate of ~ (107 years)-1.

In an accompanying paper (Asseo et al 1977) we have applied the energy principle formalism of Bernstein et al (1958) to two-dimensional equilibria of the interstellar medium; in the present paper, we give the equivalent results for the case when the magnetic field is everywhere parallel to the galactic plane. We show that it is possible to write a 1,local" stability criterium (involving only one flux tube) and we find a lower limit to the growth rate of the instability. Several authors have noted (Baldwin 1967; Falgarone and Lequeux 1973), that the disk of galactic synchrotron emission appears to be wider than that of interstellar clouds. Badhwar and Stephens (1977) propose a new class of horizontal equilibria, which are meant to represent the present state of the interstellar medium. In their models the pro- portionality between the gas and the magnetic field pressures is not maintained ; some of these models are in good agreement with the radio continuum observations. Applying the results of section 2 to these equilibria, we find that they are all unstable at some height above the plane even if the adiabatic index of the gas is as high as 4, at least if the cosmic ray gas is of high mobility as considered by Parker (1969). 220

2. Energy principle and horizontal equilibria a) Stability criterium Let us consider one dimensional equilibria of the interstellar gas, magnetic fields and cosmic raysi-e. satisfying the relation

v F * * sir ; - "-^fr (i) where #(z) is the gravitational potential, p(z) is the gas pressure and p(z) the gas density, P(z) the cosmic ray pressure, B(z) the magnetic field strength; B istaken along the y axis, the z axis is perpendicular to the galactic plane. We define Q(z) = = total pressure. The thermal gas and the cosmic-ray gas are both assumed to obey polytro- pic equations of state : . -v* j, * ^ f < (2) Parker (1966) considers that, for the interstellar medium, y = l, while Zweibel and Kulsrud (1975) argue that it can be as high as 2. Parker (1966) and Zweibel and Kulsrud (1975) assume that r=0, corresponding to cosmic rays which circulate very rapidly along the lines of force of the magnetic field. If instead the cosmic ray gas were slow, F would be higher, with a maximum value of 4/3. Using the energy principle, we can show that systems satisfying (l) are unstable at a height z above the galactic plane if :

Y ^ y,^ - QcOf(» > _ r I&l (3) t < fcW - f'«> y) where ' denote derivatives with respect to z. As could be expected, high values of T render the system more stable (Zweibel and Kulsrud 1975). b) Growth rateof the instability As we have not, in general, found the eigen modes of our system, we cannot calculate exactly the growth rates. Nevertheless, we can find a lower bound to the growth rate (Laval et al 1965)

M J4»V VY ( 4 ) where is the change in potential energy brought about by a perturbation The most unstable perturbations have a very small dimension in the x direction, and we only consider those. Then, we find that the maximum value of u)2 at a freight z is given by

m,x f L vt> + rp J ( 5 ) where &Q'1 , CT OV (yp+rP)5- + (mm ~ ? 221

The wavelength of the most unstable perturbation along the magnetic field is given by : ^

5. Stability of the equilibria of Badhwar and Stephens (1977) - Badhwar and Stephens (1977) have solved the horizontal equilibrium equation (l) for a gas distribution given a-priori and assuming that the cosmic ray and the magnetic field pressures are everywhere equal to each other. They use Schmidt's (1965) model to derive the gravitational potential and consider several different distributions of gas. They present four models* Model I is based on the gas distribution of Schmidt (1957) and assumes identical distributions for the clouds and the intercloud medium. Model II has a very similar profile, but it assumes that the clouds have a smaller scale height than the intercloud medium. Models III and IV include a halo component for the gas, represented by a simple exponential distribution. In model IV, only the intercloud medium and the halo gas are supposed to be coupled to the magnetic field. Models III and IV give reasonable fits to the observed profiles of synchrotron emission. The one dimensional dispersion of the clouds is taken to be 6,4 km/sec; that of + intercloud medium and the halo gas, 9 km/sec. To study the stability of the system on scales much larger than cloud sizes, we regard the interstellar gas as having only one component of density ^ ~ 'cloud + ''intercloud and pressure

= - fcW^M-j^M^H*^ We have applied the results of section 2 to these equilibria. We find that, when r=0, all these equilibria are unstable at least at some height z < 600 pc if y < 4. The inverse T=ui~lof the maximum growth rate of the instability (formula 3) is represented in figure 1; for equilibria I to IV, and for (Y = l, T = 0) , (y = 2, T = 0) and (y = l, r = 4/3 ). We see that the system can only be stabilized if T>0; for instance, cases = 1 r 4 ca III and IV are stable if Y » = /3; se III is stable if y = 2, I>0,5> In^regions of instability, the system evolves in times of ~ severals 10 years. If the cosmic rays can distribute themselves along the field lines in times much shorter than 107 years, the equilibria of Badhwar and Stephens cannot represent the present state of the interstellar medium. 222

Model I

Model II

Model III

z (re)

Model IV 1 Fig. 1. Growthrate of the instability (T = ) for the four "M equilibria of Badhwar and Stephens (1977), as a function of height above the galactic disk. 223

REFERE NCES

Asseo, E., Cesarsky, C.J., Lachieze-Rey,M.and Pellat R. 1977 This Conference.

Badhwar, G.D. and Stephens, S.A., 1977, ApJ212, 494.

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PARKER INSTABILITY AND COSMIC

RAY ESCAPE FROM THE GALACTIC DISK

13 2 A 2 3 E. Asseo ' , C.J. Cesarsky , M. Laclyieze-Rey and R. Pellat

1. Observatoire de Meudon, Meudon (France) 2. Service Electronique Physique, CEN/Saclay (France) 3. Centre de Physique Theorique, Ecol/e Polytechnique, Palaiseau (France)

We have derived an energy principle for studying the stability of two-dimensional equilibria' of a system of gas, magnetic field and cosmic rays, in t/he galactic gravitational field. We give simple stability criteria for the conditions considered by Parker, a gas of yadiabatic index y =»1 and cosmic rays of adiabatic index TM 0 ; in these criteria, the effects of the curvature of the field lines is apparent- We discuss possible final equilibrium states for the Parker instability, and its rarte of growth when starting from a curved equilibrium. /

1. Introduction - Following Bernstein et al (1958), we have derived an energy principle for studying the stability of two- dimensional equilibria of a system of gas, magnetic field and cosmic rays, in the galactic gravitational fieldr. The stability criteria obtained are given in section 2; these criteria permit, in a very simple way, to reach definite conclusions regarding the type of curved equilibria considered by Mouschovias (1974). JThe growth rate of the Parker instability for the case of horizontal stratified equilibria, is at most of the order of the inverse of the fre^ fall time, ~ (lO'' years); the mean age of galactic cosmic rays in the solar neighborhood is also ~ 10? years (Garcia Munoz et al 1977, Webber et al 1977).In section 3, we show that unstable modes of two - dimensional equilibria with curved field lines can grow in times which are shorter than the free fall time. Thus, cosmic rays can inflate a bubble at th/e border of the galactic disk in times shorter than their escape time; ihis mechanism is capable of letting cosmic rays out of the disk, and the mean age merely represents the diffusion time between inflating bubbles.

2. An enfergy principle for the interstellar medium - The stability of hydromagnfetic systems which are too complicated to be studied by the normal modefe technique, can be tested instead using a variational method , based ofi an energy principle. One tries to find the perturbation g that minimizes the potential energy of the system; if the change 6W(|) of the pot eiycial energy is negative, the system is unstable. In fact, it is often /ossible to prove that a system is unstable without completely mini- mizing 6W(§), as we shall see. Bernstein et al (1958) developed a particularly elegant method for applying the energy principle to hydromagnetic systems. Let us choose coordinate axes such that the z axis is perpen- d&cv1ar to the galactic plane, and the galactic field lines are in the -plane yz. We supposed that : a) the adiabatic index of the gas is y b) the cosmic ray gas, which does not feel the gravity, behaves like a gas of adiabatic index f; (we return to this point later). 6^9004#5 229

THE TWO-TIER MODEL OF COSMIC-RAY , ESCAPE FROM THE GALAXY

M. M. Shapiro and R. Silberberg

Laboratory for Cosmic Ray Physics Naval Research Laboratory Washington, D. C. 20375

Various models of cosmic-ray confinement -are explored. A model is proposed that is intermediate between the "closed galactic halo" model of Peters and Westergaard (P-w) and the canonical "leaky box"= But unlike P-W, the inner confinement volume is larger, including low-density regions adjacent to the spiral arms. This allows for decay of more than half of the 10Be at E ^ 500 MeV/u and survival of most of it at « 5 GeV/u. It is shown that the P-W model, too, can be consistent with present data on l0Be and the e" spectrum. However, estimates of the confinement time inferred from the latter data can be ambiguous unless the 26A1 abundance, and e+ spectrum above 50 GeV, are measured. The second-tier confinement volume (the halo) is assumed to have a slow leak, rather than the steady state composition of P-W. While present experimental data (p,+/|j," ratio at 1 TeV and anisotropy near 10s TeV) are not conclusive, the slow leak appears favored. Methods are proposed to discriminate among several possible models of cosmic-ray confinement, and of extra-galactic origin.

1. Introduction. Two models of cosmic-ray confinement have been under consideration for about two decades; the galactic disk vs. the halo, acting as leaky boxes. Both models in their basic forms have difficulties.

With the disk model, one has to contrive ways to reduce the l0Be/7Be ratio, in order to fit the low-energy (^0 to 120 MeV/u) value of ~ 0.07 measured by Garcia-Munoz et al. (1975a). The steepening of the electron spectrum above 50 GeV, reported by Prince et al., (1977) has been interpreted to imply a high rate of synchrotron or inverse-compton energy losses, hence a confinement time of 6 to 10 million years, or, if an energy-dependent confinement time T = E~°'3 is assumed, then the time could extend even to « 10s years. Assuming an energy (or rigidity) dependent leakage rate, the confinement time near 1014 eV would be only ~ 105 years, and this seems inconsistent with the high degree of isotropy. Nagashima et al. (1975) report an upper limit of 5 x 10"4 to the first harmonic anisotropy at 5 x 1013 eV.

The halo model, on the other hand, has the problem of explaining the distribution of cosmic rays derived from 7-ray studies' (Fichtel et al. 1975, Stecker et al. 197^). These imply a larger concentration of cosmic rays in spiral arms and in the 5 Kpc ring in which much of the molecular hydrogen is concentrated. Furthermore, the substantial survival of 10Be at high energies near h GeV/u, i.e. for a time dilation factor y « 5 (o'Dell et al. 1975), presents a problem for a halo model with free particle exchange between the disk and halo. 230

If cosmic rays are injected at supernovae during the first year(s), particles suffer adiabatic energy losses bv a factor of ~ 103 (Cowsik and Wilson, (1975), Kulsrud and Zweibel, (1975). This imposes intolerable constraints on the energy input requirements of cosmic rays.

To overcome these problems, Peters and Westergaard (1975) proposed a closed galaxy model with an inner confinement region consisting of the spiral arms, and rigidity-dependent leakage of particles into the halo.

2. The "closed galaxy" model; advantages, problems and possible resolution of problems, (a) Confinement in spiral arms; flaw in low-energy ±uBe test of density of confinement volume; 26Al as test. The energy input requirements of the cosmic-ray sources are relieved considerably by a reduction of confinement volume from the disk to the spiral arms. But a problem is presented by the small ratio of 1QBe/7Be, < 0.07, (though Hagen et al. (1977) have reported 0.23 ± 0.08) observed by Garcia-Munoz et al. (1975), who interpreted the data as implying a density of ~ 0.2 atom/cm3 in the confinement volume. One way to overcome this problem is to postulate a more extensive confinement volume for cosmic rays, of "exo-arms" that include low-density regions adjacent to the spiral arms. But this approach cannot be carried too far—or the exo-arms merge and become the exo-disk of Stecker (1976). This expansion of the confinement volume would greatly reduce the relief of the energy input requirements provided by the spiral-arm confinement'model. Instead of a reduction by more than an order of magnitude, the change would become considerably smaller. However, the energy input requirements can be relieved by acceleration of cosmic rays later on (~ 100 years in the history of the supernova), as proposed by Scott and Chevalier (1975). Particles then suffer adiabatic energy losr by a factor of only ~ 10, instead of by 102 to 103 as in the case of cosmic-ray production at a young supernova). Furthermore, the increase in the estimated frequency (l in ~ 13 years according to Tammann, 1976 when corrected for obscured regions) also helps. Hence we consider the "exo-arm" inner confinement tier acceptable.

However, there is also a way to circumvent the estimated low density of 0.2 atom/cm3 of the confinement volume. (The introduction of an equilibrium distribution of path lengths at low energy would not help, since ionization losses suppress the increased contribution at longer path lengths.) But the following two assumptions would help: (a) relatively little adiabatic deceleration in the solar system, and (b) a modest amount of Fermi acceleration in interstellar space that approximately cancels the ionization energy losses of beryllium nuclei. In this case the spallation cross sections at < 150 MeV/u would be representative. The ratio

a (12C _ ioR ) —:— ^^ = 0.09 ± 0.02 at 150 MeV, a (12C - 7Be)

which is one-fourth of the value at E > 2 GeV, (Yiou et al. 1975). The observation of the Chicago group could thus be due to cross sections rather than a long confinement time in a low-density region. A test for this possibility is to measure the abundance ratio 26Al/27Al at energies near 100 tfeV/u. if the confinement time is relatively short, some 26A1 would survive; furthermore, the relative yield of 26A1 from 27A1 or from 28Si should be larger at low energy, quite tinlike the production of l0Be. Hence if the low 10Be abundance at low energies is to be attributed to energy dependence of cross sections, a measurement of the abundance of 26A1 provides a suitable test. 231

(b) Halo as a second containment volume. The principal feature of the p-W model is an outer containment volume—the galactic halo. This hypothesis is independent of the spiral-arm confinement hypothesis, which could be re- placed by leaky exo-arms or an exo-disk, if necessary. The principal virtue of this model is its ability to explain the degree of isotropy observed at high energies: the first harmonic siderial anisotropy i 5 x 10"4 at 5 x 1013 eV. An exo-arm or exo-disk model could still explain the isotropy if one assumes that the path length traversed by cosmic rays does not decrease between ~ 1011 and 1015 eV, but stays x w 1 or 2 g/cm2. In the P-W model, on the other hand, the "equilibrium halo component" takes over beyond 1012 eV (due to rapid escape of the spiral arm component), and the path length x starts to increase with increasing energy. In "the two-tier model proposed hersj such an increase is also expected.

A test between the above models is provided by a measurement of secondary-to-primary ratio, e.g., of the L/M nuclei: Does the value remain at < 0.1, or does it start to increase again beyond 1012 eV? Long exposures with transition radiation detectors, or identification of the primaries of high-energy cosmic-ray jet interactions provide possible tests.

(c) Energy dependence of leakage rate from spiral arms (or exo-arms). The P-W model predicts a large rigidity dependence of the confinement time in the arms (T R~°*5). The recent measurement- of the electron spectrum by Prince et al. (1977), using transition radiation detectors; shows the- effects of steepening above 50 GeV, presumably due to synchrotron losses or inverse compton losses. A confinement time of ~ 8 x 106 years near energies of 100 GeV was deduced. Coupling this with the R~° "5 dependence of P-W would yield T pa 8 x 10 y years near 1 GeV, quite out of line with the spiral arm model. However, the steepening of the electron spectrum could be due to intense photon fluxes or magnetic fields in the cosmic-ray source regions, and may be quite unrelated to the galactic confinement time.

A measurement of the positron spectrum (i.e. secondaries produced in interstellar space) above 50 GeV would provide a crucial test for the spiral arm confinement model of P-W.

(d) Current data on the positron spectrum. Measurements by Buffington et al^ (1975)have extended our knowledge of the positron spectrum to 30 GeV. An analysis by Giler et al. (1977) implies that the path length x is 2.8 ± 0.8 gm/cm2, from 1 to 30 GeV, quite independent of energy. They suggest that the energy dependence of ratios of secondary to primary nuclei is due to a rigidity dependent confinement of nuclei in source regions, below energies of, say, ~ 50 Gev/u. If this interpretation is correct, the rigidity dependence of the rate of escape from (or of the confinement time in) spiral arms in the P-W model should be reduced from ~ R~°" 5 to about R~°'2 for our two- tier model. The interpretation of Giler et al. (1977) would also imply that about l/2 of the 7-ray flux from the galactic disk comes from localized sources; if acceleration occurs over ~ 103 years, and the rate of supernovae is 1/13 years, there should be of the order of 70 such 7-ray point sources in the galaxy. Could present 7-ray telescopes test this hypothesis of source confinement?

(e) Origin and confinement of high-energy (E > 1013 ev) cosmic rays; tests. The qualitative diagram below shows the basic feature of the cosmic- ray energy spectrum; a power law of E-2-y between IO10 and 1013 eV, of E"3'° 232 between 1015 and 1019 eV, and a possible "shoulder" between 1013 and 15 eV.

In the previous sections we saw that in region A of the diagram, the "local" cosmic rays are confined to an exo-disk, or spiral arms, and described tests to discriminate between these. For region B (including the possible shoulder), we shall consider three alternative possibilities: (1) steady state equilibrium halo confinement- (P-W model), (2) the exo-disk model (s) where "S" stands for Stecker and (3) extragalactic origin CB-B), 1 1— Brecher and Burbidge (1972). In 1013 1015 addition, a modification of the Energy (eV) P-W model, with a slow leak from the halo, (possibly rigidity dependent) is denoted by TT for "two-tier". A set of tests for the various models is prescribed in Table 1.

Table I. Procedures for testing cosmic-ray confinement models at E s 1013 eV

Model L/M at H-VM-" a"t Anisotrqpy at Anisotrqpy at 10 TeV/u 1 TeV 100 TeV 105 TeV

P-W ) high low low \ > 0.2 TT J normal low appreciable

S \ nonnal moderate appreciable \ < 0.1 B-B J •> low low

The \i /n ratio at 1 TeV becomes high for the P-W model because in the steady state component, protons dominate, yielding a large M>+ abundance. Fig. 1 shows the ratio N /(N + N ) n p . n

Ratio of Neutrons to Nucleons, calculated from the P-W mo'del as Closed Galaxy Model a function of energy. Here Nn is the flux of.cosmic-ray neutrons (inside nuclei), and Np that of protons, including hydrogen nuclei.

Fig. 1. Eatio of neutrons to all nucleons. in cosmic rays at 1013 eV, vs. energy per nucleon, based on the P-W model. Experimental points are_ calculated from data too Ep (T«V/u) of Ashley "e£ ffK (1975). 233

The H /n" ratio of Ashley et al. (1975) has been converted to the Nn/Np + Nn) ratio, following the procedures of Erlykin et al. (197^ and 1975). Large uncertainties are associated with this calculation; the data fit well the assumption of no change in the composition, and seem to deviate by slightly over 1 standard deviation from the equilibrium model. Hence, the latter cannot be excluded either. •

. Another test between the models is provided by the anisotropy measurements near 1018 eV. Linsley (1975) at 4 x 1017 eV reports a first harmonic anisotropy of 0.072 ± 0.025. The history of anisotropy measurements should make us cautious, but by accepting this value of 1% a leaky halo could be inferred. Still another test between the models is provided by the flux of neutrinos, as discussed by us in other papers at this conference.

5. Summary. Procedures are outlined for estimating the galactic confinement time of oosmic rays below 1 TeV. Present interpretations of the low-energy 103e and high-energy e~ results are not unambiguous, if critically inspected. Procedures are outlined for deducing the origin and conditions of confinement of cosmic rays above 10 TeV.

b. References

Ashley II, G. K., Keuffel, J. W. and Larson, M. D. 1975, l^th Internat. Cosmic Bay Conf. Munich, 12, 4282. Brecher, K. and Burbidge, G. R. 1972, Ap. J. 174, 253- Buffington, A., irth, C. D., Smoot, G. F. 1975, Ap. J. 199, 669. fowsik, R. and Wilson, L. W. 1975, Conf. Papers, l4th Internet. Cosmic Ray Conf. Munich, 2, I+75. Erlykin, A. D., Ng, L. K. and Wolfendale, A. W. 197^, J. Phys. A, 7, 2059- Erlykin, A. D., Ng, L. K. and Wolfendale, A. W. 1975, l^th Internat. Cosmic Ray Conf., Munich, 6, 2OO3. Fichtel, C. E., Hartman^ R. C., Kniffen, D. A., Thompson, D. J., Bignami, G. F., Ogelman, H., <3zel, M. E. and Turner, T. 1975, Ap. J. 198, 163. Garcia-Munoz, M., Mason, G. M. and Simpson, J. A. 1975a, Ap. J. (Letters) 201, Ll^l. Garcia-Munoz, M., Mason, G. M. and Simpson, J. A. 1975b, Ap. J. (Letters) 201, Ll45. Giler, M., Wdowczyk, J., Wolfendale, A. W. 1977, to be published. Hagen, F. A., Fisher, A. J. and Ormes, J. F. 1977, Ap. J. 212, 262. Kulsrud, R. and Zweibel, E. 1975, Conf. Papers, lith Internet. Cosmic Ray Conf., Munich, 2, h65. Linsley, J. 1975, Conf. Papers, 14th Internat. Cosmic Ray Conf., Munich, 2, 593. Nagashima, K., Neno, H., Fujimoto, K., Fujii, Z., Sakakibara, S. ^nd Kondo, I. 1975, Conf. Paper3, l4th Internat. Cosmic Ray Conf., Munich, h, 1503. 0'Dell, F. W., Shapiro, M. M., Silberberg, R. and Tsao, C. H. 1975, Conf. Papers, l4th Internat. Cosmic Ray Conf., Munich, 2 , 526. Peters, B. and Westergaard, N. J. 1977, to be published. Prince, T., Mueller, D., Hartmann, G. 1977, Bull. Am. Phys. Soc. 22, 601. Scott, J. S. and Chevalier, R. A. 1975, Ap. J. (Letters) 197, L5. Stecker, F. W. 1976, The Structure and Content of the Galaxy and Galactic Gamma Rays, Internat. Symp. at NASA, Goddard Space Flight Center, p. 357. . Stecker, F. W., Puget, J. L., Strong, A. W. and Bredekamp, J. H. 1974, Ap. J. (Letters) 188, L59. Yiou, F., Raisbeck, G., Perron, C. and Fontes, P. 1973, 13th Internat. Cosmic Ray Conf., Demver, 1, 512. tef90049G 234

COSMIC RAY PROPAGATION: ENERGY-DEPENDENCE OF LEAKAGE MEAN PATH LENGTH

Pierre Fontes Laboratoire Rene Bernas, Centre de Spectrometrie Nucleaire et de Spectrometrie de Masse, Orsay, France * Jean-Paul Meyer Service d'Eiectronique Physique Centre d'Etudes Nucleaires, Saclay, France

Claude Perron Space Science Department of ESA European Space Research and Technology Centre Noordwijk, The Netherlands

Propagation calculations making use of the latest experimental nuclear cross-sections, have been carried out in an attempt to account for the cosmic ray chemical abundances and their variations as a function of energy. A survey of the available cosmic ray data has been made, and these data consistently corrected foj? Interactions in the atmosphere. Secondary to primary ratios, selected on the basis of their significance can be accounted for, either by a continuous decrease of the leakage mean path length with energy, or by two distinct propagation regimes, one below GeV/n, the other between 20 and 100 GeV/n, with a transition region in between.

1. Introduction. The relative abundances of cosmic ray nuclei have long been believed to be energy-independent, until the recent achievement of measurements at very high energy. Juliusson, Meyer and Muller (1972) showed that the relative abundances of predominantly secondary species to predominantly primary species decrease when the energy increases above ^20 GeV/n. Since then, a number of papers ,has confirmed this variation, and extended it to primary-torprimary ratios, as well as to much lower energies. However, there have been some strong disagreements between experimental results from different groups, and, as-a consequence, different interpretations have been suggested. According to some authors a propagation effect (energy-dependent path length) is sufficient to explain all variations, while others favour a source effect (several types of sources) or both.

The amount of experimental data is becoming rather large and it seemed to us that it was now possible and desirable to try to find a general trend from the whole set of. available data. In addition, there has recently been some important results on the nuclear physics side: firstly, new data on high energy heavy ion reactions now allow more refined and reliable atmospheric corrections of the raw cosmic ray data obtained at balloon altitude, secondly, thanks to the last measurements performed in Orsay and in Berkeley, most of the dominant nuclear cross-sections relevant to the propagation process have now been measured at several energies „ allowing us to calculate the production of both light and heavy secondaries in interstellar space, with a high reliability.

In this paper, our purpose is not to try to discriminate between existing propagation models nor to refine them or build up new ones, L - essentially to attempt to determine precisely which energy depentieri. ? of the 235 cosmic ray mean path length is required to explain the existing observational data on secondary to primary ratios, consistently for both light and heavy species. To do so, we shall compare the data with the predictions of a simple interstellar propagation model (leaky box), but the main conclusions should, of 'course, be valid for any other model.

2. Observational data. We shall base our study on what we believe to be the most significant ratios, chosen in the following way: we consider as secondary only those elements whose source abundance can be thought of as negligible compared with en route production, and, conversely, as primary only the ones whose interstellar production is small compared with source abundance. This leads us to exclude in this study elements like N or Ca, which are produced in about equal proportions by the source and by interstellar spallation. We also demand that the cross-sections for secondary production be measured (at least the most important ones). Finally, we make ratios of secondary element groups to their primary parents only in order not to mix source primary-to-primary ratio variations (if any) with the propagation effects we are looking for here. We thus arrive at the two 'best'-" ratios: Li+Be+BAC+O (L/C+O) and Sc+Ti+V+Cr+Mn/Fe (Sc-Mh/Fe).

One could argue that a fraction of the L nuclei is made by spallation of elements heavier than 0 (Fe, Si, Mg...) and should reflect their spectra, which many experimenters find different from those of 0 and C. Howeverthe L production from 0 and (mostly) C is overwhelming (Fontes, 1977) and justifies our choice. The disadvantage of choosing two "best" ratios is that we could not use the results of some groups at all, either because they have not measured one element (e.g. Li) or because they only give the abundances of groups different from the ones we have chosen (e.g. 17 ^ Z £ 25). However, this still allows us to use a large amount to data, and should permit more reliable conclusions.

3. Atmospheric corrections. We have used the procedure of Meyer et al. (1975), but with completely renewed nuclear physics input data (issued from most recent accelerator measurements on heavy ion reactions). These new corrections are described in some detail in another paper presented at this Conference (Meyer et al., 1977), and ive only outline the procedure here.

The cross-sections of reactions on air are related to those on hydrogen by an "enhancement factor" defined as the ratio of the cross-section for production of a particular fragment in an air target to that in a hydrogen target. The factor ra^r is deduced from (fairly scanty) observations of heavy ion reactions and is taken to be a smooth function of both incident nucleus and fragment masses. However, the observations often give only the dependence of ra^r on the fragment mass, not its absolute value. We, therefore, normalise all the cross-sections to a quantity closely related to the total reaction cross-section on air. We believe this normalisation offers a fundamental safeguard against large errors in estimates of spallation cross- sections on air. Furthermore, the very essential cross-sections for L- element production by C and 0 from heavy targets have been measured by Lindstrom et al. (1975). Thus the uncertainty of our own estimate of unmeasured atmospheric cross-sections only slightly affects our calculated production of LiBeB. We have included our estimated uncertainty of the atmosphere corrections in the errors on the derived cosmic ray abundances (30% on the formation rate of all elements, except 20% for C, 10% for Be and B, 15% for Li, 10% on the destruction cross-sections relative to that of Si). 236

Fig. 1. Examples of excitation functions Fig. 2. Examples of excitation for spallation production of.L-elements. functions for spallation production of Sc-Mn elements. 4. Nuclear cross-sections. It is of course very important for calculating cosmic ray abundances, to take into account any variation of the cross- sections with energy. For the most important reactions (productions of L- elements from C and 0, of Sc-Mn from Fe), we make use of excitation functions extrapolated from values measured at several energies, and we would like to present a few of them here, as examples. Those given in Figures 1 and 2 are quite representative of the whole set and indicate the general trend. The experimental points have been omitted for clarity, they can be found in Fontes (1975) for the spallation of carbon, and in Perron (1975), for the spallation of iron, along with the full set of excitation functions, and a discussion of the validity of the extrapolations (confirmed by the measurements of Raisbeck et al., 1975). One thing is striking, when one compares Figure 1 and Figure 2, the cross-sections for production of the L-elements (Figure 1), either increase with energy or. stay c6nstant, or, at most; very slightly decrease above a few hundred MeV/n, while the cross-sections for production of the Sc-Mn elements (Figure 2) all decrease, often by a factor of about 2, between a- few hundred MeV/n and a few GeV/n. Thus, we can already foresee a small variation of the Sc-Mn/Fe ratio due to the energy dependence of the cross-sections while no such effect can be expected for the L/C+0 ratio.

5. Propagation calculations. We used the framework of the leaky box model, because it has been widely used until now, and has been shown to account well for all cosmic ray abundances in the energy region about 1 GeV/n, if one takes the leakage mean path length equal to approximately .5 g/cm2 of hydrogen. Also, it is a good approximation to some other models, or from its parameters, it is easy to derive the parameters of other models (e.g. the nested leaky box of Cowsik and Wilson (1975), or the new closed galaxy - but open galactic arm - model of Peters and Westergaard (1977)).

The calculations have been performed by means of a computer code due to Comstock (1969, and unpublished) taking into account ionization energy losses and all possible nuclear reactions. When no experimental excitation function was known, we used the formulae of Silberberg and Tsao (1973), but these calculated cross-sections only play a minor role in our calculations as emphasised elsewhere (Perron, 1976; Fontes, 1977). All primary species have been assumed to have the same source spectrum (power law in total energy/n with index 2.5), and LiBeB and Sc-Mn to be absent at the source. 237

-i—i—i—i i i | 1 1—i—i—i—i—i—i—p I CARTWRIGHT et al.(1971) • SMITH et al. (1973) • WEBBER et al. (1972) a JULIUSSON (1974) a WEBBER et al. (1973) * JULIUSSON et al. (1975) + JULLIOT et al. (1975)

"T t

ENERGY (GeV/n)

Fig. 3. L/C+O ratio in cosmic rays. Full symbols refer to data that we have consistently corrected for interactions in the atmosphere (and to satellite data), open symbols to data corrected by the original authors. Curves are 2 calculated interstellar values. A is in g/cm of hydrogen3 R in GV/c.

6. Discussion. Figure 3 shows the L/C+O ratio as a function of energy. We have used full symbols for the data that we have corrected for interactions in the atmosphere (and for satellite data), and open symbols for data corrected by the authors themselves (i.e. when the raw data were not available to us). The energy windows or thresholds have been omitted for clarity, integral measurements have been plotted at an effective energy which is M..9 times the threshold energy. There is a rough agreement between all groups, but also some discrepancies, much larger than the statistical errors, which it would be highly desirable to clarify.

Obviously, there is no way of explaining all the data points by a propagation with one constant mean path length A, and we have adopted a rigidity dependent A of the form: A = AR~S. We have chosen the rigidity because it is through this quantity that particles are sensitive to confinement by magnetic fields, but a similar dependence of A on the energy, as has been adopted already by several other authors, (Audouze and Cesarsky, 1973; Webber et al. , 1973) gives results which are not significantly different, even at low energy. The calculated curves on Figure 3 refer to the interstellar ratio, while the measurements, of course have been performed near the earth. It should thus be kept in mind that, because of solar modulation, the low energy data points correspond to an interstellar ratio at a somewhat higher energy than the measured one. The two curves, corresponding to A = 8.5 R-0-^ g/cm2 of pure hydrogen (i.e. ^5.2 g/cm2 at 1 GeV/n, for A/Z=2 nuclei), and A = 10.1 R~u g/cm2 (i.e. V7 g/cm2 at 1 GeV/n) can be considered as the lower and upper envelopes of the data points. The best fit would be obtained with A = 10.1 R~0,1+ g/cm2 (^6.2 g/cm^ of H at 1 GeV/n, equivalent to «v,7 .4- g/cm2 of 90% H + 10% He), but in view of the discrepancies between the data from different groups, we do not give too much weight to this fit.

This kind of variation of A has now become classical. However, when looking at Figure 3 with an unprejudiced eye, one finds no clear indication of a variation of A between 20 and 100 GeV/n (see also Juliussc.., 1974, for 238

various secondary-to-primary ratios, which all show the same pattern). The data rather suggest two propagation regimes, corresponding to the two plateaus on Figure 3: one below say 5 GeV/n, with A ^5.5 g/cm2, the other between ^20 and 100 GeV/n, with A VL.7 g/cm2. A transition region extends from 5 to 20 GeV/n. A simple extrapolation of the data above 20 GeV/n does not suggest that the amount of matter traversed decreases and tends to zero above 100 GeV/ n, as commonly stated. Clearly,more data (particularly spectra in the transition region) are needed to decide whether this picture is correct or is just a fortuitous effect of data scattering.

ENERGY (GeV/n)

Fig. 4. Sc-Mn/Fe ratio in cosmic rays. Symbols and curves as for Fig. 3. The data of Maehl et al. (1976) refer to Sc-Cr/Fe ratio.

We now come to the Sc-Mn/Fe ratio shown in Figure 4. Only Juliusson (1974) provides very high energy data, with low statistics and an inaccurate separation of Mn from Fe. We thus first grouped his 6 measurements into 3 to improve statistics and computed the Sc-Mn/Fe ratio from his data in two ways: firstly, from the individual element abundances, secondly, by correcting the Sc-Cr/Fe+Mn ratio using a value of 0.25 for Mn/Sc-Cr5 obta'ined as the mean of the other measurements made at lower energies (but Mn/Sc-Cr essentially relies on cross-section ratios, and the energy should play no role). The points have been plotted at the mean of the two values, with an error bar reflecting the overall uncertainty.

Because of these large uncertainties at high energy, the need for an energy dependent A is less crucial here- Indeed., calculations with a constant A (in the range 5.5-10 g/cm2) lead to a Sc-Mn/Fe ratio which slightly decreases as foreseen in Section 4, between -vl and a few GeV/n and is not inconsistent with the data. We also show in Fig. 4 the calculated curves corresponding to the two assumptions made above: A varying continuously like R_s, and two different constant A at low and high energy. They are also consistent with the experimental data,

We note, however, that the curve corresponding to A=10.1 R-0*3. which , passes here right in the middle of the points around 1 GeV/n, was the upper envelope of the L/C+0 ratio. We also note that some of the points at low energy lie somewhat higher than the curves. Although taking into account solar modulation would slightly reduce the discrepancy, this could be the 239 indication of an interesting effect, which needs further confirmation. This could also be, at least partly, due to different atmospheric corrections, since the points which have not been corrected by us (open symbols) lie generally higher than those we have corrected (full symbols). Maehl et al. (1976) have presented calculations made with a constant A (5 g/cm2 of 90% H + 10% He, equivalent to g/cm2 of pure H) which fit their data quite well down to the lowest energy. Our results (see our curve with A=5.5 g/cm2) are in significant disagreement with theirs. The reason for this disagreement is not clear, it is not likely that it is entirely due to these authors using calculated cross-sections instead of experimental ones in our case.

7. Conclusions. From the present comparison of propagation calculations with the experimental data of many groups, one could simply conclude that both light and heavy secondary cosmic ray abundances are well accounted for by propagation with a leakage mean path length A varying like R~s, with s in the range 0.3-0.4, and the value of A at 1 GeV/n in the order of 6 ± 1 g/cm2 of H for the light elements and 7.1^ g/cm2 of H for the heavy ones (the uncertainties reflect the scattering of the experimental points).

However, the data can equally well be accounted for by two distinct energy.independent regimes of propagation. Below GeV/n, the leakage mean path length is in the order of 5.5 g/cm2 of H, between 20 and 100 GeV/n, in the order of 1.7 g/cm2, and the data show a transition region from ^5 to ^20 GeV/n.

8. Acknowledgements. We are indebted to G.M. Comstock, G.M. Raisbeck and F. Yiou for use of the propagation program. One of us (C.P) was holding an ESA research fellowship during this work.

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ICRC stands for International Cosmic Ray Conference.

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CONSTRAINTS ON THE COSMIC RAY HALO/DIMENSIONS

F. C. Jones and F. W. Stacker

NASA/Goddard Space Flightf Center Greenbelt, Maryland 207M U.S.A.

We consider diffusion halo models of various sizes. In such models, the scale perpendicular to the plane has a strong effect in determining the distribution of cosmic rays. Radial distributions are calculated for cylindrical coordinate models. Y-ray longitude distributions are calculated andr compared with the SAS-2 data. Assuming the sources to be supernova remnants or pulsars, only cosmic-ray nucleon halo models with an upper limit scale height of 3 kpc provide a good fit to the -i-tfay data. Consideration of the Y-ray latitude data javes a half thickness of 2+2 kpc for the cosmic-rav electron halo.

1. Introduction. Recent analyses have questioned the existence of an extensive halo or favored a weak non-confining halo (Webster 1975) or a very thin halo or thick disk of a tew kpc extent (Ilovalsky and Lequeux 1972, Baldwin 1976). The case in Support of an extensive radio halo has been reviewed by Ginzburg and Ptuskin (1976).

In view of the situation with the radio data, and the additional present uncertainty regarding the age of galactic cosmic rays, (see, e.g., Ginzburg and Ptuskin 1976) it would seefm desirable to have an independent test of the existence and extent of a/cosmic ray halo. Such a test Is furnished by the recent observations of the distribution of galactic 100 MeV Y-rays. (Fichtel et al. 1975) and thfeir interpretation (Stecker 1976a, 1977).

If cosmic rays are produced primarily as a result of supernova explosions or in pulsars, the striking correlation of the galactic cosmic ray distribution and the/supernova remnant distribution implies source dominated diffusion (Steftker 1975a). This argues against trapping of cosmic rays in a large halo with multiple reflections of cosmc rays at the boundaries, which would produce a more uniform distribution of cosmic rays in the galaxy than the Y-ray observations imply (Stecker 1976a, 1977).

The existence of/any type of closed galaxy model with long term ( ^ 108 yr) confinement of cosmic rays is thus brought into question. This includes the close

2. Method. In the models we examine here, the cosmic-ray sources are assumed to be «;onfined to a thin disk of half thickness LQ; the cosmic rays subsequently Aiffuse in a disk of half, thickness L (L^LQ). We assume cylindrical ^ymmetry about the z axis which is perpendicular to the disk surface and/the diffusing volume is taken to be of infinite extent in the radial direction r. The cosm.Tr. ray particles are free to diffuse In z and r until they reach the surfaces z = + L at which point they escape freely;