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THE HIGH ENERGY COSMIC RAY SPECTRUM S. Olbert Department of Physics Massachusetts Institute of Technology In the cosmic ray spectrum above about two Bev it is meaningful to set down a single energy spectrum as typical: in contrast to the wildly fluctuating energy spectrum at lower energies, which will be discussed by Meyer and by Van Allen, the spectra above two Bev are stable within about 20 percent. The energy dependence of the high energy cosmic ray spectra for particles of different charge are shown in the following table: Designation Charge , , JJE) Range of Validity Notes (no/mZ/ster/sec) (Bev/nucleon) /j P 1 4000 E-1. 15 2-20 Steepens gradu- ally: E-2 > 10° Bev. No cut-off at 1018 ev. Q 2 460 E-1-6 1.5-8 L (Li, Be, B) 3,4,5 ~50%ofM? Difficult to meas- ureâsee text. M (C, N. O, F) 6, 7, 8, 9 24 E-l- 6 3-8 H > 10 16E-2â¢Â° 3-8 Little is known about spectrum at higher energies. For protons many detecting devices have been employed: Geiger-Muller counters, proportional counters, ion-chambers, Cerenkov counters, cloud chambers, etc. At low energies the Earth's magnetic field provides a spectrometer. At higher energies the cosmic ray events are too rare to be detected directly, so scintillation counters are employed to detect electrons produced in the air shower. In this case, the number of electrons passing any level of the atmosphere provides a good measure of the energy Df the primary without too much dependence on the model of multiple meson production which is assumed. [The discussion of measuring techniques will 53
not be given in as much detail as OLBERT provided--those readers interested in techniques may consult review articles such as that of Singer (1958)]. It is important to note that there is no indication of any cut-off in the proton cosmic ray spectrum, even at 10l8-iol9 ev; this point will be of importance later. The errors probably do not exceed 5-15 percent in the spectral region from about 3-20 Bev and at the highest energies the errors are probably not more than a factor of two; in between there are some gaps which are not as precisely defined. Heavy and medium weight particles in the 2-20 Bev range have been studied almost exclusively by means of photographic emulsion tech- niques. One attempts to identify the particles from their tracks--by delta- ray counting for example--but it must be recognized that the mass spec- trum of particles is undoubtedly modified by fragmentation in the residual atmosphere above the detecting station. Various authors have published relative abundances of C. N, and O nuclei. Some of their results are quoted below, along with the Suess-Urey cosmic abundances and Aller's (1960) latest solar abundances: C N O 24 16 6 27 32 14 39 9 37 41 4 8 31 25 24 Cosmic Rays (various authors) ! 2 6 Suess-Urey 9.3 2.4 25 Aller The cosmic-ray results are in fairly good agreement with one another. They diverge considerably from the Suess-Urey cosmic abundances, par- ticularly in the C:N ratio, but are not appreciably at variance with Aller's solar abundances. [Aller notes that the f-value for oxygen is not well known, and that better f-values and model atmosphere calculations are required for carbon.] At higher energies little is known about relative abundances or energy spectra of the medium and heavy weight nuclides due to the scarcity of such events. It does appear, however, that the total medium-weight particles are about 2-1/2 to 3 orders of magnitude less abundant than protons, and that the heavy weight nuclides are about 3-1/2 orders of magnitude less abundant throughout the energy range from 1 Bev up to a few hundred Bev. [No significant disagreement with either the Suess-Urey or Aller abundances.] The greatest uncertainties, both in energy spectrum and identifica- tion, are at Z = 3, 4, 5. First of all, these particles are far harder to 54
detect on emulsions than the heavier particles. Secondly, so few of these particles are detected that they could all have been produced by fragmenta- tion of heavier nuclei in the atmosphere; it is still an open question whether there are any La, Be, B nuclei in the primary cosmic -ray flux at all, al- though current opinion favors the existence of a primary ratio of L to M particles of perhaps 50 percent. These nuclei are especially worthy of attention when cosmic-ray spectrometers are carried above the atmosphere. If nuclei are also sought which are almost exclusively fragmentation products--H2, H3, He?--it should be possible to settle the debate on whether the light- and medium-weight cosmic ray nuclei are really only fragments of, say, iron. It is also important, of course, to try to improve air-shower detection systems so that nuclear interactions with (i-mesons can be studied, and so that other components of showers can be studied which appear with lower fluxes than the electrons. Time delay circuits set up in connection with the numerous scintilla- tion counters used in air shower research are used to define the angle of attack of primary cosmic rays. By plotting angles of incidence vs. side- real time it has been possible to seek point sources of cosmic rays in the galaxy with better than 5o precision. Except for anisotropy in the direc- tion of the sun, however, the galactic cosmic ray flux appears to be ex- tremely isotropic. Cocconi (1956) has found that the degree of anisotropy 5, where 8 = Maximum Galactic flux - Minimum Galactic Flux (1) Average Flux is less than 10-3 for particles up to l015 ev and less than 0. 01-0. 02 for particles up to 1Q18 ev. There is a possibility of gaining valuable information on the structure and composition of our Galaxy by looking for pure electron-photon showers caused by energetic .y-rays that arose when a high energy particle struck quiet matter at some distant point in the Galaxy. These pure photon showers would be free of all particles but electrons and photons because the probability of photonuclear reactions is truly negligible compared to ionizations. They could easily be detected by circuits set to detect elec- trons in anticoincidence with nucleons. The frequency of these showers would serve to measure the interstellar galactic density, since the produc- tion probabilities are reasonably well known. The â¢y-ray flux, unlike the ordinary cosmic ray flux, should be highly anisotropic; it should be largely confined to the dish of the Galaxy and concentrated toward the galactic center. [Information on material densities in the galactic center would be especially valuable, since it is in this region that dynamical determinations of the mass density have lowest weight. The interest in this problem is heightened by the recent observation that neutral hydrogen is streaming from the galactic nucleus (van Woerden, Rougoor, and Oort 1957).] 55
Certainly this technique could provide some important information not available to radio or optical astronomy. The origin of cosmic rays is not yet settled. Certainly the sun can- not be producing the high energy flux since particles of more than 1013 ev would not be deflected enough by magnetic fields within the solar system to appear as an isotropic flux. Rather it appears that particles are ejected into interstellar space by various objects --flare stars, novae, supernovae, etc. --and then accelerated by collisions with hydromagnetic waves "mag- netic clouds" in the galactic magnetic field (Fermi, 1954). Acceleration is the result of these collisions because head-on collisions, which transmit energy to the particles, are statistically favored compared to overtaking collisions, which remove energy. The general form of the acceleration equation is = aE - P(E) (2) where n is the number of collisions, a is a parameter describing the efficiency of acceleration (a is of order k*â where k = 4/3 for a random C2 velocity distribution of ionized particles in a gas cloud) and p is a collision- loss parameter which decreases with increasing energy. It is easy to understand why a power law spectrum results from such an equation if in- jection is continuous, and it is also plain that the highest energy particles will be the oldest. Variations in wave structure, relative velocities and wave spacing, magnetic field topology, damping parameters and the energies of injected particles have been employed to explain the observed energy spectrum for primary cosmic rays. The isotropy of the flux can also be explained as a result of the trapping of cosmic ray particles by the Galactic magnetic field and the resulting diffusion of the particles through- out the galactic halo. Nonetheless this picture is incomplete in several respects. First, it is clear from equation (2) that a critical energy of injection is required before the Fermi acceleration mechanism can begin to be effective. For protons the critical energy is only 1 Mev, a reasonable enough injection energy, but for iron nuclei the critical energy for acceleration is 400 Mev, which poses a real injection problem. Second, since the index of the power law spectrum of cosmic rays is known, the parameter a is fixed; the resulting value of a demands relative magnetic cloud velocities the order of 100 km /sec. Such relative velocities are about ten times larger than would be anticipated on other grounds. Third, cosmic ray particles with energies in excess of 1018 ev cannot be trapped even in the galactic magnetic field, so apparently their source is extra-galactic. (Galaxies may simply exchange between themselves particles which they cannot trap.) 56
There is no obvious reason why the spectrum of particles above this critical energy for galactic trapping should fit smoothly to the spectrum of trapped particles, but it does. Other theories of the origin of cosmic rays have been proposed; Ginzburg (1958), for example, suggests that the cosmic ray flux is a re- sult solely of supernovae acceleration and diffusion throughout the galactic halo; this averts the first difficulty mentioned above but not the second and third, and it introduces many problems of its own (such as an expected cutoff in the proton spectrum at 1015 ev). But in any event it is challeng- ing to realize that in studying the cosmic ray energy and mass spectra we are gaining valuable information about element synthesis and stellar evo- lution not only from our own Galaxy, but from other galaxies as well. Cameron: It would be worthwhile to seek .y-rays from M31. Our Galaxy would not interact with these \â; M31 is massive enough and subtends a large enough angle in the sky to favor detection as a discrete y-ray source. REFERENCES Aller, L. H. (1960) Chemical Composition (Interscience Press, New York). Cocconi, G. (1956) I1 Nuovo Cim. 3, 1433. Fermi. E. (1954) Astrophys. J. 119, 1. Ginzburg, V. L. (1958) Progr. Elem. Particle and Cosmic Ray Physics IV, 339. Singer, S. F. (1958) Progr. Elem. Particle and Cosmic Ray Physics IV, 205. van Woerden, H., Rougoor, G. W., and Oort, J. H. (1957) Compte Rendus Acad. Sci. Paris 244, 1691. 57
