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SUI 'PLEMENTO AL VOLUME XIV~ SERIE X N. 2, 1959
DEL NUOVO CIMENTO 4 ~ T r i m e s t r e
Origin of Cosmic Radiation.
B . PETERS
Tara Institute of Fundamental Research . Bombay (*)
1 . - I n t r o d u c t i o n .
The propert ies of cosmic ray particles in the neighbourhood of the ear th
have been s tudied mainly with the help of balloon borne part icle detectors.
I n fo rma t ion on cosmic r ay particles in other, more d is tan t pa r t s of the
universe comes f rom astronomical , expecial ly radio as t ronomical observa-
tions. One measures the e lect romagnet ic radia t ion emi t ted b y energetic
electrons moving in magnet ic fields (synchrotron radiation). Nuclei of compa-
rable energy radia te less energy than electronsby a factor (M/mo) 4 and are
therefore not observable with these techniques.
The da ta on cosmic r ay particles which have been collected b y these methods fo rm the basis of n theory, developed m~inly by ~KLOVSKIJ [1, 2] and GINZBURG [ 3 ] . This theory deals with the origin of radio noise as well as
with the origin, the accelerat ion and the p ropaga t ion of cosmic radiat ion. I t
covers, therefore a much wider field t han earlier theories on cosmic ray origin.
i t is not ye t complete and impor t an t exper imenta l and theoret ical questions remain to be discussed. ~ever theless , it has had some remarkab le success in correlat ing exper imenta l da ta and does not seem to have encountered serious
obstacles so far.
In its bures t outline the theory muy be presented as follows: abou t once every hundred years a stellar explosion occurs in our ga laxy which is so spee-
tabular t h a t during its brief period of highest luminosi ty the s tar is designate4
as a super nova. Less spectacular events, so-called novae explosions, occur
a t the ra te of abou t a hundred per ye'~r, and are, therefore abou t ten thousand
t imes more frequent .
An explosion leads to the expulsion of a large amoun t of gas, which sub-
sequent ly expands .into the surrounding sp,~ce with ~ veloci ty of the order
of :1000 km/s and breaks up into tu rbu len t elements. The turbulence of the
(') At present at the Institute for Theoretical Physics, University of Copenhagen. The Author takes pleasure in expressing his gratitude to professors N. Boim, A. BOHR and J. K. BOGGILD for their hospitality.
O R I G I N O F C O S M I C R A D I A T I O N 437
resulting clouds leads to the build-up of magnetic fields. Ionized particles moving in the clouds can be accelerated in various ways, mainly perhaps in collisions with the resulting magnetic inhomogeneities by a statistical mechanism originally discussed by FERMI [4, 5].
When the gas envelope has expanded sufficiently so that magnetic field strength and density approach that of the surrounding inter-stellar space, the accelerated particles begin to escape into the main galactic volume. Here, their direction is rendered isotropic by further collisions with magnetic inho- mogeneities, which now however are too rare to lead to an appreciable further increase in particle energy.
In the interstellar space, the particles suffer energy losses due to various processes. Electrons lose energy through ionization of the interstellar medium, through bremsstrahlung in collisions with atoms, through collisions with thermal photons (inverse Compton effect) and through synchrotron radiation. The nuclear component loses energy through ionization and nuclear interactions. The nuclear collisions lead to meson production and, thereby, to the creation of new high energy electrons and positrons through ::-~-e decay. In the case of complex nuclei, the collisions lead also to spallation reactions and thereby, to a degradation of the charge spectrum and washing out of its structural details as well as to a general shift towards lighter elements.
This picture has been developed quantitatively so that one can attempt an interpretation of:
P the intensity, frequency spectrum and polarization of the optical and radio emission from the remnants of super nova explosions;
- - the properties of radio emission from other parts of the galaxy and
- - t h e intensity, energy spectrum and composition of the primary cosmic radiation.
The strength of the theory, as compared to earlier attempts, lies mainly in the fact that it successfully links astrophysical and cosmic ray observations.
In discussing the origin of electromagnetic radiation emitted by super novae and the origin of galactic radio noise, we shall follow GINZBURG and ~K~OVSKIS rather closely. Some of their arguments have also been used in the later discus- sions dealing with the nuclear component of cosmic radiation.
2 . - T h e or ig in of radio no i se .
Identification of radio emission and of strongly polarized light with the radiation emitted by relativistic electrons moving in magnetic fields is bused .on the following evidence:
2 8 - Supplemento al Nuovo Cimento.
4 3 8 B. PETERS
a) The angular coordinates of historical super novae outbursts in ou r
galaxy coincide with centers of strong emission of radio noise.
b) One of the strongest emitters, the Crab ~ebu la (super nova of
1054 A.D.), is at the same t ime a strong source of radiat ion in the optical region The light which it emits has quite different properties from the light emi t ted by hot gases. I t is so intense that , ff it were due to atomic transitions, it would require an expelled gas cloud weighing more tha t ten solar masses, which seems unlikely. I t exhibits a continuous spectrum with no spectral lines. The dependence on wavelength is more adequate ly represented by a power law
than by Flanck's radiat ion formula. Finally, the light is polarized and~ as one increases the resolution and looks at smaller and smaller elements of the
tu rbu len t cloud, the degree of polarization increases. I t seems~ therefore, tha t
polarizat ion is nearly complete, and tha t failure to observe very strong
polarizat ion is due only to the fact t ha t the direction of the polarization vector varies for different parts of the nebula.
On the s trength of this evidence, there can hardly be any doubt tha t the radiat ion is due to the motion of electrons spiraling in m~gnetic fields.
Electromagnet ic theory permits to calculate the number and energy of electrons giving rise to such radiation.
A simple calculation for the Crab )Tebula may be useful because it is t he
essence of the theory tha t one can establish, without arbitrariness or serious ambiguities, a relation between the number and the energy spectrum of electrons and the intensi ty and f requency spectrum of synchroton radiation.
An electron spiraling in a magnetic field emits the greatest power at a
frequency,
v ~ 4x \mc] me" ~= 1.~.:10~H mc 2 H z .
Here E is the energy of the electron and H is the magnetic field component,
perpendicular to its direction of motion. The energy radiated in various f requency intervals is given b y
P ( v , E ) d v = ] 6 e H mc 2 p 2~m~x dr.
p(x) is a known function of f requency with a fairly shurp m~ximum at x = 0 . 5 . The total energy radiated by an electron per unit t ime is
dE f p 2 c / e ~ \ 2 [ E \ ~ ( E ) ~ dt (v,E) dv--~-- -- H 2 - - ~-~
ORIGIN OF COSMIC RADIATION 439
This means tha t if synchroton radiation losses dominate, it will have radiated
half of its energy in a time
T�89 = [ 3 c \ m c ] \mc'~]\mc'2]] - - H 2 E years .
We now apply these formulae to the Crab Nebula. The Crab Nebula is
at ~ distance R : 4200 light years from the solar system. The energy
received on the earth has been determined accurately at 2 : 4 3 0 0 A and is
F~ : 2.10 -'-'3 erg/cm' s (Hz). If one then assumes tha t all electrons have just
the correct energy to give their maximum radiation at ~ = 4300 A, their number
must be
with an energy
4:~R~Fa 2 "10 ~a N+= p(v::~, E) H electrons,
[ 4 z c [mc'lt�89 101~ E o - e V .
Assume tha t the energy radiated by the Nebula w~s not smaller in the
past than it is today ; then if we choose H > 10 -~ G, electrons which began
radiat ing 900 years ago, when the Crab Nebula was born, have already los~
at least hMf of their energy. The total energy given to these relativistic elec-
trons since the super nova explosion is then of the order of
~ = W~ ~ = NoE~ -900 = 3.5-10 ~7 erg, T�89
independent of the field strength H. If, on the other hand, we assume H < 1 0 -~ G, then the electrons accelerated
in the earliest stages of the super nova ~re still radiating and the energy of the
relativistic electrons necess:~ry to produce the observed light emission will be
larger, namely
Thus, a resonably conservative estimate of the number and energy of
relativistic electrons and of the field H of the Crab Nebula is
N e 2. ] 047 electrons,
E e -= 101~ eV.
W e = 3" 10 ~7 e rg ,
H e = 1 0 -~ G .
440 B. PETERS
A similar calculation in the radio band shows tha t there radiat ion must
be due to about h r = 105~ electrons of energy E ~ 5.10 s eV or a to ta l energy of B: ~ 1047 erg. For the radio source in Cassiopaeia A (super nova of 369 A.D.)
which is the strongest in our galaxy, one obtains an energy est imate which is ma ny times larger t han for the Crab lqebula. N e = 10 ~2 electrons above 5-10 s eV and We m~n ~ 1049 erg. Such calculations can be refined somewhat,
bu t the results do not differ appreciably. One can also calculate the radiat ion spectrum which would be produced
by electrons with a given energy distribution, f.i. ; the power law
Ke dE ~ro (E) dE =
E ~ �9
I t is easily shown tha t this leads to a radiat ion spectrum of the form
Kv I~ dv -- d r .
,~,( ~, - 1 ) / ~
In the case of the Crab lqebula, the radiat ion spectrum depends on the f requency as v-0.3 and requires, therefore, an electron spectrum proport ional
to E -j.6. This is flatter t han the part icle spectrum of cosmic radiat ion observed
on the earth. In Cassiopaeia A, I v,~ v -~ and the electron spectrum is of the
form E -~.~ which closely resembles the energy spectrum of the nuclear com- ponent observed at the top of the atmosphere.
Apar t f rom the strong point sources of radio noise associated with expanding envelopes of super nova explosions, there is a general background of radio noise in our galaxy which outside of the galactic plane depends only weakly on coordinates and is produced in an approximate ly spherical system of radius
50 000 light years surrounding the center of the galaxy. At a wave length of a few meters, therefore, the size and shape of our galaxy is ve ry different f rom the fiat disc-shaped spiral observed in visible light. A similar si tuation
exists in M31, a spiral galaxy resembling our own and also in other galaxies
of the same type. F r o m these observations one m ay conclude tha t relativistic
electrons as well as gas clouds and magnetic fields exist in a spherical volume surrounding the galactic disc.
A cloud moving in the known gravi tat ional field produced by the galactic mass which is mainly concentra ted in the galactic disc cannot reach such a great distance from the galactic plane unless its veloci ty u is of the order of or larger t han 100 km/s. The pressure exer ted by the gases must be counterac ted by the weight of the overlaying gas layer. F ro m this one can evaluate roughly the gas densi ty o. The clouds will also give rise to magnetic fields which con- t r ibu te to the pressure to be counteracted by gravitat ion. The energy stored in the field, H2/8zc, is probably in equilibrium with the kinetic energy of the
ORIGIN OF COSMIC RADIATION 441
clouds, (1/2) @u 2, bu t in any case is not likely to exceed it. F r o m such consi-
derat ions one can es t imate the gas densi ty and magnet ic field a t var ious
distances f rom the galactic center. For the halo (*), surrounding the galactic
disc ~KLOVSKIJ [2] assumes:
At a radius r ~ 30000 ly At a radius r > 30000 ly In the galactic disc itself one usually assumes
i = 10 -2 atoms/cm 8 H 6.10 -6 G 3' 10 -3 atoms/cm 3 H 3 10 -6 G 1 atoms/cm 3 H 6 10 -6 G
Hav ing es t imated the s t rength of the magnet ic field, one can now analyse,
the radio emission f rom the halo and finds t h a t the radia t ion is p re sumab ly
due to electrons with an energy spec t rum of the fo rm
g e Ne(E) dE = E~ .~ d E ,
t h a t the densi ty of electrons is fair ly uni form th roughou t mos t of this sphere,
and t h a t the space densi ty of those electrons whose energy exceeds 0.5 or 1.0 GeV is of the order of 10 -12 par t ic les /cm 3.
The theory now asserts t ha t the super nova and possibly also nova explo-
sions in the galactic disc supply the energy which is emi t ted in the fo rm of
radio waves by the galactic halo. One a rgumen t is based on the fact t ha t the
energy injected b y super novae is of the same order of magni tude as the ou tpu t
of radio noise. Here one assumes t h a t the energy given to electrons in the average super -nova envelope is a t least of the same order as the min imum es t imate of W e m 3.1047 erg obta ined f rom the Crab Nebula (the energy of the source in
Cassiopea A is 100 t imes greater). One es t imates the frequency, vs~, of super- nova outburs ts in our ga laxy as one in every hundred years. (This takes into account t ha t a large fract ion of the outburs ts are hidden f rom our view b y
dense dust clouds and could not, therefore, have been detected before the
adven t of radio as t ronomy). The part icle energy released into the galactic
halo must , therefore, be of the order of Wevss = 1038 erg/s. On the other hand
the to ta l radio emission of the galactic halo has been es t imated within a factor
two to be F --~ 2.5.1038 erg/s. Thus it seems tha t super nova explosions can
provide the necessary energy.
~KLOVSKIJ presents another interest ing a rgumen t in favor of the connec-
t ion between stellar explosions and galactic radio noise (quoted b y GINZBURG [6])
(*) The physical conditions which exist inside the galactic halo are not yet known with certainty. (See Proc. 3rd Symposium on Cosmical Gas Dynamics, Rev. Mod. Phys. 30, 925, 1958).
442 B. PETERS
The clouds of Magellan, which are small galaxies adjacent to our own, are quite weak emitters of radio noise. Stellar explosions of the ~ o v a type are also much less f requent there than in our galaxy. (No comparison can be made between the rates of super novae outbursts because they ure too rare.) This observation gives some support to a theory which links those two pheno- mena. I t also implies tha t the electrons which radiate within the halo of our
galaxy cannot easily escape through its boundary and are, therefore, unable
to fill the volume occupied by the clouds of Magellan.
3. - T h e n u c l e a r c o m p o n e n t of c o s m i c r a d i a t i o n .
So far the theory has no connection with the pr imary cosmic rays observed in the neighbourhood of the earth, except in so far as it suggests more refined exper iments : it states tha t in addition to the pr imary nuclei which have been
observed, there should be pr imary electrons with energies of about 1 GeV or larger and a density which in our neighbourhood should be about the same as in the rest of the galaxy, namely ~ 10 -12 partieles/cm 3. Cosmic ray measu-
rements up till now can only confirm tha t the density of high energy electrons
is not higher than this value. P r imary electrons have not ye t been observed; the flux predicted by the theory lies close to the limit of sensit ivity of the
exper iments which have been carried out so far. Secondly, the theory asserts tha t the electrons should have a differential
energy spectrum proport ional to E -2.~, very similar to the energy spectrum of p r imary nuclei, which behaves like E -~.5.
Bu t a real connection between the theory of the origin of radio noise and the origin of p r imary cosmic ray nuclei is established with the help of the fol- lowing argument : one knows of only two ways in which high energy electrons can come into being, (a) they may be the decay products of unstable particles produced in high energy nuclear interactions, or (b) they may have been accel- era ted by some process involving electro-magnetic interactions.
Whether one uccepts (a) or (b) one is led to the conclusion tha t the creation of high energy electrons implies the existence of high energy nuclei. In case (a)
this is obvious. In case (b) it follows from the fact tha t wherever there are free electrons there must be ions and it seems difficult to think of mechanisms which will successfully aeceler.~te electrons wi thout accelerating ions.
According to this theory therefore, emission of radio noise implies the presence not only of high energy electrons bu t also of nuclei with probnbly still
higher energies. These particles are accelerated in super nova- (and perhaps nova-) explosions and are released into the interstellar space when the magnetic field densi ty of the expanding gas envelope has reached the value which it has in the surrounding medium. This m,~y take from 1 000 to 3 000 years. Then
ORI(HN OF COSMIC ItAD[ATION 443
the envelope cerises to be a strong radio emit ter . The life t ime of super novae
,envelopes can be es t imated f rom tile number of r~dio sources which are act ive
in our ga laxy to -day and f rom the ra tc a t which explosions occur in our and simil~r g~daxies.
4. - The primary cosmic radiat ion observed near the Earth.
Before we go fur ther into the relation between cosmic ray nuclei, super
novae and galactic radio emission, it m a y be useful to summarize ve ry briefly
the existing informat ion on p r i m a ry cosmic radia t ion in the neighbourhood
of the e~rth. The radia t ion consists of the nuclei of various elements ranging
in a tomic weight f rom hydrogen to iron or nickel (PETERS [7]). The energy
spec t rum follows a power law of tlle form
KA N , ( E ) d E = ~ d E ,
where K A is a constant for a given e lement of a tomic weight A and E is the
to ta l energy of the p r i m a r y nucleus (including rest mass) (KAPLO~ et al. [8],
McDoN.~LI) [9]). F r o m a kinetic energy of �89 GeV per nucleon to a few thousand
GeV per nucleon the exponent ? h,~s the same value namely 7 ~ 2.5 for all
components . At higher energies one does not ye t know the relat ive s t rength
of individual p r im~ry components , bu t only the to ta l number of p~rticles as
a funct ion of energy. The spec t rum continues to be of the fo rm E r (LAL [10]). Beyond E ~ 104 GeV the exponent begins to increase slightly ~n4 re~ehes 2 .75--3 .0 a t E ~ 108 GeV. The largest ~ir showers observed until now corre- spond to ~ p r imary p~rticle with an energy of at least 2-109 GeV (CLAR~ et
aL [11]). I f it was a heavy nucleus its energy per nucleon was p robab ly of the order of a few times 107 GeV.
~ o electrons and no ~-rays have ~s ye t been observed in the p r ima ry ra- diat ion. At ~ par t icular energy, electrons, if present , are known to comprise
less th~n one per cent of the p r i m a ry flux. (CRITCI~FIELD et al. [12]).
Various processes e~m lead to changes in the n u m b e r of cosmic ray particles
incident on the ear th (Do1~A~ []3]). Dis turbances on the sun and the eleven
yea r sun spot cycle which affect the in tensi ty of non-relat ivist ic cosmic ray part i-
des, c~n occasionally m:~ke themselves felt up to energies of abou t 10 GeV.
When the solar surface is quiet, cosmic r ay in tens i ty is a t its m a x i m u m ~nd, therefore, p robab ly approaches the t rue value which it has in ou te r space.
The sun itself can occasionally ~ct ~s an emi t te r of energetic nuclei. Such ou tburs t s which are connected with 1,~rgc solar flares ~re however ex t remely r a r e ,
sO
444 B. PETERS
Pr imary cosmic rays whose energy exceeds --~ 20 GeV ~re not affected b y solar activity, they show no t ime variution and are, therefore, complete ly isotropically distr ibuted in the surrounding space.
Le t us now briefly describe the chemical composition of the p r imary ra- diation (see PWTE~S [7], APPA RAo et al. [14]). When the comparison is made
between p~rticles of equal energy per nucleon the hydrogen-hel ium ratio of 15 is the same as the corresponding abundance ratio es t imated for the universe
as a whole. The elements C, ~, O and the heavier elements up to iron seem
to be five to ten times more abundant with respect to hydrogen in cosmic r~dia-
t ion than they ~re in the universe. The group of elements Li, Be and B whose
universal abundance with respect to hydrogen is low (3.10 -9) ~re ~ 10000~
times more abundan t in the cosmic ra4iation. The large discrepancy between the abundance of the last ment ioned group of elements in the cosmic radiat ion and its abundance in the universe as ~ whole, is connected with collisions of
complex pr imary cosmic ray nuclei in interstellar space. We shall re turn to
this point l~ter. When the comparison is made between particles of equal kinetic energy
(not energy per nucleon), then hydrogen accounts for only half of the intensity,
helium for one quarter, the group of light nuclei C, ~ , O ~nd ~11 elements
heavier than oxygen account each for one eighth of the to ta l intensity.
I f we confine ourselves to particles whose kinetic energy exceeds 0.5 GeV/nu- cleon, the particle density of the nucleon component in the neighbourhood of the ear th amounts to 1.7"10 -1~ nucleons/em 8 and the energy densi ty to 0.56 eV/cm 3. This energy density is somewh~rt larger bu t of the same order of magni tude as tha t of starlight in our parts of the galaxy.
Informat ion on cosmic radiat ion in the neighbourhoo4 of the ear th is based on nuclear emulsion- and on counter- and ionization chamber measurements c~rried out near the top of the atmosphere; in the ease of the very largest energies, it is b~sed on measurements of large p~rticle showers observed on the ground.
5. - The chemica l compos i t ion of nuclear primary radiat ion and its h i s tory
of m ot ion .
A number of conclusions can be drawn from the chemical composition of the nuclear component which are re levant to the origin of cosmic radiation. The mere fact t ha t the pr imary r~diation contains not only nucleons bu t also complex nuclei shows, tha t the particles cannot h~ve t raversed a large ~mount of m~t ter af ter acceleration, not more, in any case, than corresponds to one
or two mean free paths for collision of iron nuclei in interstel lar hydro-
O R I G I N O F C O S M I C R A D I A T I O N 445
gen. This amounts to perhaps 5g/cm ~. A more precise value is obtained from the relative abundance of Li, Be, and B, those light nuclei which
are extremely rare in the universal abundance of elements, but which ap-
pear in measurable amounts in the primary cosmic radiation. In the upper
atmosphere one observes that the ratio of (L iq -Be§ to (C+1#§ is much larger among primary nuclei incident under large zenith angles than it is among
those coming from the zenith direction. The ratio increases rapidly with the thickness of the air layer which the particles have traversed before reaching the detector. This gives a clue as to why these light nuclei are present in the
primary radiation with a relative abundance which is 100000 times higher than in the universe as a whole. They arise in nuclear collisions by partial break
up of the heavier primary component, in particular in collisions of carbon with
hydrogen. C-p collisions lead in more than 70 % of all cases to a residue of atomic
number Z = 3,4 or 5. (The remaining cases are those where the carbon nucleus is completely disintegrated into nucleons and a-particles.)
The ratio ( L i § to (C§ ~ 8~o which is observed at the top of the atmosphere (APPA RAp et al. [14]) implies that the nuclei which reach the solar system have traversed only about one half g/em ~ of hydrogen (but in any ease not more than one g/cm ~) since the early stages of acceleration when their energy had reached the few MeV/nucleon necessary to overcome
Coulomb repulsion and produce nuclear reactions. The condition that the
primary particles have traversed only a very small amount of interstellar
matter when they reach the solar system is not easy to satisfy and places strong
restrictions on acceptable theories of cosmic ray origin.
Because the amount of matter which has been traversed is small, one can conclude that the relative abundances of the main nuclear components have not changed much during transit through space. The chemical composition of the primary radiation reflects the composition of the source region; the com- paratively high percentage of nuclei in the range of atomic numbers between carbon and iron must be a property of this source. The fact that the flux of helium nuclei in the cosmic radiation is of a magnitude to be expected from its universal abundance suggests that the inital acceleration takes place in a region which is sufficiently hot and rarified to insure that helium atoms are comple-
tely ionized in spite of their high ionization potential. One of the most remarkable features of the primary radiation is the fact
that all components have the same energy spectrum over a very large range of energies. This is not only true for the heavy particles which, once they have been stripped of electrons, have identical charge to mass ratios and therefore, follow identical trajectories in an electromagnetic field; also the proton
component, for which the charge to mass ratio is always higher than for complex nuclei, has the same energy spectrum. The experimental fact~ tha t the energy distribution does not depend on the charge of the nuclei is, of
or
4 4 6 B. PETERS
course, a s t rong restr ict ion on acceptable explanat ions of the mechanisms
for part icle acceleration.
A successful theory will have to explain fur ther why, a t least in our neigh-
bourhood, electrons are much rarer than nuclei of comparable energy. I t
mus t account for the to ta l cosmic r ay in tens i ty and suggest an adequate source
~o supply the necessary energy. Fur the rmore , it mus t provide an explanat ion
for the high degree of spat ia l i so t ropy in the cosmic ray flux near the earth.
Le t us see how the super nova theory deals with these problems.
6. Cosmic ray nuclei and electrons in the galactic halo.
We have a l ready ment ioned tha t the magnet ic fields which seem to exist
in the galactic halo and in the galactic disc are of the same order of magni tude
and t h a t the radio noise emi t ted f rom the halo region does not depend s t rongly
on coordinates. Therefore, the densi ty and energy distr ibution of electrons
also should be reasonably cons tant th roughou t the main body of the galaxy.
This m a y be assumed to hold also for the nuclear component and one m a y
therefore t ake for d is tant regions of the ga laxy the same nucleon energy
dens i ty (W~= 0.56 eV/cm 3) which is found near the earth.
An interest ing question is whether the electrons, which ~re found at grea t
distances f rom the galactic plane, :~re those which were originally dispersed f rom the gaseous envelope of super nova explosions and have diffused into
the halo, or whether they are locally produced as decay products of mesons resul t ing f rom nuclear interact ions of p r i ma ry nuclei in interstel lar space.
There are fair ly strong arguments in favour of the la t te r hypothesis the
mos t i m p o r t a n t being tha t , as shown below, the energy given to electrons produced as a result of nuclear interact ions in the interstel lar gas appears to
be of the same order of magni tude as the energy radia ted by the electrons
which are reponsible for the emission of radio noise f rom the galactic halo.
The average t ime T, between nuclear interact ions of p r imary protons is
1 Tp = ~tGc '
where one m a y take for the gas densi ty n = 10 -2 hydrogen a toms /cm a and for the p-p cross section a = 30 mb. One then finds T - - 10 t7 s = 3.109 yrs.
This is comparab le though less than the age of our ga laxy es t imated as 6.109 yrs.
I n a nuclear encounter a high energy pro ton loses an es t imated 30% of its
ene rgy to meson production. One third of this t ransforms into neut ra l mesons
a n d escapes f rom the ga laxy in the fo rm of ~,-rays. Of the remain ing two
thh'ds, 26~o are t r ansmi t t ed to electrons via ~-tz-e decay.
O R I G I N OF COSMIC R A D I A T I O N 447
t I e a v y nuclei also contr ibute to this electron component . Their life span
be tween collisions is shorther than t ha t of protons, but the result of first col-
lisions is m'~inly the bre.d~up of the complex nuclear s t ructures into smaller
f r agments ; the conversion of their energy into mesons does not proceed much
fas ter than in the c~rse of protons.
One may, therefore, es t imate the energy input into the electron componen t
to be Pe=-~'O,30"O.26"(WN/T~)V- 5"10~7 erg/s, where V - - 106s cm ~ is the
es t imate4 volume of the galactic halo.
With the assumpt ions made for the gas- and magnet ic field densi ty in the
halo the main energy loss of electrons with more t han 0.5 GeV is due to syn-
chrotron radiat ion. The power input of 5-10 :.7 erg/s can, therefore, be compared
d i rec te ly with the measured power radia ted b y the ga laxy in the form of radio
noise. Within a factor two this has a value of 2.5.10 ~s erg/s. I n view of the
roughness of the es t imates involved, it is s tr iking t h a t the two numbers come
out to be of the same order of magni tude.
h i addit ion to calculating the to ta l energy which goes into the electron
component , one can also es t imate the electron energy spec t rum if one is willing
to make certain simplifying assumptions abou t the meson product ion process.
We shall assume tha t in the energy in terval of interest , the degree of ine-
lasticity, t ha t is the fract ion of the avail~ble energy which goes into meson
product ion, remains constant . We fur ther assume t h a t in this in terval the
mul t ip l ic i ty of meson product ion varies with p r ima ry energy as E ~. The average
e n e r g y of the mesons and their decay products varies then as E "~ and a diffe-
rent ia l nucleon spec t rum propor t ional to EN r gives rise to an electron spec t rum 4 - - 2 propor t iona l to Eo , where ~ = 3 Y Using the exper imenta l exponen t
: y : 2.5 for the nuclei, one obtains ~ ~ 2.67 in close agreement with the
value 2.64 derived f rom the wavelength dependence of galactic radio emis- sion. Thus, it seems t h a t an electron density, which is one hundred t imes
smaller than the nucleon densi ty an4 has near ly the same energy dependence, could be produced by collisions of cosmic ray nuclei with interstel lar hydrogen
and could give rise to a galactic radio emission with in tensi ty and wavelength
dependence in agreement with wha t is being observed. There is, however, an unresolved difficulty with this picture. I f one con-
t inual ly injects electrons with an energy spec t rum propor t ional to E~ ~ and if
t hese electrons are subject to ~ ra te of energy loss propor t ional to E~ (as they
are when synchrot ron radia t ion dominates other losses), then a s teady s ta te
spec t rum is established with an exponent ~ + 1 . The t ime necessary for
reaching this s teady s ta te is of order 1'~ which under the conditions prevai l ing
in the galactic h,do lies between 10 s and 109 years. One should, therefore,
e x p e c t an electron spec t rum in the ]lalo which is s teeper t han the spec t rum
of cosmic ray nuclei assumed to be responsible for their production. This
difficulty has not been resolved. The question as to whether the cosmic r ay
448 B. PETERS
electrons in the halo are accelerated together with the nuclear co m p o n en t and get there by diffusion, or whether they are secondary to the nuc lear
component cannot yet , therefore, be answered with confidence.
7. - The energy requirement .
The to ta l energy to be supplied by the super nova and nova mechanism
should be compared with the rate _P~ at which cosmic ray nuclei lose energy
to the charged and neutra l meson component . Using the same constants a s before one finds /)~ ~ 2.6.108Serg/s. Assuming a f requency of super novae outbursts , Vs~ ~ 10-2/year ---- 3-10 -20 s -1, the average super nova should supply
_PN/vs~ ~-1048 erg. This is approximate ly equal to the energy est imate which
we have made for the high energy electrons in the Crab Nebula.
Of course, one has no r ight to assume tha t super novae outbursts in o u r
ga laxy have occured at a constant ra te or t ha t the size of the galaxy and its f ! ' field and ma t t e r density have remained unchanged for a period of length 1 , .
The est imates are made here only to show that , so far, no violent discrepancies:
in orders of magni tude arise from the postulates of the theory.
8. - The d i f fus ion of cosmic ray nuc le i in the galaxy .
Next , one m a y consider how this picture of cosmic ray nuclei cont inuously colliding with protons of t h e interstellar gas can be reconciled with the fact. t ha t the nuclei observed in our neighbourhood have not suffered m an y collisions: and have not t raversed more than one g/cm '2 of hydrogen before arriving.
GINZBURG [3] has discussed this problem. He has used a model in which the tu rbu len t magnetic clouds are t rea ted as scattering centers, and the motion of cosmic ray particles is described as a spherically symmetr ic radial diffusion of particles outwards from the galactic center where most of the super novae explosions are assumed to occur. In such a model the chemical composition of primaries near the galactic center will be tha t of the source, and the larger the distance from the center, the older the particles, which means tha t they
have on the average t raversed a greater amount of gas and suffered a greater number of spallation producing collisions. GrNZBURG has tr ied to show that~
it is just possible, by choosing a ra ther large distance L(3.102~ cm) between scat ter ing centers, to keep the rat io ( L i + B e ~ - B ) to (C-~N-~O) below 1 0 % at a distance f rom the galactic center corresponding to tha t of the solar system. Wi th in errors, this would still be consistent with the composition observed fo r the particles incident on the atmosphere.
One can, however, raise objections to this calculation. Firstly, the yield
O R I G I N O F C O S M I C R A D I A T I O N 449
of Li, Be, B fragments in collisions of heavier primaries with protons is likely to be considerably larger than assumed by GI~zBu~G; the values used by him were derived from experiments involving the f ragmenta t ion of nuclei in colli- sions with complex target nuclei ra ther than with hydrogen. The second serious object ion is tha t a model of diffusion which demands irregular and randomly
oriented magnetic fields is not applicable to the motion of particles in the
galactic disc, where apparent ly the fields are not chaotic bu t are oriented along the spiral arms. Since the solar system is located inside a spiral arm,
the particles which reach it f rom the direction of the galactic center must
spiral along those lines of force. The resul tant anisotropy in the motion of
particles in the galactic disc is reflected in an anisotropy of radio noise, as
was recent ly pointed out by T u ~ E R [15]; it gives rise to a br ight belt of radio emission which is perpendicular to the galactic plane and to the direction of our spiral arms and seemingly passes through the sun.
If one assumes tha t cosmic ray particles reach the solar system by traveling along our spiral arm, there is no longer any difficulty with keeping the amount
of ma t t e r t raversed sufficiently small to account for the scarcity of fragmen- ta t ion products among the complex pr imary nuclei.
Assume an isotropic emission of particles f rom the super nova envelope.
Then the average amount of ma t t e r t raversed by a particle traveling a dis-
tance L along the spiral arm is given by
1
_/" d cos 0 ( x ) = eL I c o ~ - ' d
cos 0 = Cos 0ma.x
where 0 is the pitch angle of the spiral motion. I t is reasonable to assume tha t the drif t velocity of the particles, c cos0, can, except for brief periods, not be smaller than the veloci ty u with which clouds of gas and resul tant distortions
of magnetic fields t ravel in the galactic plane. One can then write cos 0ma x = U/C .and
C <x> = ~)L log --.
U
O u r distance from the galactic center L =- 25 000 light yrs. The mat te r density
in the disc is usually taken as ~ = 10 - ~ g/cm ~, and the velocity of clouds as u - - 5 km/s. This leads to x = 0,25 g]cm 2, which is less t han the max imum
permissible value of 0.5 to 1.0 g/cmq There is, therefore, no inconsistency in assuming tha t the particles which
one observes entering the earth 's a tmosphere originate near the center of the galactic plane and t ravel along the spiral arms where the magnetic field is
known to be fairly homogeneous.
5 5 0 B. PETERS
The spiral motion automatical ly insures an isotropic distribution of par- ticles in the plane perpendicular to the spiral arm. I t does not, however, provide symmet ry in the forward and backward directions along the arms. The sym-
m e t r y which one observes in the pr imary radiat ion which enters the atmosphere
must be the effect of a reflection of particles by magnetized gas clouds presum-
~bly in the p lanetary system. There is evidence tha t such reflections of part ic les in the neighbourhood of the sun do, in fact, take place. On Feb rua ry 23, :1956
a ve ry large flare occurred on the sun and a large burst of nuclei, accelerated
at the sun, struck the earth. Most of the particles were of low energy, bu t there were some with an energy as high as 50 GeY. The particles cont inued to arrive for ma ny hours af ter the flare had subsided. ~ 'hi le the flux initially was highly anisotropic, a tendency for reaching isotropy was observable, as soon as the visible flare had disappeared and complete isotropy was established
soon thereaf ter (DOR~A~', [13] LiJs~r and SI~reso~, [16]). This must have been due to reflections from magnetic inhomogeneities inside the p lanetary system
located within a few, light minutes from the sun. I f a similar configuration of
magnetic fields extends over a much larger distance, particles with correspon-
dingly higher energy will be rendered isotropic b y the same mechanism. If the
magnetical ly disturbed region surrounding the sun extends to a distance of the order of a light year, the observed isotropy could be locally produced even for particles whose energy is great enough to initiate ve ry large air showers.
In the picture outlined here the isotropy which one observes for the cosmic ray particles entering the earth 's ~tmosphere is essentially a local phenomenon and is due to the fact tha t we are located in the neighbourhood of a star which ejects ionized gas clouds and therefore surrounds itself with turbulent mag- netic fields. In the space between stars the radiat ion in the spiral arm m ay not be isotropic and the distribution of radio noise is an indication of that . Of course particles which reach the solar system may already have suffered some reversals of direction in the spiral arm before arrival. There could not however have been more than two or three such reversals, otherwise, the amount of gas t raversed by particles before arrival would have to exceed the permissible l imit derived from the ch~rge composition of pr imary nuclei.
Once the particles leave the spiral arm and enter the galactic halo the fields are probably more randomly oriented and in tha t region the motion of
particles can perhaps be adequate ly described as diffusion. We have seen t h a t it will take a t ime of order Tp, which is of the order of the age of the galaxy~
before this halo is filled to its saturat ion value with cosmic r,~y nuclei. A large fract ion of the older particles will h~ve already suffered collisions with a resu l tan t change in atomic weight and atomic number. Presumably, therefore, the galactic h 'do contains fewer complex nuclei them are to be found in the neigh-
bourhood of the earth.
O R I G I N OF COSMIC R A D I A T I O N 451
9. - Condit ions at the galact ic boundary .
I t is interesting to consider the question whether particles which approach the boundary of the galactic halo, are efficiently reflected, or whether they
can escape into extragalact ic space. If the magnetic fields arise enth'ely f rom
a system of currents within our own galaxy, the magnetic lines of force are
closed and reflection should be very efficient. If, on the other hand, there are large extragalactic currents so tha t our galaxy is magnetical ly linked with other systems, particles will be able to escape and travel beyond the galactic boundary. We have already mentioned tha t the low level of radio noise in the
clouds of Magellan speaks in favor of the retent ion of particles within the
boundaries of the galactic halo. Apar t from that , there is no strong a rgument at present which has a bearing on this question. I t is t rue tha t if the loss of
particles through the boundary were appreciable, the power ou tpu t of the
sources of cosmic radiat ion would have to be correspondingly higher. I t must,
however, be remembered tha t the loss of particles through the boundary does not only depend on the number of magnetic lines of force leaving our
gal~xy. I t also depends on the diffusion length in the halo which means effectively on the mean distance between magnetic inhomogeneities which act ~s scattering centers. If the diffusion length is very small, particles will
in general lose their energy by nuclear collisions before reaching the boundary. Exist ing estimates, though not very reliable, indicate tha t the diffusion length
is probably sufficiently small compared to the radius of the galactic halo so
tha t diffusion length ra ther than the reflectivity at the boundary determines the space density of cosmic radiat ion in the galactic halo.
lO. - Cosmic ray nuc le i in super n o v a enve lopes .
We shall now briefly discuss conditions for particle acceleration in a super nova. One of the first questions one c~m ask is. Does the acceleration occur during the explosion itself or ~t some la ter stage by a mech~mism which ope-
rates in tile expanding gas envelope? A simple calculation shows theft the first a l ternat ive would lead to con-
t radict ion with exper iment ; if the acceleration had taken place during the explosion or during the earliest phase of the gas expansion, the amount of
mat te r t raversed by the accelerated particles would have to exceed consi-
derably the upper limit of ] g/cm" set by the relative abundance of Li, Be
and B in the prim~ry cosmic radiation. Suppose one considers the Crab nebula as typical and follows the astrophysical est imate tha t the gas which was expelled by its central star has ~ m'tss of approximate ly 0.1 solar masses.
4 5 2 B. PETERS
Then the gas density in the envelope is
0.1Mo ~(t) = ~ ( R o + vt)~ '
where v is the velocity of expansion and Ro the radius which the envelope had when acceleration began. The composition of the nuclear component requires tha t x (the amount of ma t t e r t raversed by the particles during the
expansion of the envelope) is less than i gm/cm ~. Therefore
x =f~c dt 0
< 1 g/cm z ,
where T is the t ime at which particles escape and the envelope dissolves into the outer space. One finds tha t only small values of t can contr ibute appreciably
to the integral and tha t therefore the result does not critically depend on the durat ion T of the expansion process. One can write, therefore
[ 0.1Mo ]�89 R o ~ ~ - - ~6"1016 [~7c(v/c)x] cm .
This is 4 000 times larger than the distance from the sun to the ear th :and implies tha t the cosmic ray nuclei have been accelerated several decades a f t e r the original explosion.
Similarly, one can show tha t in the earliest stages of super novae act iv i ty the energy loss of electrons due to the inverse Compton effect will be so large
as to effectively prevent their acceleration. The problem is, therefore, to find an accelerating mechanism which will
work long after the expulsion of the gas. A very a t t rac t ive hypothesis originally proposed by FERMI [~:], is t ha t particles are accelerated by a statical mechanism. The nuclei collide with magnetic clouds which move with the velocity u. The
par t ic les are reflected provided the clouds are larger than the particle 's radius of curvature . There is a tendency to establish a Bol tzmann distr ibution and
to reach a s tate of equipart i t ion of energy between the particles and the enor-
mously more massive clouds. This tends to increase the particle energy at
the expense of the clouds. The process is t ru ly statical in the sense tha t it
does not depend on the details of the interaction, f.i. i t does not depend on the s t rength of the field H, nor on the electric charge Ze carried by the particles. On the average the increase in energy per collision amounts to
~2 AE ---- ~. E,
ORIGIN OF COSMIC RAI) IATION 45,'~
where E is the par/i(.le cner~'y including rest mass.
energy becomes :
E = M c ~ e x p J ~ ] ~ , . .
After n collisions the
I f the entire prot'ess lasts for a t ime T, the probabi l i ty t ha t a p a r l M e will have
undergone between n and n + d n collisions is ~'iven by
W(,)<lr~ ::: ~ exp d~l,
where z = L/v is the mean t ime interval between such collisions, v is the
p a r t M e veh)city and L is the average distance between the clouds. This leads
to an energy spee t rum
K d E c" L cL W(E)d(E) = E r ; where y ~ 1 + u ~ , ~ 1 + u 2 T .
Tile mechanism was originally supposed to be operat ive ill the interstel lar
space. Bu t there tile cloud velocities u seem to be too small and the distance
between clouds L too large to provide a sufficient ra te of acceleration. I t may,
however, be operat ive in the envelGpe of super novae. I t would satisfy impor t an t
requi rements imposed by observat ion:
, ) I t leads to a power spec t rum whose exponent is independent of the na ture of the particle, in par t icular of its eleetrie eh.u'ge and of the charge to
mass ratio.
b) I t is effective in any tu rbu lan t gas cloud and does not require critically
adjus ted configurations of fields.
c) The physical constants appropr ia te to an expanding super nova
envelope are sut,h tha t they could lead to the observed exponent of the power
speotrum.
d) The constants are such as to make possible the acceleration of nuclei
at a ra te which is larger than their rate of energy loss even if a part icle carries
a high nuclear chm'ge and s tar ts out a t a fair ly low energy.
c) The ,~eceleration is likely the last long enough to permi t some nuclei
to reat,h the highest energies observed in cosmic radia t ion; the dimensions and
magnet ic fields in the envelope could be adequate to re ta in such particles provided they are heavy nuclei so t ha t their m o m e n t u m per nucleon does not
have to exceed a few times 10 TM eV/('.
29 - :~'Upl)h'menlo al A ' m w o ( ' i m e n , lo.
454 B. PETERS
There are, however, some difficulties with this picture. One is, t ha t tile exponent of the power law is very sensitive to the value of not ve ry simply
related quantities. The life span of the super nova envelope, T, the velocity,
u, and the size L of the turbulen t elements. While it is possible tha t in a par t icular envelope these constants combine in such a way as to give a value
for y which is close to the exper imental ly determined exponent , there seems
to be no obvious reason why different super novae should not have values of 7, and, therefore, radio f requency spectra, which differ ve ry considerably from each other. ~ o t many centers of radio emission have been observed so far, bu t those which have been investigated, suggest a ra ther narrow range of values, 7, lying between ].5 and 3.
More serious perhaps is the problem of the ratio between energy stored
in the electron component and energy stored in the nuclear component . When
operat ing for a fixed period the Fermi mechanism accelerates particles to an
energy proport ional to their rest mass. The energy in the nuclear component
should~ therefore, be circa 2 000 times larger than tha t in the electron com- ponent . I f one takes into account tha t electrons may be handicapped because of the m a ny mechanisms by which they can lose energy in the interval between
accelerating collisions, the ratio becomes still larger. An energy which is 2 000 times higher than tha t present in relativistic electrons would exceed the entire kinetic energy of the super nova envelope and could, therefore, not
possibly be t ransmi t ted to the nuclear component by a Fermi mechanism. One might think tha t the ratio of nuclei to electrons could be reduced by
assuming tha t while nuclei and also some electrons are accelerated by the Fermi mechanism, the major i ty of the electrons in the super nova envelope have not been accelerated in this manner bu t arc the result of nuclear interactions. The rat io between high energy electrons and high energy nuclei could then be determined in a way analogous to tha t which was discussed in connection with the electrons in the galactic halo. This, however, leads to another diffi- culty. The chemical composition of the nuclear component would be greatly al tered if one permi t ted more than 2 % of the protons and a correspondingly larger fract ion of complex nuclei to collide while moving inside the super nova
envelope. I t is, therefore, not possible to obtain in this manner a lower ratio
of nuclei to electrons wi thout at the s~me t ime altering the chemical compo- sition of the nuclear component in a way which is not consistent with
observation. One is apparent ly forced, either to abandon the Fermi mechanism and
assume tha t most of the energy tha t appears in relativistic particles comes f rom the star itself ra ther than from the kinetic energy of the gases in the envelope, or else to assume tha t one has overlooked un impor tan t feature in the accelerating process which favors electrons over protons. Such a feature m a y be the fact tha t ~-decay of radioactive nuclei provides a strong source of
ORIGIN OF COSMIC RADIATION 4 5 5
electrons which are already relativistic and will therefore, gain energy more
rapidly than they would if they had to s tar t at low energy.
I t would be most impor tan t to discover the electron component in the
pr imary radiat ion and to measure the sign of charge. In our par t of the galaxy where the primaries have undergone only few collisions before arrival, the
electrons are probably those dispersed by the super novae ra ther than decay electrons of mesons produced in nuclear interactions after the nuclei had escaped
into the inter-stellar space. The origin of electrons in the super nova envelope could then be decided by measuring their ch'~rge. They will be negative if
t hey bare atomic electrons or result from the E-decay of neutron-rich nuclei. They will be half positive, half negative if they originate in nuclear interactions.
Another impor tan t exper iment would be to determine the atomic number
of the primaries giving rise to extensive air showers. I t is known tha t the com-
position of the pr imary cosmic radiation does not depend on energy in the
interval extending from less than i GeV/nueleon to more than 1 000 GeV/nucleon. Once particles have been accelerated to such an ultra-relativist ic energy, it
would be difficult to devise a mechanism which can distinguish between par- tMes of different rest mass and discriminate against light or heavy nuclei in fur ther acceleration. I t is therefore reasonable to assume tha t the same com- position which one observes at lower energy persists in the energy range
where air showers are produced. This means tha t protons, a-particles, the
C, N, O group and the heavier primaries each have a comparable share in
producing air showers of a given size. I f now one accepts a theory where the mechanism of acceleration is confined
to a restr ic ted space, the acceleration will be te rminated when the radius of curvature of the particle trajectories becomes comparable to the 4imensions of the region in which the mechanism operates. Then for each component the max imum energy will be tha t corresponding to this max imum radius of cur- vature . I t follows tha t the highest par t of the pr imary energy spectrum should
be popula ted entirely by the heaviest nuclei. I t would be impor tan t to ver i fy this prediction. I f it turns out to be true,
then the largest Mr shower observed so far with an energy a few times l0 is eV
was produced by a p r imary particle with magnetic r igidity H R a few times
1014 G e m . I t seems possible tha t particles up to such a rigidity can be retained
in super nova envelopes. I f on the other hand, the largest air showers are to
be a t t r ibu ted to protons, then the magnetic r igidity of the pr imary would have to exceed 7.10 l~ G cm. The t ra jec tory could not be contained unless
there are considerably higher magnetic fields in a super nova envelope than
are generally assumed.
456 B. PETERS
R E F E R E N C E S
[I] I. S. SKLOVSKIJ: Dokl. Akad. Nauk, SSNR, 91 (3), 475 (1953) and other references given in GINZBURG [3].
[2] 1. 5. ~KLOVSKIJ: Suppl. Nuovo Cimeuto, 8, 421 (1958). [3] V. L. GINZBUR(~: Progr. in Elementary Particle and Cosmic Ray Phys., vol. 4
{Amsterdam, 1958). [4] E. FERMI: Phys. Rev., 75, 1169 (1949). [5] E. FERMI: Astrophys. Journ., 119, 1 (1954). [6] V. L. GINZBURG: Fortschr. d. Phys., 1, 660 {1954). [7] B. PETERS: Progr. in Cosmic Ray Phys., vol. 1 (Amsterdam, 1952). [S] M. F. KAPLON, B. PETERS, H. L. REY~NOLDS and D. M. RITSON: Phys. Rev.,
85, 295 (1952). [9] F. B. McDONALD: Phys. Rev., 109, 1367 (1958).
[10] D. LAL: Proc. Ind. Acad. Sci., 38, 93 (1953). [11] G. CLARK, J. EARL, W. KRAUSHAAR, J. LINSET, B. RO~SI and F. SCHERB: Naivete
180, 353 (1957) [12] C. L. CRITCHFIELD, E. P. NEY and S. OLE8KA: Phys. Rev., 79, 402 (1950). [13] L. I. DORMAN: Cosmic t~ay Variations, English Translation. [14] M . V . K . APPA RAO, S. BISWAS, R. R. DANIEL, i . A. NEELAKANTAN and
B. PETERS: Phys. Rev., 110, 751 (1958). [15] H. TtlNMEIr Phil..Mag., 3, 370 (1958). [16] R. Lt3ST and J. A SIMPSON: Phys. Rev., 108, 1563 (1957).
