SUPPLEMENTO AL VOLUME III , SERIE X BT. 1, 1 9 5 6 D E L NUOVO CIMENTO 1 o S e m c s t r e

The Nature of Cosmic Radio Emission and the Origin of Cosmic Rays.

V. L. GINzBu~G

Academy of Sciences o] the U S S R - Moscow

CONTENTS. - - 1. Introduction. - 2. The magnetic bremsstrahlung nature of cosmic radio emission. - 3. The origin of cosmic rays.

1 . - I n t r o d u c t i o n .

In order to formulate a theory of the origin of cosmic radation (c.r.) it is ob- viously necessary to have a certain amount of information on the composition, energy spectrum and spatial distribution of the c.r. outside the earth's atmos- phere, in the solar system, in the Galaxy and between galaxies. However, up to very recent times only data (and very incomplete at that) on cosmic rays in the immediate vicinity of the earth (at top of atmosphere) have been available. As a result of this, various theories of origin of the cosmic rays were founded on ra- ther arbitrary hypotheses and even the foundamental question concerning the sources and mechanism of acceleration of c.r. particles r,emained obscure. One Of the main aims of the present paper is to demonstrate that with the develop-

ment of radioastronomy this state of affairs has radically changed. Thus, if one

interprets the non-thermal cosmic radio emission as being a type of magnetic bremsstrahlung (radiation from electrons accelerated in interstellar magnetic

fields) then radioastronomical data permit one to determine the spectrum

and concentration of relativistic electrons of the primary c.r. in the Galaxy and beyond it. Thus the theory of origin of c.r. can rest on a reliable foundation; it now becomes a branch of astrophysics based on empirical data. The nature of cosmic radio emission will be considered in the present paper and a theory of the origin of c.r. based on radio astronomical data will be descri- bed (a more detailed account of the theory is given in [1-3]).

THE NATI.IRE OF COSMIC RADIO EMISSION ETC. 39

2. - The Magnetic Bremsstrahlung Nature of Cosmic Radio Emission.

Cosmic radio waves emitted with a continuous spectrum consist of radiation from discrete sources and of (~ general ~ cosmic radio emission which varies re- latively slowly with the galactic coordinates. The general radiation can in turn be resolved into metagalactie and galactic components. Finally the galactic radio emission may be divided i n t o thermal and non-thermal components. The first of these is the thermal radio emission from interstellar gas and, similarly to the gas, it is located in the plane of the Galaxy. Naturally, the corresponding maximum effective temperatur e of the radiation, T~, cannot exceed the ki- netic temperature of the gas and therefore cannot exceed ~ 10 000 ~ How~: ever, in the direction of the Galaxy anticenter and pol e the optical thickness of the gas is small and even for waves in. the meter band the thermal radio emission intensity is weak (To~f ~ 1000 ~ ; ~he same m a y also be said about the metagalactic radio emission. On the other hand the total intensity of cosmic radio emission of wave length say of 16.3 m travelling from the galactic pole corresponds to an effective temperature Te~ ~ ,--50000 o. This signifies that there exists some type of non-thermal general galactic radio emission which depend s weakly on the galactic coordinates and which compared with thermal and metagalactic radiation is of decisive importance in the meter band. From an analysis of the cosmic radio emission isophotes it has been concluded [4] that the non-thermal galactic radio emission comes from a quasispherical sub-system, a sort of corona which surrounds the stellar Galaxy. The radius of this sub-system is R ~ 3 +5.10 ~ em. Diffuse interstellar gas with a concentration of n ~0.1 cm -s possesses about the same spatial distribution [5].

A convincing proof of the existence in the Galaxy of radio sources distri- buted in the manner described above is the discovery [6] of a similar i( radio corona ~ around the nebula ~ 3 i in Andromeda which resembles our own Galaxy.

What is the nature of t h e non-thermal galactic radio emission? Even at the present time attempts are made to explain One radio emi~si0n as originating in a l~rge number of hypothetical radio stars invisible in the optical range of the spectrum. This assumption, which for a number of reasons has always seemed to us to be improbable, becomes altogether untenable after the dis- covery that the discrete sources of cosmic radio waves are nebulae and not stars. There is therefore absolutely no justification in assuming the existence of an enormous number [4] of radio stars possessing some very queer ProPerties and a very unusual spatial distribution. The(( magnetic bremsstrahlung hypO- thesis ~) which associates non-thermal cosmic radio emission with the waves ra- diated by relativistic electrons moving in the interstellar magnetic field [7-9,~1-3]

40 V . L . GINZBURG

seems to be much sat is factory in this respect . I t will be shown in the following t h a t not only this hypothes is c~n be made to agree with the p robab le values

of the interstel lar magne t ic fields and with the concentra t ion of relat ivist ic

electrons, bu t t h a t i t is ve ry frui t ful for radio a s t ronomy as a whole and for

the theory of origin of c.r. As is well known, in a magne t ic field H an electron moves along a helical

p a t h ~vith a cyclic f requency

eH mc ~ (1) (-oH . . . . ,.

mc E

where E is the to ta l electron energy. I n the u l t ra relat ivist ic case, which

is the only one of interest here, th~ electron radia tes electrom~gfietic w~ves

~lmost exclusively into a narrow cone whose angular aper ture is 0 .-~ mc~/E << 1

in the direction of ins tantaneous velocity. Therefore, if the electron moves

in circle, an observer a t rest will <~ see )~ radia t ion pulses of dura t ion

At o ~ E / \ e~ / '

where r is the radius of the orbit. If, however, the electron moves along a helix and the angle a be tween veloci ty and field is not too small (*) then

At~..(mc/elt• ~, where H i is the componen t o f the magne t i c field

perpendicular to the direction of motion. The radia t ion spec t rum will cor-

respondingly consist of over tones of the f requency ~% and pract ical ly m a y be

considered as a continuous spect rum, the m a x i m u m being a t a f requency

~m~,~, 1~At.-. (eH• ~. Calcuiatibns show (see for example [10]) t h a t the energy rad ia ted b y an electron per second in a f requency range dv is

P(v, E) dr, where

P(v, E) ~-- PO') ~--- 2zP(o)) ---- 16 p ---- 16 - - wa• 17(u)

(2)

[ ~s• me E ' ~ m - - ' u~ me ~ , u = :Y(u)- -

Values of the funct ion Y(u) are given in the table ; in the l imit ing cases

(3) co << 1 : I7---- 0.256, w__ >>1 : IZ(u) ---- (27~)�89 u~ exp [ - - (4/3)u~]. eom wm 16

(*) The radiation will be of a different nature if the angle a H O'~mc2/E; this case is of interest for the theory of solar sporadic radio emission [11].

THE NATURE OF COSMIC RADIO EMISSION ETC. 4'1

u 17(u) u 1F(u)

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

0.256 0.204 0.156 0.115 0.081 0.055 0.036 0.023 0.014

1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.5 4.0

0.0085 0.0050 0.0028 0.0015 0.0008 0.0004 0.0002 0.00004 0.000006

The funct ion p(w/o~,.) has a m a x i m u m at co = 0.5co~, where i t equals 0.1.

Thus a t the m a x i m u m

(4)

e a ~ { • [ P(v~.x) = 1.6 - - 2.15-10-22H• erg/cycle

mc 2

vm.x = 0.5 = 1.4" lOeH• ~ cyele/s 6

The intensi ty observed a t the ear th will be

(5) I, = l /P(v , E)No(E, r )dEdr ,

where h r (E , r) is the differential electron spec t rum a t the point r . In t eg ra t ion

is carried out along the r ay of Vision and i t is assumed tha t , due to the r a n d o m

dis t r ibut ion of the field H, the radia t ion on the average is isotropic (hence the factor �88 in (5)). This assumpt ion means t h a t the formulae are correct to a

fac tor of the order of uni ty . Absorpt ion and possible influence of the re-

f ract ion index (which m a y be different f rom uni ty) have not been t aken in to account as they are of no consequence in the following exposit ion (see [1]).

I f the electron spec t rum does n o t change along a p a t h R and has the fo rm

(6) iV e ( E ) = ] s -~

then

(7) 0

=- ~ me ~ [ m---'3c-~-] U(y)KRv (1-~w2

- - 22 8 (y 1)/2 ( ~ + 1 ) / 2 (F 1)/9 2 1.3" 10 - (2.8" 10 ) - U(),)KRH• 2 - e r g / c m cyc le s t e r a d i a n ,

4 2 V. L. GINZBURG

co

where U(~)~fY(u)u(3r-5)14du and, for example, for y----1, 5/3, 2, 3 and 7 0

the funct ion U(~) has the corresponding values 0.37, 0.163, 0.128, 0.087

and 0.153. Da ta on non- thermal galactic radio emission in the band 1.5 m < 2 < 17 m

indicate tha t in a first approximat ion (*)

C (8) I~ , ~ a - ~- a 2 ,

F r o m (7) and (8) we obtain

a ~ 5.10 -~1 erg/cm 3 cycle s t e r ad ian .

(9) ~, ~__,~ 3 , I , _N 3.] . lO-15H*j.KR). --~ 5 �9 10=~12

and hence KH~.R,~ , I .6 .10 -3. For the reasonably highest=values of R,-~5.10 ~ cm and H• ~ 1 0 -s oerstod one obtains a minimum value K~: - - , 3-10-~9 ~ ~_

~__ 10-5 (eV):/em 3.

To be cautious we pu t K_~_ 10 -6 ~nd thus arrive at the following electron

spectrum co

106 1 3 2r > E6) = I N ( E ) d E ~ 1~ (10) No(E) --~ ~ ( e V ) - c m - , J - - ~ e m -3 ,

E+

where E and Eo are measured in eV. Hence N e (E > 109 eV) _~ 5.10 -13, which is not in contradict ion with da ta on cosmic ray electrons near the ear th (for more details see [9]). On the other hand N e (E > 10 s eV) ~-~ 5.10 -11, which in order of magni tude equals the concentrat ion of all p r imary cosmic ray part- icles incident on ~he ear th (due to high la t i tude cut-off cp ~ 109 eV). Taking into consideration the form of the funct ion Y(a), it may be shown ~ tha t the spectrum (10) should refer to the region 2.10 s < E < 3.109; uncertaint ies in the da ta permit one to lower t h e value No (E > 109 eV) by several times.

Therefore, as t h e magni tude of the interstellar magnetic field ( ~ 1 0 -5

oersted) required by the hypothesis of the magnetic bremsstrahlung agrees

with other estimates of this quant i ty and this hypothesis also yields a reason-

able value for the electron concentration, one m ay conclude tha t the magnet ic

bremsstrahlung explanat ion of the non- thermal general galactic radia t ion is

probably correct. Moreover, this hypothesis automat ical ly explains the fact t h a t not more than 1% of the pr imary c.r. with E ~ 1 0 ~ eV incident on the ear th consists of electronS. The reason of this is t ha t electrons lose energy in magnetic bremsstrahlung (which is negligible for protons and nuclei). If one

(*) More accurately Iv=a~, -a, where a=0.8--1.2.

THE NATURE OF COSMIC RADIO E M I S S I O N ETC, 43

also assumes (and ~his seems quite natural) tha t electrons, protons an d nuclei in the energy region E ~ 101~ eV are generated by the pr imary c.r. sources

with a spectrum of the same type of (6), with 7 ---- ~o --~ 2, then, due to deceleration of the electrons in the magnetic field, the electron spectrum will

have the same form as (6), bu t with 7 ---- 7o -k 1 ~-~ 3 (see [1-3, 9]). Accord- ing to (10) this is just the type of spectrum one would expect on the basis of

radio astronomical da~a (*). The proposed magnet ic bremsstrahlung mechanism m ay also be responsible

for radio emission from powerful discrete sources [7, 8]. As a ma t t e r of fact in such sources as a Cassiopeiae, ~ Cygni, a Tauri, To~ ~ 107 degrees, whereas the electron kinetic t empera tu re is much smaller. I t is impossible to explain the radiat ion from such galactic sources as ~ Cassiopeiae or a Tauri as ori-

ginating f rom hypothet ica l radio stars; t h e magnetic bremsstmhlung hypo- thesis, on the other hand, does not require any impossible assumption about the magnetic fields or the electron eoncehtrat i0n in the sources.

If the electron spectrum and the magnetic field in the source are indepen- dent of the coordinates, then the radiat ion flux from the source will be

(11) F~ ~ I v d ~ ~ (~, E)No(E) d E ,

where V is the volume of the source and R i s the dis tance f rom it. Under the opt imum conditions (4)

(12) _F~ _-- 1.6 eSH~ N~V .N~V ~ mc 2 4~R2 -- 1.7 -10-~aH• ~ erg/cm cycle,

where No is the concentrat ion of electrons; it is considered tha t these possess an energy corresponding to the frequency v =Vmax (see (4)). For ~ Tau- ri: R N 5.1031 cm, V ~--: (4gr3/3) ,-~ 10 56 cm ~, while in the meter band

F~ __~--~ 2.10 -~o erg/cm ~ cycle

and is independent on the frequency. Pu t t ing H • ~ H ~ 10 -4 which seems

to be allowed [12] we obtain f rom [12) N V,-~10 5~ and Ne,-~10-e em-3;

obviously, these values are the minimal ones. By using formulae (7) and (10) one can determine the electron spectrum, and the energy in discrete sources can

(*) Wandering of protons and nuclei in interstellar space should not change their spectrum and therefore, near the earth, y= yo~2, which is the experimentally observed value for E ~.~ 109--1011 eV.

4 4 V. L. GINZBURG

be obtained. F e r n Tauri (Crab nebula) 7 --~- 1, NoV,.-~ 1051 for E ~ 2.5.10 s eV, and the total energy Of relativistic electrons with E ~ 2.5.108 is approxi- mately W--~ 104~ -1049 erg (see [12] for further de~afls). Compared with other powerful sources the source in Taurus should be considered exceptional (*) because, in the majority of powerful sources (mostly extragalactic) 7 ~ 3; for Cassiopeia one also has N e ~ 105~ and W--~ 104s erg. The Crab nebula (a Tauri) is undoubtedly an expanding envelope of the supernova of 1054 A.D. According to [14] all other powerful g~lactie discrete sources are also enve- lopes of supernovae (thus Cassiopeia is ~ supernova of 369 A.D.).

We thus arrive at the conclusion that the torn.1 energy of relativistic electrons in the envelopes of supernovae is of the same magnitude as the energy of the optical radiation produced during the outburst. The radiation of powerful extragalactic discrete sources, according to the mass of collected d~t~, should also be attributed to msgnetic bremsstrahlung [15]. Thus, radio astronomy presents the possibility or detecting relativistic electrons in various parts of the universe. In particular, it is found that large amounts of electrons exist in the envelopes of supernovae and, possibly, of novae [12, 16, 17]. I t seems dif- ficult to overestimate the significance of this circumstance for the theory of the origin of c.r.

3 . - The Origin of Cosmic Rays.

Data on the distribution of relativistic electrons in the Galaxy speak against the theory of solar origin of c.r. and also against the hypothesis of their meta- galactic origin. One must therefore conclude that the main part of c.r. is generated somewhere in our Galaxy; these rays fill the Galaxy and form a quasi spherical system (mentioned in w i) with R ~ 5.10 ~2 cm. I t is furthermore natural to suppose that the primary c.r. sources are supernovae and novae [1-3; 12, 17] the envelopes of which contain fast electrons and probably protons and nuclei. As time passes (in about 1000 +3000 years) the supernovae en- velopes smear out and the c.r. which previously diffused from the envelope become completely distributed throughout interstellar space. Now the part- iclcs wander through interstellar magnetic fields, diffuse towards the peri.- phery of the Galaxy and simultaneously lose energy in nuclear collisions and, later on, in ionization collisions. Instead of nuclear collisions, electrons undergo bremsstrahlung collisions with the nuclei and with the electrons of the inter- stellar gas.

(*) The large amount of high energy electrons in ~ Tauri makes it probable that the magnetic bremsstrahlung mechanism is also responsible for the continuous optical radiation of the nebula [13].

THE N A T U R E OF COSMIC RADIO EMISSION ETC. 45

The electrons also 10se energy in magne§ processes discussed in w 1. For a number of reasons, the acceleration of c.r. particles in the interstel- lar space [18] does n o t seem to be an effective process anti .even at very high energies (E ~ 1013 eV/nuCleon) it probably is of no significance (see [1]). This conclusion [2] is not affected by a t tempts , which seem very inconvincing to

us, to re ta in the theory of interstellar acceleration by assuming tha t the life t ime of the particles in the Galaxy is determined by their ra te of exit f rom it [19, 20]. On the other hand Fermi 's statist ical acceleration mechanism [18] should be very effective [21] in tu rbu len t envelopes: of supernovae, where it is probably the main acceleration mechanism. Such is the picture One can draw of the origin of e.r. using radio as t ronomy data. I t is impossible for us in ~his paper to consider the theory in detail (see [1-3]) and we will therefore

discuss some of the more impor tan t points of the problem. A most impor tan t condition which any t h e o r y of origin of c.r. must satisfy

follows f rom energy considerations. I f the cross-section for energy transfer's between protons colliding in interstellar space is a ~ 2.5.10 -~e cm 2, then on the average the life t ime of fast protons in the Galaxy should be T N 4.103 years~-, ~-10~es (the concentrat ion of interstellar hydrogen is t aken to be on the average n ~ 0.1 cm-a). The e n e r g y densi ty of cosmic rays is w ,-~ 1 eV/cm 3, the to ta l energy being W,.~ wV~., 1063 eV, as the Volume of the Galaxy V ~ ~(dz /3 )R 3 ~ 1068 cm 3 for R ~-, 3 .10 ~ cm. I t is thus clear t ha t the power of the sources of primary~c.r, should be W / T ~ 105~ eV/s --~-104~ erg/s. This value is probably too high by one or two orders of magnitude, as most likely the accepted values of W and R are too high)~ Thus

(13) W/T,~ l0 ss + 10 ~~ erg/s .

Assuming tha t during s u p e r n o v a outbursts, say, 10 a8 erg appear as c.r. (see above) one finds t ha t average power of the source should be ~ 103s erg/s as on the average supernovae outbursts take place at least once in 300 years ,-~ --, 10 l~ s. I t is l ikely t ha t supernovae outbursts occur much more often, bu t because of absorpt ion they remain invisible (this a rg u m en t belongs to I. S. ~KLOVSKI5). Fur thermore , according to the est imates in [1, 2], the contri- but ion f rom novae m a y reach 3.1040 erg/s. Thus supernovae and novae can

satisfactorily provide the energy balance. I t should be noted tha t energy

considerations suggesting supernovae as possible sources of c.r. were proposed

previously [22]. However, these arguments acquire new significance when

one associates them with radio astronomical data which confirm the generation

of c.r. i n the envelopes of supernovae. I t should also be noted tha t on t h e

average the power of the e.r. generated by the Sun is of ~ 10 ~1 erg/s and therefore even 1011 stars of the solar type would yield only 103~ erg/s, which is by 6-8 orders lower then the required value (see [13]).

46 V. L. GINZBURG

I t has already been mentioned that in envelopes of supernovae and novae the particles are mainly accelerated by a statistical mechanism. This m6cha- nism is capable of accelerating protons and light nuclei (*) to the highest energies observed in cosmic rays, i.e. up to E ~ 10 is eV [1, 21] . ~ t the same time it should be emphasized that many details of the acceleration mechanism in expanding turbulent envelopes are still obscure. For this reason a reliable theoretical prediction of the spectrum of generated particles Cannot be given; moreover for different sources the spectra are different (for details see [1]).~ The spectra of electrons, protons and nuclei generated in the envelopes are probably of the same form and on the average, for energies E ~ 10 xl, ? ~ 2. Magnetic bremsstrahlung losses in interstellar space result in a softening of the electron spectrum (and therefore ? ~ 3; see above).

The proton and nuclear spectra will remain unchanged (even when nuclear collisions are taken into account) if the energy of the secondary products (i.e. energy after the collision)

(14) E~ = (~E1 ,

where 6 is independent or depends only slightly on the primary particIe energy El. The explanation of this is that relation (14) is a scale transform- a~ion, and collisions of this type do not lead to changes in the power exponent in spectra of the type (6). There are data which support this point of View [2, 23]. Furthermore, according to the theory outlined here, one should expect tha t in a first approximation a stationary state should exist in the Galaxy, i.e. tha t the concentration of the various particles should be independent of time. On the other hand, the primary c.r. sources form a plane subsystem, lying in the plane of the Galaxy (this is exactly the way novae and probably supernovae are distributed). "This leads us to the result that an approximate equilibrium number of Li, Be and B nuclei should be present in the c.r. incident on the earth; thus the concentration of these nuclei should be about four tenths the c0neentration of all other nuclei [3]. This is exactly the value which the latest avai labledata yield [24]. Furthermore, according to our point of view, the high latitude cut-off in the c.r. spectrum cannot be explained by ionization losses and is probably due to the existence of a magnetic moment of the so- lar system[9]. This conclusion is in accord with data [25] indicating that the: high-latitude cut off is of a magnetic nature.

Finally, special attention should be paid to secondary electrons and po- sitrons produced in the Galaxy during nuclear collisions between cosmic pro- tons and nuclei. Thus, basing on the data of [23], it should be expected that in

(*) In the simplest case of statistical acceleration a particle of energy M c 2 acquires~ when accelerated for a,time t,, energy E = M s 2 exp [~t] that is, the energy is propor- tional to the rest mass,

THE NATURE OF COSMI~ RADIO EMISSION ETC. 4 7

each collision about 5 % of the energy of the p r i m a r y particles shvuld be gi-

ven to electrons and' positrons [2, 3]. I t can be shown [2] t ha t in the absence of interstellar magnet ic fields the

amount of p r imary c.r . electrons and positrons with E > 10' eV should be comprised Within,-~ ] - - 5 ~ , even if t hese particles were produced exclusi- ve ly in nuclear collisiofis. TI~is value becomes about 10 times smaller if magnetic bremsstrahlung energy losses are t aken into account . H o w e v e r there are reasons

to believe tha t electrons are also PrOduced in the pr imary sources (see w 1), thei r number being larger than tha t of the secondary electrons. Similar considera- tions and also the computat ions carried out in w 1 indicate~(if no other fac tors must be taken into account) t ha t the number of p r imary c.r. electrons near the

ear th with E ~ 10 ~ eV should be about 0 . 1 - - 0 . 5 % of the number of p r imary protons with E ~ 10 ~ eV. Some of these electrons are secondary and c~n be separated f rom the primaries, as the number of secondary electrons and po- sitrons should be about equal, while in supernovae envelopes one should expect t ha t only electrons be accelerated. Accordingly, a s tudy of the pr imary electron-positron component near the ear th seems to be of special importance. Other possible means of checking the ideas outlined in this paper are discussed in [3]. Therefore, in conclusion we confine ourselves to the s ta tement that , as the previous discussion seems to indicate, the present data and conceptions

support the picture of the origin of c.r. proposed in this paper and, a t ~ny

rate, do not contradict it.

R E F E R E N C E S

[1] V, L. GINZBURG: Usp. Fiz. Nauk, 51, 343 (1953); Fortschritte der Physik (Berlin), 1, 659, (1954).

[2] V. L. GI~Z]~URG: Dokl. Akad. Naulc SSSR, 99, 703 (1954). [3] V, L. GINZ~URG: Proceedings of 5th Conference on Cosmogony (Moscow, 1955). [4] I. S. ~KLOVSKIJ: Astron. ~u. SSSR, 29, 418 (1952). [5] S. B. PIK]~L'NER: Dokl. Akad. Nauk SSSR, 88, 229 (1953). [6] J. E. BALDWIN: Nature, 174, 320 (1954). [7] H. ALFV~ and N. H]~I~LOFSON: Phys. Rev., 78, 616 (1950); K. 0. KI]~I"E~H~U]~R:

79, 738 (1950). [8] V. L. GINZBVR~: Dokl. Akad. Nauk SSSR, 76, 377 (1951); G. G. G]~TMA~C~V:

Dokl. Akad. Nauk SSSR, 83, 557 (1952). [9] V. L. GINZBURG, G. G. GE~A~C]~V and M. I. FRADKIN : Proceedings of 3th Confe-

rence on Cosmogony, p. 149 (Moscow, 1954). [10] V. V. VLADIMIRSKIJ: ~U. Eksper. Teor. _Fiz., 18, 393 (1948). [11] G. G. G~T~A~C]~V and V. L. GI~ZBURG: Dokl. Akad. 2Vauk SSSR, 87, 187 (1952). [12] V. L. GINZBVRG: Dokl. Akad. Nauk SSSR, 92, 1133 (1953). [13] I. S. SKLOVSKIJ: Dokl. Akad. Naulc SSSR, 90, 983 (1953). [14] I. S. S~:LOVSK1J: Astron. ~,u. SSSB, 30, 15 (1953).

4 8 V . .L . GINZB~RG

[15] I. S. SKLOVSKIJ: Dokl. Akad. Nauk SSSR, 98, 353 (1953). [16] J. G. BOLTON, G. J. S~ANL]~Y and O. B. SLEE: Austral. J. o] Phys., 7, 110 (1954). [17] I. S. ~KLOVSKIJ: Dokl. Akqd. .Yauk SSSR, 91, 475 (1953). [18] E. FERMI: Phys. Rev., 75, 1169 (1949). [19] E. F]~R~I: ~strophys. Journ., 119, 1 (1954). [20] P. MOI~RISON, S. OLBE~T and B. RossI: Phys. Rev., 94, 440 (1954). [21] V. L. GINZBVRO: Dokl. Akad." .Yauk SSSR, 92, 727 (1953). [22] D. ~ER HAAR: Rev. ,Mod, Phys., 22, 119 (1950). [23] S. N. VERNOV, N. L. GnIGOROV, G. T. ZACEPIN and A. E. CU])A~OV: Izv. Akad.

,LYauk SSSi~, Set. Fiz., 19, 493 (1955). [24] M. F. KAPr.ON, J. H . Noo~ and G. W. RACETTV.: Phys. 2~ev., 96, 1408 (1954). [25] R. A. ELLIS, M. B. GOTTLIEB and J. A. VA~r ALLEn: Phys. l~ev., 95, 147 (1954).