gamma ray astronomy and the origin of cosmic rays

Gamma Ray Astronomy and the Origin of Cosmic Rays

REINHARD SCHLICXEISER

Max-Plunck-Institut fur Radioastronomic Bonn, BRDI)

Summary

The classical production processes for high energy gamma radiation in the interstellar medium are discussed and confronted with recent satellite observations. It is shown that gamma ray data in their present form do not provide definite conclusions on the origin of cosmic rays. Some current ideas on the nature of gamma ray point soiirces are presented.

I. Introduction

Cmtnid ganinia rays at e believed to result riiainly from interactions of cosmic rays with iritcistellar titattei nnd tadiation fields. Hence the question of the origin of cosmic gairirna rays is closely related to thp origin of cosmic rays which is a long standing problem of

rgy astrophysics. Regarding the electron component of cosmic rays, the discovery of tlic universal 2.7 K microwave hlockbody radiation (PENZIAS and WILSON, 1965) has iiiade a galactic origin probable. Relativistic electrons in the metagalaxy with the saiw intensity as measured near the solar system would produce much 1iiore X-ray Imckgronnd radiation by iriverse Coiiipton interactions with the niicrowave photons than is observed (FAZIO et al., 1966). Regarding the nucleon component of cosnric rays, conclusions on their origin are expected from gamiiia ray and neutrino iistronnmy. I t is one purpose of this work to discuss carefully the ability of gamma ray astrorioiiiy with rcspect to this question. The satellite experiments SAX-2 (FICHTEL et xl., 1975) and COS-13 (SCARSI et id., 1977) - hoth of which use spark chamber telescopes - have measured the celestial distri- I)ution of gainilia rays n i th energies larger than 50 MeV Ititli reasonable accuracy. We, thercfore, restrict our discussion of gamma ray astronomy to this energy range and neglect low-energy ganiiiia ray production by theriiial brerrisstrahlnng emission models as well as gainina ray lines (see RAarATy et al., 1979). We start by discussing the classical production processes for high energy gamma radiation arid their effect on the radiating particles (S 2). In S 3 wc confront ganiiira ray observations with the pi edictions of diffuse ganinia ray astronomy and siiinriiarize the pwsent status of the discussioii. $ 4 is devoted to some current ideas on thc dis- coreiwl phenonwnon of point sources in the gamina ray sky.

96 l%EINRARD SCELICKEISER

XI. Cosmic Rays as Part of the Universe

1. Our present view of the structurc of the universe

In order to discuss relevant production processes of high energy ganirna rays we have to recall astronomical observations concerning the structure and the content of our galaxy and the universe. All with the human eye visible stars are niembcrs of a large stellar system - called Milky Way - which has the forin of a flat disk with a radius of 30 kpcl) and a height of 0.5 kpc. The solar system lies nearly in the middle of the disk roughly 10 kpc away from the galactic center. With respect to the center the galactic coordinates ( P I , bII) have been introduced. These are the angles of a spherical coordinate system with the solar system as origin; the direction (ZJI = 0") bI1 = 0") points to the galactic center. A galactocentric cylindrical coordinate system (R, p, z ) is also quite usefiil. Beside our own Milky Way, there exist numerous other stellar systems, the galaxies. The space between the stars of the Milky Way is populated by interstellar matter, the total mass of which is about 10 percent of the mass of the galaxy. This matter consists of interstellar dust and gas with a mass ratio of 1 : 100. The nature of interstellar dust is still unresolved. Interstellar gas consists mainly of hydrogen which appears in different states : H I-, H 11- and H,-hydrogen. Our picture of the large-scale distribution of the interstellar niedium has changed drastically during the last years. Observational techniques and results are carefully discussed by BURTON (1974, 1976) and MCCRAY and SNOW (1979). The neutral, atomic hydrogen (H I-hydrogen) is either clumped in H I-clouds or distributed diffusely ("intercloud niedium"). The large-scale density distribution may be represented by (GORDON and BURTON (19761, BURTON and GORDON (1976)).

~ H I ( R , Z ) = wylI(R) exp ( - ~ ~ / [ 2 h ~ ~ ~ ( R ) ] ) (1)

where the dispersion hHI(R) is equal to 120 pc for R snialler than 9.5 lrpc and increases a t a rate dhHIldh? = 0.05 with increasing R. The radial distribution n,Tll(R) is displayed in figure 1. As one can see, between R = 4 kpc and R = 15 kpc the distribution is nearly constant n,TI1 _N 0.3 H atonis crrr3. The important component of interstellar matter is the molecular hydrogen H, which only can cxist in dark cool clouds in order to survive against the ionizing UV-radiation. Roughly 60 percent of the mnss of the interstellar gas (MEZOER, 1975) appears in this form. The spatial distribution of H,-hydrogen is measured indirectly by observing the 2.6 inn1 emission line of carbon nionoxide CO, since collisions between GO and H, in the clouds art probably responsible for the excitation of the carbon monoxide (SOLOMON, 1973). The large-scale density distribution niny he represented by

nH,(R, Z ) = n&,(R) exp (-~2/[2h;,,]} en-3 (2)

where hs, = 50 10 pc and wit(R) is shown in figure 1. The radial distribution r&,(R) exhibits a maximum between 4 and 6 kpc and has density values between 0.6 and 1.8 H,- niolecules ~ r n - ~ i n the inner cycle of the galaxy whereas in the outer regions (R > 12 kpc) niolecular hydrogen is practically absent. In the vicinity of young, bright 0- and B-stars, the interstellar gas is ionized by the intense ultraviolet radiation of these stars. These regions are called H 11-regions. Their radial density distribution is similar to that of moleciilar hydrogen.

l) 1 kpc = lo3 pc = 3.086 . loz1 cm.

Gamma Rag Astronomy and the Origin of Cosmic Rays 97

Besides this "classical" picture of the interstellar riiediuni, observations of the soft X-ray background (TANAKA and BLEEKER, 1977) and the interstellar 0-VI absorption line (JENKINS, 1978) have revealed the existence of a further component of the interstellar gas: a dilute (n < 10-3 hot (1' ci 105 - 106 K) corona type plasma which may occupy up to 80 percent of the volume of the interstellar gas. This component is believed to result froin intersecting supernova reninants (Cox and SMITH, 1974). Outgoing supernova shocks sweep up interstellar material, leaving behind a dilute hot gas. Model si- mulations (SMITH, 1977) indicate that there is a certain probability that a new outgoing

4.5

cm-3

4.0

3.5

3.0

2.5

2.0

1.5

1.0

0.5

0. c

I I I I

----__ I I I I 1 I I

0 2 4 6 8 10 12 14 16 18 R l k p c l

Fig. 1. Radlal density distrlbutlon of atomic (HI) and niolecular (H,) hy(lioge~i 111 the galaxy (GORDON and BURTON 1976) Courtesy of The Astrophysical Journal.

supernova shock crosses an oldexisting supernova remnant, so that the shock propagates preferentially in this iiicdiunl giving rise to a network of dilute, hot plas~iia in the niatter

(i) a niatter disk interwoven with a network of hot dilute "tunnels" (COX and SMITH, 1974), (ii) interstellar niatter clumped in clouds embedded ina bath of hot, dilute plasma (MCKEE and OSTRIKER, 1977). Theoretical problems concerning the stability a d the structure of this new component are still unresolved. The spare between the stars is further populated by a cosinic photon and particle radiation. Figure 2 shows the estimated energy densities of the electromagnetic radiation in different frequency ranges. Shown are galactic and extragalactic values. The latte, are derived by comparing corresponding intensities froin the galactic poles (bT1 = &90°) with those from the galactic plane (61' = 0'). The rnetagalactic component dominates only in the microwave and X-ray frequency range.

1"

disk. Depending on initial conditions we niny end up with two typicP1 configurr CL t ' Ions:

R M l - R 0 U - V SXR XR Y Fig, 2 . Kstiiimted eiiergy densities ol electroriiagiietir ratliat,ion in diflereiit frcqueiicy ranges in galartir and nletagalactic

slywe (LR: Lorry-waveieiigth radio maws, 31: inicrowaves, IR: inirarfd, 0: olitiral photons, UV: ultraviolet rad- iatiuii, SXR: soft X-rays, SIL: X-ray-<. y:y-rass). Iteprodnred I roiii SILK (1070) by Courtesy of Space Science Reviews.

The interstellat.electroiiiagnetic radiation field in the vicinity of the solar system may he represented by the sum of diluted blackbody distributions plus the isotropic niicrowave background (YICCINOTTI and BIGNAMI, 1977). Table 1 gives the parameters temperature Ti and energy dmsity w, of the vp...rions components. The parameters of the infrared component are very micertain (PICPINOTTI and BIGNAMI, 1977). The energy density of the ionizing UV-radiation (navc1cr;gth i < 912 8) near the galactic plane, zu,, -= 1.25 . eV c 7 r 3 (ALLEK, 1973), is urrich snialler and therefore neglected.

Table I Electromagnetic radiation field in thc vicinity of rile ~o la r system

The cosmic particle radiation coiiiists prethniinantly of p r ~ t o n s m i d s-pi t ic lc s. R o u g k l ~ 1 peiecnt of the cosmic rays arc clrctrons, positrons c+ as well as negations e . Due to the nitrltiplc deflection of these charged particles in cosmic inagiletic fields, the ohse I 1 t d intensity is practically isotropic, for energies imaller than 1W6 eV. Figure 3 shows tlir observed intensities of cosmic piotons and a-~sarticles near the solar system. Belo\+ 1 GeVinuc the spectra are influenced by solar iuoddation. 9 1 higher energies the Ppectra may be represented by a single power laiv Z ( E ) = K . E-p with K and p constant and positive. Due to the influence of cosmic niagnetic fields, it is inipossible to observe directly ih(, intensity of cosniic rays with energies snialler than 101ceV inother regionsof thennivelse. This c m be done only indirectly by measuring the electroniagnct ic radiation that restilts from interactions of cosmic rays with other components of the interstellar niedium. In the following we therefore discirss the radiation and intei action processes of eosiiiir rap c,lectroris and nucleons.

(hirini,i l&iy Astronomy and the Origin of Cosniic Rays 9 9

, i\ , 10 -

001 0.1 1 10 102 103 K ine t ic Energy ( M e v / n u c )

I4p. 3 . Ol>sc~vcd intensity of cosmic ray protons and a-particles in the vicinity of the solar SyStClll (\\rER131CI: 1!)73).

2. Interactions of cosmic electrons

Due to the content and structure of the galaxy and thc universe, the following interaction processes may occur (FICHTEL et al., 1976) : a ) synchrotron radiation in cosmic magnetic fields h) inverse Conipton scattering of ambient photon gases c) non-thermal electron bremsstrahlung in the interstellar gas d) ionization and excitation of atoms and niolecules of the interstellar niediinn.

We discuss each process in turn.

a ) Synchrotron radiation

Synchrotron radiation is the radiation of a relativistic, charged particle which moves in a spiral orbit in a magnetic field. The energy loss of a particle of mass M , energy It: and charge ( Z . e ) by synchrotron radiation in a magnetic field with strength H is given by ( PACHOLCZYK, 1970).

6 is the angle between the direction of electron rnowment and the iiiagnetic field lines. -4s one can see, synchrotron losses of protons and charged niiclei are smaller hy a factor ( M / Z m , ) * as the losses of electrons a t thc same energy. By integrating the product of the number of electrons per voluiiie and solid anglt. iinit times the total radiation of a single electron per frequency unit, one finds - after suni- niing over polarization states - the synchrotron volunie eniissivity at thc position (211, b*I, .T) - which is the ratliatcd power per freqnency, vohme and solid angle iinit -

100 ~ ~ E I X H A R I ) SCHLICKEISER

as (PACHOLCZYK, 1970)

where

00 1/3 e3 s(v; l I J , b", x) = - H ( P , blJ, x) sin -8 dEN(h'; 111, blI, x) P(v/vc)

4nnzec~ 0

(KSl3(s) : modified Bessel function of second kind with index 5/3) ; 3el

4nrne3c5 v, = - H - sin 6 - E2 Hz (5)

is the critical freyiiency, in the vicinity of which the synchrotron emissivity has its niaxiiniim. Using nunibera one finds the mean energy of the radiated photons in terms of the magnetic field strength and the energy of the radiating electron as (STECKER, 1971)

(Ey) N 2 - 10-1l H, (Gauss) [E(GeV)]2 GeV (6)

where H , = H . sin 6.

For the astrophysically important casc of single power law dependence of the spatially isotropic differential electron number density

N ( E ; l I I , b", X) = i'70(Z1I, b'J, X) * E-P ( p > 1) (7)

expression (4) reduces to (PACHOLCZYK, 1970)

x N,,(ZII , b", x) [H(Z", 6'1, 5) sin B]p+1/3 v - p / 2 t'rg s -1 ciil 3 stcbr Hz-'

( 8 ) (l ' (z): gainma function). At frequencies v > 50 MHz one may neglect the absorption of synchrotron radiation by free-free transitions with the thermal electrons of the interstellar gas and the influence of the ionized medium (Razin-effect) (RAMATY, 1974). Integrating the v o l m i ~ emissivity along the line of sight results into the specific synchrotron intensity from the direction (Zrr, b l I ) :

CQ

i s T n c h ( v ; ZIT, b") =- dxa(v; Z J 1 , h", x ) erg s-* cn-2 ster-1 Hz-I. (9) 0

h) Inverse Conipton scattering

The inverse Conipton effect of high-energy electrons traversing a photon gas has heen originally discussed as an energy loss process of cosmic electrons by FOLLIR (1947) as well as FEENBERG and PRIMAKOFF (1948). SAVEDOFF (1959) and FELTEN and MORRI- SOR (1963) have pointed out that this interaction may be an important source of cosmic high-energy photons. In this interaction the photon receives part of the kinetic energy of thc, relativistic electron arid is scattered into a higher frequency range.

Gamma Kav Astronomy and the Origin of Cosmic. Rays 101

Assritiiirig that target photons and relativistic electrons are spatially isotropic distri- hilled - for anisotropic problems see JONES et al. (1974) - the differeiitial cross sc'c- tion for this process is given by the Klein-Nishina fornnila (e.g. ~ A U C H and ROHRLICH, 1955) averaged over initial photon polarizations and suinnied over final photon polarizations (~~INZBLJRG and STROVATYKII, 1964 ; JOXES, 1968; BLUMENTHSL and (iOC'LD, 1970) :

wliere I# is the electron energy, e and Ey are the photon energies before and after the scattering respectively. uyr = 6.65 - cni is the Thonison cross section whereas

a n d

This cross section defines the probability that an electron of energy E generates a photon of energy Ey by scattering a target photon of energy E. Prom the kinematics of the scattering process, the range of q is restricted to (BLUMENTHAL and GOULD, 1970)

(electron Lorentz-factor y = E/(mec2)). The intensity of Cotripton scattered photons froni the direction (Ezl, brl) is obtained hy integrating thr cross section (10) multiplied by the electron intensity distrihiition I ( E : 1 I I . b", s) and target photon distribution n(&; P, brl, x):

m a , W

I c ( E y ; l z I , br l ) = - dx d e n ( € ; I", brr, x)

photons c n r 2 s-l ster-' e\'-l.

.\ssuining that both distributions - I ( E , r ) and n(&, r) - are separable firnctions in energy and positron T , as well as a single power law dependence of I ( E , r ) :

dEu(E,, F , E ) I ( E ; I", bI1, .r)

(14)

4n S ' S 0 0 S Emin

I ( # ; I", b", X) = N,(l", b", X) * E:-P (P > 11, (15)

WP tiiay write (14) as m

1 P

Ic(lCy; I", b") == dxS(EY; I", b", x). 0

The differential otnnidirectional soiirce function X(E,, T ) gives the number of Cotlipton scattered photons per volume, time and energy element :

102 REINHARD SCRLICKEISER

wit,h the integral %

and the dimensionless parameter

.s = F . Ey/(.m,c2)2 (20)

which determines the domain of scattering. Expression (18) is exact and shows, that S(E,, T ) also is a separable function in energy and position. The quantity w ( r ) is called

target photon energy density, if ds E n ( s ) = 1.

In order to reduce the general result (18) to simpler expressions, asymptotic fornis haw been discussed in the literature:

W

0

(i) Thomson limit : s Q 1 (ii) near Klein-Nishina limit: s 5 1 (iii) extreme Klein-Nishina limit : s > 1.

For values of s smaller than 1 (cases (i) and (ii)) the integrand in (19) can be expanded hy keeping only the lowest order ternis i r i ( 4 . s ) ~ / ~ , so that the g-integration can be performed. The first four order terms are (BLUMENTHAL and GOULD, 1970; SCHLTCK- EISER, 1979)

(2la)

(2lc) (p4 + 12p3 + 62p2 + 164p + 209) ( p + 1) ( p + 3)

2(P2 + 4P i- 11) ( P + 5 ) (17 + 7 ) +

For large values s > 1 (case (iii)) BLUMEKTHAL and GOULD (1970) derived

B(l)(s > 1, p ) -+ 2-(p+l)s-(Pt1)/2[ln (s) + C ( p ) ] ( 2 2 )

where C ( p ) is a parameter of order unity.

Caiim,i Ray Astronomy and t,he Origin of Cosmic Rays 103

With the zeroth nrtles tcimi BO(p) onr derives the well-known approximation of (18) in the Thonison limit

photons c 1 r 3 s-1 cV-1 ( 2 3 )

a single power law in By with the spectral index ( p + 1)/2. I n the Thoinson limit the vneryy loss of the electron and the mean energy of the scattered photon are given by

(24a)

iwpcctively, whese (c) is the mean energy of the target photon gas (see 25). Conipton losses of coslnic ray protons and charged nuclei would he smaller by a factor ( M / M ~ ) ~ lo6 than losses of electrons of thc wine eneigy.

A :o 10

10 8 Upper Bound of the

Thomson Domoin

Mean Energy < E > / e V

Fig. 1. Crit,ical gariniia ray energy E ' wliicli is a reasonable upper bound forusing the Thomson lii i i i t approxin~ation as >i Iutiction of tlic mean energy (z) of the target photon distribution for different va1ues:of the electron spectral indrxp The values of ( F ) cover the spectral range from radio (R), microwave (M), infrared (I- It), optical ( O ) , ultraviolet (U-V) and X-ray (XR) wavelengt,lis, Reproduced from SC€ILICKEISER (1979) by Courtesy of The Astrophysiral Jollrllal.

The question of validity of the Thoinson limit in the context of calculating galtima ray source fnnctions is answered in figure 4. It shows that ganinia ray energy E',O up to which the Thonison limit may he used, as a function of the mean energy (c ) of the target photon distrihntion for ciiffe~cnt ralnes of the electson spectral in(1c.u 11. The incan

104 REINHARD SCHLICKEJSER

energy is defined by

It can be seen that for all values of p - in order to calculate y-ray source frrrictions from inverse Corupton scattering a t Ey 2 100 MeV - the Thomson liiiiit of the Klein- Nishina cross section is not applicable if target photon gases with mean energies greater than 1 eV are involved. With other words, as long as we consider the scattering of radio, microwave or infrared photons, we are allowed to iise the Thomson limit (23). However, if we discuss the scattering of optical, ultraviolet or X-ray photons into the y-ray range, we have to go back to the cxact result (18). In later sections, we will refer to this resrrlt.

c) Bremsstrahlung

The exact bremsstrahlung cross section is derived by the methods of quantum electro- dynamics (HEITLER, 1954, JATiCH and ROHRLICII, 1955 ; MCCONNELL, 1958). The differential cross section for scattering of a relativistic electron in the field of an aton) can he written in general as (BETHE and HEITLER, 1934)

where B. = 1/1:37.037 is the finc structure constant, yo the classical electron radius, E the initial electron energy and Ey the energy of the bremsstrahlung photon. ~ # I ~ ( E ~ , E ) and &( Ey, E ) are energy dependent scattering fiinctions which depend on the properties of the scattering system.

Tab le 2 for the hydrogen atom and heliuin atom

(from BLUMENTHAL and GOULD, 1970) Scattering functions GI and

A H He

0 0.01 0.02 0.05 0.1 0.2 0.5 1 2 6

10

45.79 45.43 45.09 44.11 42.64 40.16 34.97 29.97 24.73 1H,O9 13.65

44.46 44.38 44.24 43.65 42.49 40.19 34.93 29.78 24.34 17.28 12.41

134.60 133.85 133.11 130.86 127.17 120.35 104.60 89.94 74.19 54.26 40.95

1 3 1.40 1 :10.31 130.33 129.26 126.76 120.80 105.21 89.46 73.03 51.84 37.24

When the scattering system is an unshielded charge ( Z . e), then = (b2 = Z2+, where

Goura (1969) has considered the astrophvsically iiuportant cases of bremsstrahlung scattering in the field of hydrogen and hrlirrtii atonis. Given in table 3 are the scattering

Gamma Ray Ast,ronomy and the Origin of Cosmic Rays 105

and +2 when the target is a hydrogen atom or a helium atom as a function functions of t,he parameter

Eymec2 40cE(E - By)' A =

For A > 2 one should use (27). If the scattering system is a hydrogen molecule H, the cross section crlIz(Ey, E ) is given by 2 . aHI(Ey, E ) where the error is smaller than 3 percent (GOULD, 1969). The total energy loss of a relativistic electron by bremsstrahliing in a inediuin with s different species (atoms, ions and electrons) of corresponding densities n, is obtained by

E

where the respective targets define the scatteringfunctions c#Jic,,(i = 1, 2) of o,(E,, E ) . Explicit sitnple expressions for (29) can be found only in the strong-shielding ( A < 1) and weak-shielding ( A > 1) limits (BLUMENTHAL and COULD, 1970). In the case of weak- shielding one finds for an overall neutral plasma

($1 = -4ixro2cE 2 nZ,Z(Z + 1) Z

(30)

(weak-shielding or completely ionized).

(30) is appropriate for E 5 30m,c2/Z, hut is exact for all E for a conipletely ionized medii i l i i . In the strong-shielding limit E 2 30mec2/Z, the scattering functions for the nentral species of the medium are constant - see table 2 - and practically equal

c#J1 _N c#J2 N @ (strong shielding). ( 3 1 )

In this case the total energy loss (29) reduces to

-ixro2 cF: ns@ eV s-1 (strong shielding). (32) S

In the intermediate case d N 1, the Ey-integration in (29) has to he done n~ii~~ericallg. However, in the range d II 1, and +, are nearly equal and slowly varying fiinctions of E,,. Hence, in a first approximation (BLUMENTHAL and GOTJLD) +(By, E) iiiag be taken oiit of the integral and set equal to its value a t the characteristic energy E , = 1/2# which corresponds to d = m,c2/(4aE). In this case one finds

(33)

;\s 0110 can see from (32) and (33), the total energy loss rate is linear proportional to electron energy F:, in contrast to synchrotron (3) and inverse Coinptonlosses (24a) where n (1iIitdratic dependence has been found. The differential intensity of brenisstrahlnng photons from the direction ( / ' I , b") is given hy

IR(Ey; I", b") = - 4n r d z p l E I ( E ; 111, b", x ) . n , ( l I I , b", x) o8(EY, E ) ] 0 E y

photons r m - 2 S-1 stcr-1 eV-1. (34)

106 PIKINHART) SC-HLICKEISER

We neglect the ionized part of the iriterstellar rticdiiim which hasalowdensity (see 8 2.1) and take into account that

(i) the heliu tti/total hydrogen-iatio in the interstellar medium is 0.1, and ( i i ) the ratio o f the scattering functions &&,/+lIs Y 3.0 in the strong-shielding limit (ser

table 2 and (31)). For energies E and I!&, greater than 15 MeV we then find

.y ns(l.1 > = [%r(l*) + 2%r,(r)l m(Ey, w + nHe(9-1 OI<e(& F:)

= W~d7? + 2 n d r ) l o d E Y , El- S

(35)

For a single power law depertdcnce of the electron intensity (15) we derive from (34) and (35) :

where the omnidirectional diffcrential hemsstrahlung soitrce function per eqii iwlwt hytlrngcn atoiti is given by

with 2(x - 2 )

S x ( x + 1) ' f(.) = 1 - (38)

STECKER (1977) first has given this result i n this form. In the case of t\\o-fold pouci Ialv dependence of thc electron intensity

m e finds

ctn-3 s-1 cv-1 for E,, 5 E ,

(39)

where x = K,(r)/K,(?") x- ErF-8 T con st.

Gamma Kay Astronomy and the Origin of Cosmic Rays

The incan energy of the brenisstrahlung photons is roughly given hy (DILWORTH, 1973)

107

1 y 2

( E ) = = - - . f r : e v .

d) Ionization

The energy loss of relativistic particles traversing atomic matter by ionizing and ex- citing neutral atoms has been carefully discussed by GOULD (1972, 1975). For the ionization loss of rirgatrons and positrons he finds

(43)

where a sum over varioiis species with respective nuiiiber densities nd has to be perfor- tiled. For negatrons

Bs-neg = Z,(h [y3~21n,c3/(AE)s] - 0.2841, (44)

where 2, is the number of atomic electrons in the atom s, (4fl)III = 15 eV and (AE)He = 41.5 C V (DALGARNO, 1962), y = E/(mec2) denotes the electron Lorentz-factor. For wlativiFtic energies ( y > l), (44) and (45) are practically identical. *

Synchrotron losses

00

OOi 01 0 3 I 3 10 30 100300 3000 Electron Energy / GeV

Fig. 5 . Eiiergy loss rates of electrons in int,erstellar space (I: Ionization, B: Rrelnsstrallllliig, (‘: (’onipton Scattering, S: Syiiclirotroii rsdiatioli). Iiidrx 2 al CI refers t o roiiigonmt 2 0 1 table 3 .

108 REINHARD SCHLICKEISER

e) Summary

In order to understand the relative importance of the discussed electron energy loss processes in the interstellar medium, we have calculated the respective loss rates by using the values of the parameters measured near the solar system (see 5 1, nHI, + 2nHs, = 1.14 H I = 4 - Gauss). Figure 5 shows the results. As one can see, ionization losses dominate for electron energies smaller than 3OOMeV. In the range 300 MeV to 8 GeV electrons lose their energy predoniinantly by bremsstrahlung in the interstellar gas whereas a t higher energies Compton and synchrotron losses dominate. It is interesting to note that the inverse Compton losses against starlight are negligible against the losses against infiarcd radiation (&) and niicrowave photons

A discussion of the energy loss processes in other regions of the interstellar space demands the knowledge of the parameter values there. GOVLD (1975) has considered electron loss rates in the intergalactic medium. A s one can see from figure 6, due to the small matter densities, Compton and synchrotron lames dominate already for energies greater than 50 MeV.

(cBB).

f 2 3 4 5 5 7 8 1oa I

Fig. 6. berm loss rates of electrons in intergalartir space. Shown is the logaritlini o l T ~ ~ T where T~ =~ 1,3 H.-l

(Ho ~ GO knr s-l Mpc-': Hubhle constant) is the cos~nic expansion t h e and l/% = (dEki f ) /E. Reprodnrrd from GOULI) (1075) by Courtesy of The A8trophgsical Jonrnal.

3. Interactions of cosmic nucleons

In the last section we have seen that the cross section of electroniagnctic interactions (bremsstrahlung, inverse Conrpton scattering and synchrotron radiaticn) of the niicleon componects of cosmic rays are nruch smaller than those of electrons of the sanie energy due to the larger mass of the nucleons. Hence, these interactions are not important for the production of cosmic photons. Pnrthermore, a t nucleon energies snialler than lo1' eV these interactions do not affect the propagation of cosmic ray nuclcons (OSBORNE, 1975) ; however, at higher energies other type8 of intcractionswith low-entrgy photon gases may inflrience the nucleon energy spectrim1 (HTLLAS, 1975; PUCET et a]. , 1976).

Gamma Ray Astronomy and the Origin of Cosmic Rays 109

On the other hand, inelastic nuclear reactions of cosmic ray nucleons with atoms and molecules of interstellar matter are important for the production of cosmic ganinia rays as well as the propagation of the nucleons. In inelastic (p-p)-, (p-He)- and (a-H)- collisions mainly charged and neutral pions are produced. The charged pions & decay into riiyons and neutrinos, and the rnyons decay into electrons. These decays are regarded as the most important secondary source of cosmic electrons and neutrinos. Neutral xO-mesons decay after a mean lifetime of 9 . 10-l' s into two high-energy gamma rays. The differential, omnidirectional ganinia ray production rate a t the position ( P I ,

b I I , x) is related to the differential, omnidirectional pion prcduction rate Q,p(E,; P I , b", x) by (CAVALLO and GOULD, 1970, SCHLICKEISER, 1974)

w qn(Ey; I", b", x) = 2 s dEnQno(En; 111, 611, x) [En2 - w~~%*]- l '~ photons eV-l s-l, (46)

Eyf ((mncZ)'/4 Ey)

where (STECKER, 1971; BADHWAR and STEPHENS, 1977)

m

&,.(En; l I I , b l I , x) = 4n . 1.64; I dE,I(E,; V1, bI1, x) u(En, E P ) pions eV-l s-lt (47) 'th.no

a(En, h',) denotes the differential cross section for neutral pion production in p-p- collisions and I(E,, Y) refers to the differential intensity of cosmic ray protons at the position r . The factor 1.64 takes into account the influence of (p-He)- and (a-p)- collisions, the cross sections of which are not well known, and is based on the chcniical composition of cosmic rays and the interstellar matter (BADHWAR and STEPHENS, 1977).

For a long time only measurernents of thc total cioss section of p-p-collisions denotes the threshold encrgy for no-production.

have been made (eg. BRACCI et al., 1973; WHITMORE, 1974). With the help of pheno- nienological models for the pion prcduction conclusions have bten drawn on the be- havioiir of the differential cross section o(En, E,) if only (48) is known. A detailed discussion of thcse calculations can be found in the bcok of STECKER (1971). Recently, differential cross sections for the inclusive reaction p + p .+no + x have been measured (DIDDENS and SCHLUPMANN, 1971 ; CAREY et al., 1974). By fitting these data, BABHWAR and STEPHENS (1977) have derived an analytic expression for the differential cross section which is consistent with current ideas on the scaling of cross sections at high energies. Figure 7 shows the differential and integral photon production rates of Badhwar and Stephens which have been calculated by using the demodulated cosmic ray proton spectrum measured near the solar system. There is reasonable agree- ment with earlier calciilations of STECKER (1970) and CAVALLO and GOULD (1971). The apparent syinnictry around lj2 m,a2 M 70 MeV of the differential photon production rate in a lg-Ig-plot is noteworthy. In particular one finds (STECKER, 1970)

&.(> 100 MeV) = (1.3 + 0.2) . l0-z5 s-l (49)

for cosmic ray proton spectrum parameters measured near the solar system. Using these production rates calculated for parameter values near the solar system and assinning that the shape of the cosmic ray nucleon energy spectrum does not vary with

position T, I p ( E p , 1') = N C - r ( r ) Ip(El l , r . , ) /N, 7(vs), where T, denotes the position of the solar system, the differential intensity of +'-decay gamma rays froni the direction ( Z I I ,

b I J ) is given by m

photons e w r 2 s ster-I. (50)

The study of ganinia rays froni &decay therefore allows to investigate the large-scale distribution of cosmic ray niiclcons if the interstellar gas distribution is known, a fact that has stiniulated ganiiiia ray astronomy for a long time. STECKER (1973) has shown that the majority of gamma rays froin no-decay are produced by cosmic nucleons with energies between 1 and 30 GeV.

Yig. 7. Differential iind

111. Diffuse Gamma Ray Astronomy

In this section we discuss the results of gamma ray astronomy under the hypothesis I1i:tt all ganinia rays are produced by cosmic rays in the diffuse interstellar medium. There- fore we neglect for a moment the contribution of point soiirces which is discussed in 5 IV. We are especially interested in the question of the origin of cosmic ray nucleons and their relation to gmnrna say astronomy. First, we estimate the importance of electron interaction processes in ganima ray production in comparison with the Contribution from +-decay. The efficiency of an inter- wtioii process to produce ganirria rays is characterized by the integral omnidirectional source function S( > E,) calculated for parameter values measured near the solar system. This sourcc function gives the number of gtznima rays with energies greater than E, 13er t imv unit and volume element (0111-~ s-l).

1. Synchrotron radiation in the interstellar magnetic field

A simple cstiniatiori (STECKER, 1971) shows that synchrotron radiation in thc interstellar niagnetic field is negligible as il production process of galactic gamma radiation. Takinga typicalfieldstrength of HL = 4 . 10-6Gauss wc findfrom (6) that electrons with

(;;iinrn;i Ray Antroiiomy and the Origin of C ' c k n i i r , Rays 111

c ii 6 i s'1.g~ of :{ . 10' ( k V art: T I ied in orckr to prodrice :L ganiiiia ray with an energy of 100 llel-. Foi coi'iparison : if Cortipton interactions with starlight photons of roughly the same energy dciisity and mean energy of about 1 e l 7 are considered, it only rtqiiii'cs

a 4-(:eV electron to produce a 100 MeV-ganiiita ray. Siich electrons are a t least 14 oLders of itiagnitudc :tiore plentiful than 3 . lo7 GeV electrons due to the stet ppowerlaw energy spcctruv of cosmic ray electrons. HDwrvcr, synchrotron radiation may be important for gainnia ray production 111 cosmic objects with strong magnetic fields like pulsars.

2. Inverse Compton scattering of microwave photons

Before we start this application, \te introduce the so-called graybody energy distribution of target photons which is a diluted Planck spectrum :

15w(r) &a

n4(liT)4 exp (Elk?') -- 1 7ZO(&, T ) = -. eV-' c 1 r 3 .

Expression (51) is characterized by two paraineters: the teiiiperature T and the photon energy density W ( T ) (see (16)). In the special caw of a blackbody distribution

For a grayhody distribution the mean energy of the target photons (25) reduces to (FELTEN and MORRISON, 1966)

( E ) N_ 2.7kT eV. 153)

The iuiiversnl microwave background radiation - which is believed to be the relict of the primeval fireball in which our universe has been formed - follows a blackbody tiistrihiition with temperature 'P1)n = 2.7 K, so that according to (52) and (53) WIIB = 0.25 ( > \ 7 c 1 r 3 and (&)13R = 6.3 . Thc iiiean energy of clectrons producing gaiiinia rays with energies greater than 10 MeV in thiq interaction has to be greater than 50 GeV (see (24b)). We may use the results of section TT.2. i r i the Thoinson liniit. At electron energies larger than 40 GeV all measured viicrgy spwtra iiciii' the solar system may be represented by a single power law N ( E ) = N,, . 1C-P (ANANU ct a]., 1975; h f l i r m m and PRTXCE, 1977). By integrating (23) we firid

eV.

45 . a,, . 1 0 ] ) H

( / I - 1) 9 F ( p ) ( m a r 2 ) I - p ( k T I i , ~ ) ( ~ -w N f. I:: Y - ( ~ l ) / ~ photons 0111-3 S-1 X,r,i( ' Ky) =

(54) W h t T i .

( r ( z ) : gamma function, [(z) : Rieirmnn's zeta fiiiiction)

is l a bulated by BLUMENTHAL and GOCLD (1970). As one can scc the source fiiriction Sun(> I&) depends on the temperature l'r3kI, encigy dciisity WuIc and the parameters of the cosiiiic ray electron spectrum mc,asirred in thr solar vicinity, AT,, and p. Whereas for the niicrownve radiation field lYn,; and TYHH are

2 Xeitschrift , , l b tschrittc (lei PllySik''. lid. 09, Hett :>

112 BEINII ~ R I ) SCIIL~CKEISER

T a b l e 3

ray electron energy spect)rirum Source functions XBn (> 30MeV) and S ~ H (> 100 MeV) for different estimations of the lord cosmic

Experiment 1’ Ne* 81>1: (> 30 MeV) SIIII (> 100 NeV)

ZATSEPIN, 1971

MULLER and MKYER, 1973 SILVERBERG e t al., 1973 ANINU e t al., 1975 DXUUHERTY et al., 1975 ~ E I E R et a]., 1975 HARTMANN et al., 1977 MI~.:~wAN and EARL, 1977 Aizn et al., 1977

rsnrr c t .[I., 1973 2.70 3.20 2.66 3.20 2.69 2.80 3.00 3.401) 3.40 :3 .:lo

9..W . 10k3 2 .76 . 1 0 - 2

7.90 ‘ 10-2 1.16 ’ 10-2 1.40 ’ 10-2 1.33. 10-3 8.00. 10-2 8.00. 10-2 6 . 3 7 .

:w. 10-3

C . 1 ..32 . 10-27

1.80. 10-27 3.08 . 10-27

9.40. 10-27 6.55. 10-27 2.40. 10-27 2.14. 10-27 2.14. 10-27 2.72. 10-27

5.40 . 10-27

2.63. 10-2: 5.02 . 10-28 1.14 . lW7 1.44. 3.40 . 10-27 2.23. 10-2‘ 7.20 . l@’* 5.04. 5.04. 10-28

6.81 . 10-2s

X a , in c r r 2 s-l ster-’ GeVP-l S,l,i (> 30 MeV), SLIn (> 100 MeV) In em-3 spl

l ) only valid for energies greater than 40 GeV

quite well known, the nieasiired cosmic ray electron spectrum above 100 GeV is rather unknown (ANAND et al., 1975) which iniplies an uncertainty in the exact value of (54). Using various recent nicmurernents of the local cosniic ray electron spectrum H L, calculate the integral source function SLIB (> 30 MeV) and Ssn (> 100 MeV). The rvrults are shown in table 3. The various values differ a t least by a factor of 6 for gauinia ray energies greater than 100MeV (SCHLICKEISER and THIELHEIM, 1977a) and 5 for E, > 30 MeV respectively, dependiiig on the choice of the electron spectrum parattieters.

3. Inverse Corripton scattering of infrared photons

The diffuse photons in the infrared band probably result from thermal emission of interstellar dust grains. The known experimental frequency distribution may be represented by a graybody spectrum with temperature T I R = 30K and energy density WIR 0.2 eV c n r 3 (PICCINOTTI and BIGNAMI, 1976) although these values are rather uncertain ( PICCINOTTI and BIGN~MI, 1977). According to (53) this temperature corresponds to a inean energy of (&)In N 7 . I n order to produce ganinia rays with cncrgies between 1 MeV and 10 GeV electrons with typical energies between 5 and 500 GeV interact (see 24b)). At all electron energies the Thomsori limit is valid. The rnajoiity of the measureiiients of the electron spectrum in these energy ranges is consistent with a single power law distribution. Analogoris to (54) we find for thc omnidirectional integral source function

eV.

In table 4 we have ealculatctl this quantity for energies greater than 30 and 100 MeV by using various nieasiirenwiits of the elcctron spectrum in the range 10 to 50 GeV. As one can see the uncertainty in the electron spectrum parameters implies an uncertainty in hoth results of a factor 4. Thc above nirntioned uncertainty of W,, and TIR rimy give rise to further uncertainties.

G m m a Ray Astronomy and the Origin of Cosniic Rays 113

4. Inverse Conipton scattering of starlight

In 5 11.1 the local diffuse starlight was represented by the sum of two gray-body coni- ponents which refer to different populations of stars.

Table 4 Sourc~e functions S I R (> 30 MeV) and S I R (> 100 MeV) for different estimations of the local

cosmic ray electron energy spectrum

Experiment P Npa SIR (> 30 MeV) 81, (> 100 MeV) ~ ~ ~-

MULLEI~ and MEYER, 1973 2.66 3.28 ' 10-J 1.64. 10-27 6.06. 10FR SILVERBERG e t al., 1973 3.20 7.90. 10-2 5 . 5 0 . 10-27 1.47 . 1 0 - 2 7

DAUGHERTY et al., 1976 2.80 1.40. lo-' 4 .14. 1.40. 10-27

M e s o 4 ~ m d EARL, 1977 3.40 8.00. 10-2 2 .77 . 10-27 6 .53. 10-28

\VERHE:R and ROCKSTROIT, 1973 3.00 1.00. 10-2 1.18. 10-27 4 .27 . 10-" Ah 4x1) et XI., 1975 2.69 1.16 * lo-' 5 .18 . 10-97 1 . 8 7 . lo-"

FREIEI~ ct A,, 1975 3.00 1.35. lo-* 1.92. 1 0 - 2 7 5 .76. 10-28

S, ~ in cm-2 s-l 8tcr-l GeVP--l AS,, (> 30 MeV), S I R (> 100 MeV) in en-3 s-I

a) Spectral type B

The frequency distribution of the first component of young hot stars is represented by a gray-body distribution (51) with Wsu = 0.09 eV and Tsn = 2.104 K (PICCIWOTTI and BIGNAMI, 1976) which corresponds to ( E ) ~ ~ = 4.65 eV according to (53). I n order to produce gamma rays with energies between 1 MeV and 10 GeV in this interaction, electrons with typical energies between 200 MeV and 20 GeV are involved. We know froni our discussion in fj 11.2b that the Thoinson limit of the Klcin-Nishina cross section is not applicable here for the calculation of gamma ray source functions. How- ever, we may use (21b) in order to correct for higher-order terms in the cross section. The recent work of SCHLICKEISER (1979) has shown that this approximation can be used for gamma ray energies smaller than 1 GeV. By using (21b), (18) and (51) the differential omnidirectional source function may he written as

N,s(mp2)1-P F ( p ) (kTsr,)P-3'2 Ey-(P+1)'2 . f&),.,.(p, By, Ts,,) 45bTwSI: S, , , (EY) = 2n3

photons eV-1 0111-3 s-l (57) with the dimensionless first-order correction function

if a single power law dependence Xe8 . E-p of the electron spectrum is assumed. The correction frrnction, which is eqrral to unity in the Thomson limit, contains the correc-

2"

114

lnterstdiar Differentia/ Electron S'ecfrum

ZZZ Cummings et al [1973) ...... Goldstein et a / . (1970)

10-6 1 _Demodulated: Daugherty E: a / . (?97S)

) r Fits : 1 Cowsikand Voges(1974/ Shukla and P a d (1976)

10 30 100 300 1000 3000 1000, Electron Energy/MeV

Fig. 0. Various estimates 01 the differential iiitrrstcllar c o m i c ray c1cc:lrori slxctrutn lor energies hetweeli 70 MeV and 10 GeV. Reproduced from S('Im1CREIRER and TIrtaLHEIiX (1978) by courtesy- 0 1 Wonthly Notices oi the Royal As troiioini ra l Society.


tion5 to the Thoinson liniit and is calculated for different values of 1) and T 7 TSrI ill figriro 8. For energies greater than 200MeV, there are clear deviations of /&:l(p, l?,,, 7’sLt) froiii unity, giving rise to a steepening of the inverse Compton ganinia spectruili (37) at highel, energies. Figure 9 shows the estimated cosmic-ray clcctron spectra a t uicr gies smaller than 10 GeV. These spectra have been derived either by deniodulating observations i r i the Interplanetary space (DALGHERTY et al., 1975) or by interpreting the galactic nonther nial radio background flux (GOLDSTEIN et al., 1970; CUMMINCS et al., 1973). The results of the first method are influenced by the uncertainties of the niodulation theory (FISK, 1976) ; the second method isliniitcd in accuracy due to uncertainties of the values of the interstellar magnetic field and the density of the ionized interstellar gas througholrt the p,zlttsy, which have to be known in order to account for the partial absorption of radio signals a t frequencirs below 50 MHz. As one can see froni fignre 9, even a t energies greater than 400 .MrV thc electron spectrum is uncertain a t least hy a factor 4. .\I1 aiithors agree about the o(wir1ence of a “break’’ in the electron spwtruin aiound 2 (ki’ (METER, 1975). Therefore in a exact calculation we are not allowed to use (57) v hich has been derived under the assumption of a single power law. However, we uiay IISC’

the following approximation: According to (24b) electrons of energy E , - whcw the hrcali shoiild occur - produce gamma rays with typical energies around

which for E , = 2 CkV is EYc = 95 MeV. If X(Ey, p , , Ki) and f ~ ~ ) , l ( p l ) denote thtl differential soiii’ce function (57) and the correction function (58) respectively ralrulatc d with electron sprvhmrn parameters K , and pi (see (39)), we derive the omnitliiwtiori:iI integral so i r r (~~ function for gamma ixy energies greater than EYc = 95 MeV to

,’&I!(

m

&<Ky 2 ICY<) = J dtS(t; S, K2) f ( t o l , ( ~ )

EY

116 R EINHAR D SCHL~CKEISER

(61)

EY;(S-1 ) /2 (kT’s, ) ) l /2 fi;>8-2)/2 - H(c9)

2 [ s - 1 TIL,C2 s - 2 + ~ ( 8 ) (7n,c2)l-s (1i27sny-3/2 K

photons c n r 3 s-I . According to PICCINOTTI and BIGNAMI (1976), this simple approximative calculation overestimates thc exact unhandy result; but the error is small: even a t EYc the appros- iiiiative rcsult deviates only hy 50 percent from the exact one. Referring to the mentioned uncertainties in the electron energy spectrum, our approximation is very reasonable. Table 5 shows the calculatedintegral source function SSR(> 30 MeV) and Xsu(> 100 Me\-) for varioiis estirnationsof p , s, ITl and K2. The fluctuations in the parameter values imply uncw tninties of both source functions by at least a factor 4: in clear contradiction to the result of Z’ICCINOTTT. and BKINAMI (1976) who have estimated this uncertainty to be only 20 p t ” ~ n t for gzmnra ray energies greater than 100 MeV.

b) S],ec>ttxl typc Ci-K

The frequency distribution of the second coinponent of stars of typc G--lC niay be rcpwsented by a gray-body spectruni of energy density TV,, = 0.3 e V ~ n 1 - ~ a i d teiii- peratiirr TSK = 5000 K \\ hich co1wsponds to ((53)) ( t )SK 1.16 e\-.

1 First Ordt-? Correction Factor IT= 5000DK)

O2 t t \ 0 1 L L - J I I L ’ I I I I I I f L l l l l l

10 30 100 300 1000 3000 10000 Gamma Ray Energy / M e V

Fig. 10. Corrertioii f&toi (58 ) lor 7‘ 5000 Jc :~i i ( i di l fe lmt 5alues ot p .

I n oidcr to produce ganinia rays between 1 MeV and 10 Gel7 in this interaction, elcc- trons vith energies bctwcen 400 MeV and 40 GeV (see (24b)) are involved. The calculation of the first-order correction fiirictioll j ~ ~ ) , I ( K y , p , TsI<) in this case - which i b

shown in figure 10 - demonstrates that higher order terms in the Klein-Nishina cross section .ire important. The break in the electron energy spectruni a t 2 GeV corresponds here to a hreak in the gamma my spectrum a t Eye = 24 MeV. By using the saine approximation as in the last section (59)-(61) we calculate the integral source function SS, (--- 30 MeV) and SS, (> 100 Me\‘) which arc’ shown in table 6. Since Eyc is inuch smalli~i than 100 Me\7, only the first S O I ~ ~ C C ’ fnnction is slightly overestimated by our tcbchriicjric-. As one can see fronl table 6, tlcpt,ndir:g cn the choice of the electron spectrini~ parnineters, the results are irncertnin hy at Icbaszt a factor 6 (fi& > 30 MeV) anti 4 (Ey > 100 MeV).

(Aimma Ray Astronomy and the Origin of Cosmic Rays

118 REJNHARD SCHLICKEISER

c) Total source function

Taking the results of a) and h) together we find the total source fiinction of inverse Coinpton scattered starlight to :

S, (> 30 MeV) g (1.84 - 11.80) . CIII-~ s-l

s-l, and

8, (> 100 MeV) 5 (0.67 - 2.91) .

where the enormous unccrtaintirs result from poorly known eosniio lay electron spectrum parameters below 10 GeV, as mentioiicd earlier. Due to the approximation made in integrating over the hreak energy E L , we may rcgard (62) and (63) as iipper limits.

TiLble 7 Previous estimations of the omnidirectional source function

8, (> 100 MeV) of Compton scattered starlight

Reference Ss (> I00 MeV)

BEUERMANN, 1974 HIGDON, 1974 Douus ct al., 1073 FICHTEL et a]., 1976 PICCINOTTI arid BIGXAMI. 1976 STECKER, 1977;~ SHUKLA and CRsansKY, 1977 this work

0.9 . 10-27

i . ~ . 1027 (0.35 - 3.5) . 10-25 2.0 . 10-27

1.8 , 10-27

~ ( 0 . 6 7 - 2.91). 10-27

1..54 .

1.7 . lo-?’

S, (> 100 MeV) in tin-3 s-1

In table 7 we coinpare our result with previous work of other authors. All estimations except the one of DODDS et al. (1975) are within our limits. However, i t should be noted that these authors have not taken into account higher order terms of the Klein-Nishina cross section and have used partially different representations of the local starlight frequency distribution.

5. Inverse Compton scattering of soft X-ray photor:s in hot tiinnels

A simple calculation shows that ganinia ray production by inverse Compton scattering of soft X-ray photons in hot tunnels is negligible, if not the flnx of cosmic ray electrons is enhanced drastically. One starts from the total radiative cooling coefficient I; for a low-density, optically thin gas calculated by COX and TI-CKER (1969) and RAYMOND et al. (1976) from-which one tlcrives the soft X-ray wcrgy density to

?.ox - 2- c (L.n,?t,,) cv c11t-3 (64)

11 here r N 10 pc (COX and SMLTH, 1974) is the scale height of the tuiiricl, L 5 10 *[ crg /< c i i i ~ s-1 the cooling coefficient, w e the thernial electron density and vII the total hydro-

gen density. Using the vnlw 7 1 , . ??I [ < c n r 6 one finds

((1, 5 A . 10-7 P\- CIN-3. (65)

Gamnia Kay Astronomy and the Origin of Cosmic Rays 119

Tdealizing tlhe soft X-ray photon distribution hy the inonoenergetic spectrum

with a mean energy of ( E ) ~ = 100 cV and calculating the source function i n the Thoii~s( 1 1

liiiiit which clearly overestimates its values, we find from (23)

photons c i ~ i - ~ s--1 (67)

which should he regarded as an upper liinit calculated in a rough estimation. I n this interaction cosniic ray electrons with energies between 100 and 500 MeV are involved in thc piwduction of 100 MeV gamma rays. With the paraineters of the Goldstein et al. electron spectrum below 2 GeV (see table 5 and figure 9) we evaluate (67) to

S (> 100 MeV) < 2 . 10-31 photons c 1 r 3 s-l (68)

which is a t least four orders of magnitude below the source functions for inverse Conip- ton scattering of microwave, infrared and starlight photons. So this production process is not important for circumstances similar to those near the solar systeni. However, if the flux of low energy electrons ( E N 100 MeV) is enhanced drastically, it way he significant.

6. Nonthermal electron biemsstrahlnng in the interstellar gas

In ordcr to produce gamma rays with energies lietween 1 MeV and 10 GeV in this intckr- action, cosmic ray electrons with energies between 2 MeV and 20 Ge\. are involved (see (42)). Figure 9 911 nimarizes the present information on the interstellar cosniic ray electron energy spectrum below 10GeV. Except the upper limit of Cuuiniings et al. all esti- matioiis ahove 70 MeV may be represented by a two-fold power law (39). For electron energies below 70 MeV one enters a milch inore speculative region where a high degree of uncertainty exists on the absolute value of tlhe electron flux (GAVAZZI and SIRONI, 1975). On the one hand, studies based on the frequency behaviour of the synchrotron radiation of these electrons cannot be perfornied any longer due to absorption of this radiation by free-free transition as well as to the Razin-effect ; on the other hand, an increasing fraction of observed electrons in this energy range is of non-interstellar origin. Tnterplanetary observations on board of Pioneer 10 and 1 1 (MCDONALD and TRAINER, 1976) have suggested that the inajority of the observed 0.2-40 MeV electrons are of .Jovian origin. Also, based on demodulation studies CUMMIXGS et al. (1973a) noted that the interstellar electron spectrum must flatten below 100 MeV and cannot he represented by a power-law extension of the higher spectrum. Therefore, with the current knowledge on the electron energy distribution we feel that a calculation of the bremsstrahlung source function bclow 70 MeV is rather uncertain, so that we restrict onrscJlves to ganiriia ray energies greater than 70 MeV. Calculations a t lower energies by FICHTEL et a1. (1976), Kniffen et al. (1977) and CESARSKY et al. (1978) are pure specu- lations at the present timc. For garnnia ray energies greater than 70 MeV the strong-shielding liniit is applicable. For a two-fold po law spcctriiiii we derive the integral omnidirectional source

120 REIXHARI) SCHLICKEISEB

filnction near the solar systeni from (40) to (SCHLICKEISER and THIELHEIM, 1978)

XI(( 2 Fry; ITy < E,) = 4x . 1.3aro2(nHI* + 2n,,,J $bR,

K , f ( p ) I?--) -. - f K l j ( p ) EY , K,f(s) k’,. ( > - I )

X T 1 (P - (<?-- 1 ) 2 (?I -

T.rble 8 O i i ~ i i i d i ~ ~ ~ t i ~ i i ~ i l iiitvgral hrenisstrahlung soiiice function Su (> 100 MeV) for ~ ~ ~ i r i o i i s csti~n,itions

of the local cohinic ray electron spcctrnni

Keferenrc p ; s E“ K,; K , Sli (> 100 MeV)

GOLDSTEIN rt al., 1970 l.s ; 2.5 2 3.36 ; 647.04’) ,5.02 . Cuinrnirigs et A.I., 1973 1.8 ; 2.3 1 1.34 ; 276’) (1.14 - 9.23) . 1 0 - 2 6 3 )

Consilr arid VOGES, 1974 1.0 ; 2.0 3 0.333 ; 1000 2.09 ‘ 10-26

-

D.IUCITRRTY et al. , 1975 1.8 ; 2.8 2 1.708 ; 3.51&64 2.62 . SHUKLI and P ~uT,, 1976 1.76 ; 2.95 2 1.68 ; 141G6.36 3.27 . 10-2G

E’, in GeV; K,, K 2 in e r r 2 R-l ster-1 MeVP-13”-1 Sn (> 100 MeV) in cni-3 s-1

I) spectrum (B) extrapolated to lower energies; 2, “nominal” spectrum; 3, lower ant1 uppr~ . limit; with “nominal” spectrum to 2.13 10-26 cn1-3 s-1.

Table 8 Bhows the integral onirriciirectional bremsstrahlung sourer' fimction for energies greater than 100 MeV calculated with various proposed electron spectrum parameters (K, , K2, p , s). The value c~alcalated with the upper liiiiit of CUMMINGS e t al. (1973) is obtained by nuinerical integration; the other estinintions with the help of (69). It can be scen that thew i*esults differ at least by R factor 8 depending on the choice of t h ~ electron-spectru 1 1 1 paranrci era. For energics greater than 70 MeV one finds

Si, (> 70 MeV) = (1.58 -- 18.92) - 10 2G cm s-1 (71 ~ h i c h will hc iiscd as l o w c ~ liiiiit for thc XB (> 30 MeV).

7. sllnll11aI-y

High-ciicrgy diffuse gairiina i’nq’s are prodiicd in t h c intersLellal. space hy cosniic. t . 1 ~ ~ - trons iii various intci actions n liich haw Letm disci~ssed in the preceding sections. now coinpare their iniportance with those f rom x”-ckcay prodi~ced in inclastic nilclear wnctions of cosnlic nucleons.

Gamma. Rap Astronomy and the Origin of Cosmic. Rays

T a b l e 9 Comparison of source function of diffuse high energy gamma radiation

121

process S( > 100 MeV)2) S( > 30 MeV)2) ,S(30- 100 Me\7)2 )

C‘ompton scattering of micarou.;kve photons Compt.ori scattering (0.67 - 2.91). l(t-27 (1.84 - 11.60) . 10-?’ (1.17 - 8.69) . of st~;irlight Co~iipt~on scattering (0.43 - 1.87). (1.42 -- 5.50) . lo-?’ (0.99 - 3.63) . of infrared photons

scattering

Total: electron initiated (1.32 - 10.05) . (2.12 -~ 21. 57) . 10-26’) (0.80 - 11.52) . 10-261)

(0.50 - 3.40) . (1.89 -- 9.40) . lo-?’ (1.39 -- 6.00) . 10-’Li

Total Conipton (1.60 - 8.18). 10-27 (5.15 - 2 m ) ) . 10-2’ (3.55 .- 18,:a). io-=

Rremsxtlahlung (1.14 - 9.23). (1.58 - 18.92). (0.44 - R.OlJ). 10-“l)

(1.48 0.23) . (1.04 T 0.29) . lo-’’ (4.00 - 5.20) . 10-”

l) ouly loner limit ?) AS’ (> 30 ;\lev), J!? (> 100 MeV), S (30-100 MeV) 111 c 1 r 3 s-l

a) Comparison of soiirce frinctions

Tablt. 9 coii ipres inttt;;ral omnidirectional source function of diffuse gaimiia radiation at t \ z c) c,rcvgies. The soiit’ce functions have been calculated with parameter values which

1)kd for astrophysical circumstances near the solar system. The ZO-decay sotirce ~ i s are derived In> inaltiplication of the corresponding integral production rates gure 7) with the l o d interstellar hydrogen density of 1.14 c 1 r 3 , where an error

of & 15 percent (STECKER, 1973) in the production rate has been assnmed. As on^ can see, x0-decny is doininating a t energies greater than 100 MeV. Hovever, the conti 1 tmtion of processes initiated by cosmic ray electror,s may ainonnt 45 percent of the tots11 -oiirce function where most of these “electroiiiagnetic” gamma rays steni froin ln!~insstrahlung. Previous calculations (STECKER, 1971 ; PUGET and STECKER 1974 ; Donns et al., 1975) have underestimated this contribution considerably and h a w n r g l i ~ t cd the irifliience of electromagnetic ganiiiia rays. *It lon ei, energies (30- 100 MeV) the contribution of gaiiiiiia rays from xO-tlceay de- creasw and the electromagnetic procesaes dominate. This transition from a niainly nuclear origin to an electromagnetic origin of cosmic diffuse g,zmma rays has fit st hrrn 1)ointcd oiit by FICHTEL et al. (1976), and can be seen clearly froin figure 11 which ticlinc,,itw the energy dependences of the various differential source fiinctions. The xo- tl(~euy soi i ice function is taken froin the work of STEUKER (1970) whereas electromagne- t ic s o i i i ce functions are calciilated with those paranieter values Nhich iiiaxiniize tht 111.

Onc itiiriicciiately 110tc.s the fnnrtairiental difference in their energy hehavioiii : mheieas thr. -;%pcciruni is sytriinetric aronnd 70 MeV, all elretroinagnetic proc i,rpic+~ n t c d hy power l n u s in gantnia ray energy. This ttieans that ineasuretiierits of the

rgy spwtruni of cosniic gamma raps help in finding thc doiiiir;~.i~t type of illlclcal 0 1 clectrotiingr~ctic? (1975) and STECKER (1977) have pointed out that these estimations of fcrcntial source function are only valid in typical regions of the galactic

disk ( 2 N 0) : there one expects a doniinarice of pion decay and brenisstrahlung. SCHLICK- and TTITELHEIJI (1978) ronc~1i1ck.d that tlic spcxctral hehaviour of thc p iiinia lay it- is proportioi!al to tlic siini of the pic nic and bix n i~s t rah l i in~ s c i i i w ftiiwtion

122 l< i : ix~ m u SCHLICKEISER

since both gamma ray intensities H I c' scaled by the same line-of-sight integral (see (50) and (36) - (3) ) assuming that the spatial cosmic ray electron density varies lilw the cosmic ray nucleon density ( ~ ~ ( 1 . ) oc N , .r(r)).

I 3 10 30 700 300 100030001UUUO Photon Energ;$ / MeV

Fig.. 11, 1,oc;tl diflerential ouini(lire~tioiial gittniiia ray S O I K W lunct.ions for gamnia ray energivs hetwren 30 MeV and 10 GeV. The bremsstralllullg source fuiictioii i s t!xtrapolated from 70 MeV to lower energies. The electromagnetic source Iiinctioiis are calculated with peraiiictcr \slues which niaximi7.e them.

Of course, circiiiustances exist where the performed estimation of the source functions and their ratio to each othc.1. is no longer valid. BEUERMA" (1974) and COWSIK and VOGES (1974) have noted that within the galactic center region ( R < 1 kpc) the energy density of diffuse starlight is increased hy a factor- 50 to 100 so that inveme Coiuptori scattering of starlight will doniinate there. Moreover, iiieasureinents of the long lifetime of cosmic ray nucleons (GARCIA-&{ z XOZ

et al., 1977) suggest that cosmic rays propagate predonlinantly in regions M ith loiz gas density ( ) b H < 0.2 H-atoms ci11r3). This medium may either be the mentioned intc.i*- stellar tunnel network (SCOTT, 1975) or the so-called cosiiiic ray halo around the galactic matter disk ( r J ~ ~ ~ ~ ~ ~ , 1976). I h e to the vanishing matter densities in both regions, gauiina rays froin pion decay and hremsstrahlnng are negligible. In these regions i~ doininarrcc of inverse Compton interactions is expected. Camma rays from hot tiinriels will niiiiiily be produced by invcrse Compton scattering off tnicrowave and starlight photons since the contrihntion of scattering of soft X-rays is negligihle (see 9 JIT.5). Halo gauiiilx rays

Gamma. Ray Astronomy and the Origin of Cosmic Rays 123

result i'loiii tlie same interactions since the spatial distribution of starlight photons pwpendiciilar to the galactic plane is broader than the matter distribution (SHUKLA and PAUL, 1 976), whereas the microwave radiation field is universally distributed. As has been pointed out I J Y SCHLICKEISER and THIELIIEIM (1977a) the ganirna ray eiriiisivity of Conipton sccdtered microwave photons is directly proportional to the distiibntion of the cosniic ray electron density (see (17) and (18) with Wl,(r) = If'*&):

\ ~ h o i t SUB( > E;) denotes the integral omnidirectional soiirce function (54) calculated for parameter values incasured near the solar systeni. Equation (72) is valid if one assu- mc's thtit the shape of the cosmic ray electron spectrum does not vary with position, so that (7) holds. If it is possible to separate this contribution of halo gainnia rays froni those produced in the galactic plane - which are seen too due to the particular location of the solar system inside the galactic disk (SCHLICKEISER and THIELHEIM, 1976) - dirc>ct> conclusions can be drawn on the spatial distribution of cosmic ray electrons per- peiidicular to the galactic plane and therefore on the extent of the cosmic ray halo. Ar- gurrients based on the interpretation of synchrotron radiation from high latitudes a r c limited in this respect since the synchrotron brightness (see (8)) depends on the product of the cosmic ray electron density and a given power of the rnagnctic field strength the distrihution of which is rather unknown.

b) Indications for a scft origin of galactic ganriiin rays

I>iffcr cvitial energy bpcvtra of cosniic gauiina radiation coining froiri the galactic disk havv been nieasiii ed i i i the European satcllite expcrinient COS-B (BEKNETT et al., 1077 ; Pard ct al., 1978). I n order to diminish the infhrcnce of the finite, rnergy-dependent angnlar resolntion of the COS-B telescqie, an integration over galactic latitude from brl = -10" to V I = 10" has been performed; the results are shown in figure 12 for four longittide regions. As one can see, th,, four spectra t:rt' rc;niarlisbly similar in shape. 4 pule xo-spectruiii which has bwn fitted to the observati~ns a t EY = 600 MeV is not consistent with the data, in contrast to a pure breinsstrahlung spectrnrri. This conflict of the often propscd &decay origin (RTECKCR et al., 1974; DODDS et al., 1975) has been first poirh d out hy SCHLICKEI~ER and THIELHEKM (1977b) with the help of preliminary COS-E data (REXNETT et al., 1976). Their argiinient is based on the interpretation of the dimensionless energy factor

F(70 - 300 MeV; b") E"( 300 - 2 000 MeV ; b")

R(b") rz (73)

for different longitude ranges I" E Ell, Z,] where P(dE,; bzl) denotes the measured gauinia ray i ntrnsity in tlie energy interval LIE,. Experimental cncrgy factors derived from pre- liiiiinary COS-13 d;cta havct been compared with theoretical factors and the compai ison is shown in figure 13. The theoretical factors have been calculatcd hytaking into account thrl iiniri. ericrgy-dependent angular resolution of gainnia ray detectors which coiiies from the iisc of spark chambers in experimental technique (for details see SCHLICKEISER and THIELHEIM, 1977 b). The calculations have been done for a 2-component (Tio-decay arid brenisstrahliing) and 4-component-model (no-decay, bremsstrahlung, starlight and inicrowave scattering). Source functions have been used for electromagnetic processes which mht~rr nirich smaller than the upper limits discussed 3 TTT.2-6 and shown in

124 RKINIIARD SCHLICKEISER

- I 1 - 2 10-3;

7 10-4r

c 10-5

I b 0 L

L? Fu I

c, F

- L1 C aJ L

1 0 - 6 ~ ,

6 OD< f '< 9 0 I

- I I

r I

I I / , , ! , , I ! I

0.1 1 GeV photon energy

I

I

I I I I , ,Ul I I

0.1 1 GeV photon energy

Fig. 12. Measured energy spectrum of ganirria radiation Iroiii four regions of the galact,ic disk (BEXXETT et al., 1977). The dashed and dotted lines are x"-decay spectra lit,trd to the data at 600 MeV. The straight curve is the bretnsstrah- lungs spectrum of HIaoOa (1974). Reproduced Ir-oil1 BEKNETT et al. (1977).

diation since all electromagnetic processes imply energy factors which are consistent with these values. If this preliniinary analysis will be confirmed with final COS-B data, this result will be a proof for gamma radiation from the halo. CESARSKY et al. (1978) have shown, that the nieasured spectra of COS-B are consistent with a diffuse 4-component-origin-model if the electromagnetic source functions - especially the bremsstrahlung one - take their maximum values. A variation of the clec- tron/proton ratio in the cosmic radiation throughout the interstellar space is then implied (STRONG et al., 1978). However, the discovery of several point sources (up until now 29) (HERMREN et al., 1977, WILLS eta]., 1979) in the gammaray sky map has made these conclusions uncertain. The alternative hypothesis, that a superposition of so far unresolved point sources is responsible for a significant part of the galactic gamma ray emission and its steep spectrum, is also quite popular (PINKAU, 1977, 1979). However, these point sotirces exhibit n strong concentration towards the galactic plane, so that a pure point S O I I I ' C ~ origin of galactic gamma rays would be in disagreement with the rneasured broad


350' < 1'<20°

f COS-B DATA

- R n t B + S + M

--- R,+g

from SCHLICK-

la 10 2 103 MeV 10' a- Roy Energy

Icig. 14. l)iflerentialgo~t~marag spectriiin from thedirectionof the galactic center for energiesbetween10MeV and200MeV. ILeprodured froiii KNIFI?RN et al. (1077).

126 REINHARD SCHLICKEISER

latitudc distribution of galactic gamnia rays (FICHTEL et al., 1975; MAY-ER- HAWEL- WASDER et al., 1980). For energieq helow 100 Me\' the doniinancc of electroniagnetic processes has kwrn ve! i- fied experimentally. COS-B spectra in figure 12 as well as results froni SBS-2 (FICHTBL et al., 1977) and recent balloon flights ( K N I F P E X ~ ~ al., 1978)cxhibit theex1,ectedincreassr of gamma ray production at lower gnniiiia ray energies as can be seen froin figure 14, where the differential gamma ray spectrmu froiii the direction of the galactic center is shown. As a summary we may note : Cosmic ray clcctrons are important for the interpretation of the results of galactic ganitna ray astronomy. In typical regions of the galactic matter disk mainly nonlheriiial brwiisstrahlung of rtlativistic electrons in the interstellar gas produces significant contri1,ntions. I n hot tunnels or at higher latitudes lbrrl > 3" - whcrc we observe regions of the gahxy with vanishing matter densities but halo electrons - inverse Cornpton scattering of starlight and microwave photons produces high energy gamma rays.

8. Origin of cosmic ray nucleons and diffuse gamma rays

IVc arc now going to discuss the original question raised in the introduction: Do the results of high entrgy ( E , > LOO MeV) gamma ray astronomy in their present form provide definite conclusion. on the 01 lain of cosniic ray nucleons? The answer has to be NO for the following reason. Experimental results on the energy spcctriini of galactic gainma rays a?, ~ c l l as a comparison of integral gainrria ray sourcc ftinctions rulc out the pure ZO-decay origin of galactic ganima rays with energies greater than 100 MeV. As long as longitude and latitudc profiles of galactic gamma ray eniission are given as integral intensities above E, = 100 MeV, the gainma ray intensity is con- taminated by significant contributions from cosniic electron initiated processes as well as unknown contributions from point sources. This contamination obviously fcrbids intcrpretatinii of the spatial T aiiation of ganirna ray intensity in terms of the spatial variation of the cosmic ray nrrcbl-ori density as has been done previously (c.g. BIGPITAMI and PICHTEL, 1974; STECKER 1.t al., 1974; STECKER, 1975). However, I sec three possihle alternative mcthods of answering this iniportant question :

(i) neutrino astronomy, (ii) gamma ray line spectroscopy,

(iii) gamma ray sky map a t higher threshold energy e.g. E, > 500 MeV. The first method of dctecting secondary neutrinos froin x ' -decay produced hy inelastic collision of cosmic ray nucleons with atoms and molecules of the interstellar gas (see Q 11.3 and STECKER ( 1979)) sounds vcry proniising, but the experimental difficulties of neutrino astronomy are legion. Until now only upper limits of cosmic ricutrino flux have been given and it will last dwades until w e see a clear detection of neutrino radiation. The production of gamma ray lines in the 1-10 MeV energy range by excitation of a t o m of the interstellar gas by cosmic l a y nucleons has recently been reevaluated by RAMATY et al. (1979) in detail. By measuring the spatial variation of appropriate line emission throughout the qalaxy, conclusions on the spatial variation of the cosmic ray nuclcon density iV-,(r) arc expected. A theoretical problrin in this respect niay be the contamination by background ganinla radiation from inverse Compton scattering of starlight and infrared radiation since thr source functions of there processes increase significantly with decreasing energy and niay prevail against the source fiinction of garnina rag lines. Another probleui i q the detection technique in this energy rxngc. The

G‘immn Ray Astronomy and the Origin of Cosmic Rays 127

angular resolution of pieseiit double Coinpton telescopes 1;; abo11 t 5’ whereas thc rnergy resolution is of the order of 10 perccilt FWHM at 2 MeV (GRAML, 1979). Both resolutions have to be improved in order to perform successful ganima ray spectroscopy. The ihird method seems to be the simplest and iiiost promising. If the published ganiina ray profilcs would be reanalyzed and given as integral intensities above, say, By = 500 MeV or 800 MeV, this may provide important conclusions on the origin of cosmic ray nncleoiis. First, as can be seen fioin figure 11 a t gamma ray energies greater than 500 MeV the contaiiiiriation by diffuse electroinagnetic processes inay be neglected even if the inaxiniuin valuzs of electromagnetic source functions are considered. More qnanti- tatiwly, 83 percent of the total difflise integral gainiiia ray soiirce function above 500 Iclcl’ is due to +-decay. Secondly, recent measiirenients of thc energy spectra of cosniic- ganiiiia ray point soixoes (W~LLS ct al., 1979) have shown that these (except the Vcia pulsar spectrum) are niuch steeper than the hard nO-decay gainma ray spec- trnm. This means that wc also niny neglect the contribution of discrete sources to the y;~iiiiiia ray rniission a t high energies (ICY ‘> 500 MeV). Another advantage is the much 1)ettc.r angular resolution of the gamma ray rrlescopes a t these energies. The COS-B expr~ii!itvt with a n ohsewation time of 5 yenrs (now) has collected eriough data to pro- vitlt. dc+ailed longitude and 1:~;itiide profilcs of eri~rglr tic (By > 500 MeV) gamma rays. .\s a result of this nor k I i i i L v cqxrinieri:al g~iiiinz i:iy astronomers to gioup their f lat2 thi.; w,iy.

IV. Gamma Ray Point Sources

The di~covcry of a number (at the present tiwe 29) of intense localized sources in the ganiinn isy sky has h e n reported by thc SAS-2 (Thompson et al., 1977) and COS-B (HEIMSEY el a!., 1977; WILLS et al., 1979) satellite experinicnts. Four of these sources h,xv-e been identified with known radio pulsars (HARTMANN et al., 1976), one source is

ociatcd with thc quasar 3 C 273 (SWANENBURG et al., 1978) and the source CG 353 + 14 lies in the direction of the ,U Oph cloud coniplex. Energy spectra in the range from 50 R ’ I ( x \ ’ LO 3 GeV have been nieasurcd (WILLS et al., 1979) for four of these sources - the pulsars NI’ 0636 and PSR 0833-45, 3 C 273 and CG 195 + 4. The source CG 195 + 4 is of particular interest since i t is still unidentified with known astrophysical objects. The starting point for a diqcussion of gainma ray production in point sources is the idea that thew gainnia rays result from the same types of interaction listed in 3 11. If one assumes that the phenomenon of gamma ray production in point sources may be ex- plained by a “classical” process (electromagnetic and nuclear intcractions) there arc no other interactions which have to be considered, except ga:nnia ray production by cur- vaturc mtdiation iii the magnetic field of pulsars (STURROCK, 1971; STURROCK et al., 1975). Alternatively, it is possible that this phenomenon reqiiires new type* of gamma ray production processes c.g. garrima ray emission from niini-blach-holes (PAGE and HA~VKINO, 1976) or from Penrose powered black holes (IJAFATOS, 1980). During this discr:iriori n c will follow the classical picture and assuiiie that gamma rays in point soiii w s are produced by intcractions of relativistic particles, too. We start hy discussing as an illustrative example the measrired energy spectrum of CG 195 + 4 for energies greater than 50 -MeV (WILLS rt al., 1979; HELMKEW and WEE- K E ~ , 1979). The observations are confronted with predictions of the basis types of emis- sioil I ir&ls (SCHLICKETSFR, 1980a). In order to calculate predicted energy spectra wc

1. ~h~ tiisti ihiitioiis of relativistic particles and ambient photon g,?ses arc sp3tially

as?i l i l~:(”

isoti opic,

3 Z t i i , ( l i r i t t ,,i o i t d r i i t l e ( I ( I PliysW, 13tl: 20, Hrft

128 KEIXHARD SCHLICKEISER

11. The shape of the energy spectrum of relativistic nucleons in CG 195 + 4 i5 t h c same as measured near the solar system (BIGNAMI e t al., 1976; ARDI-I,\VATI~H and MORRISON, 1978).

111. The rnei'gy spectrainof relativistic clectrons is pomer law like Ne(**) E-P fur E > li:, > ( w e c 2 ) (e.g. ,!$, = 10 MeV). This form of the electron intensity distribution is sriggrsted by iirost of the proposed cosmic ray acceleration mechanisms (CESARSKY, 1977) and is confirnrcd to hold over wide electron energy ranges by studies of the synchrotror, biightness distribution in frequency from probable cosmic ray so111 ces (ALEYANDER and CLARK, 1974) as well as observations near the solar system.

I\r. Since we don't know the freqiiencyspc ctrrini of target photon gases inside CG 195 + 4, we approximate this distribution by an idealized step-wise distribution around thcir mean enrrgy ( E ) (SCIILICIIEISER, 1980h) which is treated as a free parameter:

(0 : step function, w(r) : photon energy density).

The distribution (74) provides reasonable fits to each of the physically possible spectra (thermal brcnisstrahliing, giagbody, power, law) and keeps the number of free para- iiietrrs to a rninimirm. (:aniina ray source fririctioris &'(I#,) are then calculated for differcnt proces (fi,oiii (46)), nonthernial brenisstia1:lung (37), inverscl Conipton scattering (18) and clec- tion syncht otron radiation (8). In order to redrice the number of unknown paranietcrs in CG 195 + 4 which would enter th(3 calcnlations - thr spatial vaiiation of the dcnsity of relativistic iiucleons N c - r ( ~ ) , electinns N , ( r ) , matter density n ( ~ ) , magnetic firld strength 11, (T) , target photon enerqy density W ( T ) - Sehlickciser (1980a) considered norninlizcd (at lCAr = 145 MeV) differential gairiiiia ray spectra j (Ey ) . If absorption effects are neglected, simple expressions fot this spwtriini

can be derived for the different processes although assnniptions (I) - ( I V ) are fairly general. EAT is not a free palameter in the comparison with the normalized (at E N ) observations, although it reduces the ri iiniher of degrees of freecloni of the X2-coinpaiison.

a ) x0-decay

Here

where @(KY) is displayed in figure 7.

h) Nonthernial bremsstrahliing

For E, 2 E, we use the strong-shielding limit (37) :

jB(ZY) = (EY/EN)-p (1 free parameter: y )

which i s a single power law.

(77)

Gamma Kay Astronomy and the Origin of Cosmic R,iy> 129

c) Inverse Coinpton scattering

p 1-1)

( 2 free paianieters: ( F ) , p )

In the Thomson limit (23) j I T . ( E Y ) = (Ey/EAv)- fP+’)’‘L

(1 free parameter : 1 ) ) .

mliich is a single power law.

d) Synchrotron radiation

Here we find is( Ey) = ( Ey/E’,r)-(p+l)/z (1 free paraineter: p )

thr same resiilt as in the Thoiuson liniit.

e ) xo-decay and breinsstrahlung

111 this case

(79)

( 2 free parameter: p and 9).

IZy i.onipariiig these normalized spectra (76) - (81) with the nornialized observations we t i t i : \ find thf, favoiirite gamma ray production processes in this soiirce. The so-called S,;\.OU-niodc~l (MONTMERLE, 1979) would suggest cosmic ray-inattar interactions (76), (7?, (8 1) : Coinpton cinission models like the Sclf-Compton-Synclii~otron-in~)~~i~l (JOSES et a].. 1974: MVSHOTZKP, 1977) imply a behaviour (78) in the gnnrma ray rangtl if the t:i i get photons are energetic enough. I i i f i~ t t r e 12 u e show the coniparison for CG 195 + 4. The most probable values of the frcc paraiiietcrs arc determined by nsing the ~2-niininiuni technique describod in detail by LAIIPTOL et al., (1976). The curves shown in figiire 15 are calcnlatcd with parameter valries giving the smallest x2.

onc’ can see, the inverse Compton scattering inodel provides an excellent fit to the o b v i vat ions whvreas H single power law and a x0-spectrum as n.ell as a comhinatiori of both pivv poorer fits. T T ~ table 10 the niininnini values of x;,, per degree of freedoni are listrd for the different models expressing this result more quantitatively. We viev this a!: a stlong indication for an in~rerse Coniptonorigin of the gamnia rap rntission from C(4 195 4.

130

10 5

T\*

REIXHARD SCRLICK EISER

ico-detity 2.8 bremsstr:tlilinig 3 .9 Inverse Coniptoii statt,ering 0.8 synchrotron ixctiation 1.9 xO-rlecay + hr.enih.;t ixh!iing 2.0

In figure 16, the 1 - G contour in the (c)-p-paranieter plane is shonn, resulting from the statistical uncertainties in the gmnnia ray observations. In order to explain tile high energy garrinia ray emission froin CG 195 + 4 with an inverse Conipton origin, rather energetic target photon gases ( , I - ) 2 2 eV) are involved. This suggests thak C(: 195 + 4

: 3 t CG 195 + 4

I Acceptable Values (16 - c o n t o u r / I

O L d L l u l I l L d I l i l l l l l l I 1 1 1 1 1 1 1 1 , , u l I I I I 1 1 W I

1 0 - 8 10-6 10-4 10 -2 Mean .krget Photon Energy < E ) / M e V

Pig. 10. I - G contour in the (e)-p-parauirter plane for C G 195 + 4 ror the case of the iuverse Coiiiptoii scattering einissiou iiio(le1. The cross inarks the comhiiietion with the ~nin in i iu~i value of x a . Reproduced lroili SCHLIrAEISEIL (1 98Oa)

Gamma Ray Astronomy arid the Origin of Cosmic Rays 131

also emits radiatioii in thc ultraviolet and X-ray frequency range. h d , indeed, indications for X-ray eiiiission (2 - 6 KeL ) from CG 195 + 4 have been announced (Ju- LIEN and HELMKEK, 1978; LAMB and WORRALL, 1979; SHARE et al., 1979). SCIILICKEISER'S (1980a) work deinonstmtes that the gamma m y emission froin CG 195 + 4 probably originates by inverse Coriipton scattering of XUV-photons by relativistic clpctrons. The saiiie conclusion has been derived from an analysis of the measured gamins ray spectra of four other ganinia ray sources : 3 C 273 (JONES, 1979) and NP0532, PSR 0853-45, NGC 4 151 (SCHLICKEISER, 1980b). Taking these results together a scenario of gamma ray sources is suggested, consisting of an electron source and a source of energetic (XUV) photons, where ganinia rays are produced by the interaction of both populations. So the physics of gamma ray sources is probably closely related to the physics of X-ray S O I I ~ C ~ R . The study of gainilia ray sources may help to solve the probleins of X-ray sources, narricly to find the imderlying soiirce of power in these objects and to ansu'f'r the question of the origin of relativistic electrons which are iesponsible for inverse Comp- tori scattered gamma rays froin these objects. It is our hope that the physics of gamnia ray soiirccs will improve our understanding of production and acceleration of cosmic particles in the universe.

Acknowledgements

This paper was written during the mthor's stay a t the Institnt f u r Reine und Angewiindtc Kern- pllySik deer Universitit Kid. I thank Prof. K. 0. Thielheim for suggest,ing this work ;?nd his steady intcrrst. This work has been influenced by numerous discnssions and suggestions of collcagirrs working in the field of gxmnxi riLy astronomy. 1 thank Mrs. R. Jliiller for the careful typing o f the i~i;innscript..

References

AI~DLJTI~WAHAB, M., ~IORRISON, P., Astrophys. J. SB1, 1, 33 (1978). Aran, E., e t nl., Proc. 15th Int. Cosmic Ray Conf. (Plovdiv), Vol. 1, 372 (1977). ALEXANDER, J . . ('LARK, T. A., in: High Energy Particles and Quanta in Astrophysics, eds. F. 13.

McDonald and C. E. Fichtel, Cambridge; MIT-Press, p. 273 (1974). ALLEX, C. W., Astrophysical Qu,zntit,ies, London ; At,lielone Press (1973). ANAND, K. C., DANIEL, R. R., STEPIT

KEENNETT, K., et al., in: The Structure m d the Content of the Galaxy and Galactic Gamma Rays,

Bmxiwr, K., e t al., in: Recent Advances in Gamma-Ray Ast.ronomy, eds. K. D. WILLS and

BETHE, H. A, HEITLER, W., Proc. Roy. SOC. A 146, 83 (1934). BEURILMANN, K., in: The Context and Status of Ganinia-Ray Astronomy, ed. B. G . Taylor, ESKO

Drunanir, G . E., F~CHTEL, c'. E., Astrophys. J. 189, L 66 (1974). I<1GNA4M1, (2. F., M.KXCCARO, l'., PAIZIS, T., Astr. A4strophys. 51, 319 (1976). BLUMENTHAL, G. R., GOULD, R. J., R,ev. Mod. Phys. -3-1, 237 (1970). ISRICCI, E., DROUBEZ, J. P., F L A R I ~ X I ~ , E., HANYEN, J. D., MORRISOX, D. R. O., VERN/HERA4

73-1 (1973). BliRTON, W. B.. in: G;ilactic ttnd Estiagahctic R,adio Astronomy, eds. G. 1,. VERSCHUUR and

K. I. KELLERMAKN. Berlin: Springcr-Verlag, p. 82 (1974). BCH.TON, W. B., Ann. Rev. Astron. Astrophys. 14, 275 (1976). BURTON, 14'. R., Goizuou, $1. h., Ast,rophys. J. 207, 189 (1976). C ' \ I ~ ~ : Y , D. C., et al., l'hys. Rev. Lcttei's 33, 327 (1974).

, S. A, Astrophys. Space Sci, 36 16'0 (1975). BADHWAR, 0. D. STEPHENS, S. A., Proc. 15th hit. Cosmic Ray Conf. (Plovdiv), V O ~ . 1, 1% (1977).

eds. C. E. FICHTEL and F. W. STECKER, KASA X-662-76-154, p. 23 (1976).

B. BATTRICK, ESA SP 124, p. 83 (1977).

Sp-1.06, p. 259 (1974).

C 1x1 ~ L L O , G.. GOULD, R. J., Nuovo Ciniento 2 R, 77 (1971). C w II<-,KY, C. J., Proc. 15th Int. Cosmic Ray Conf. (Plovdiv), Vol. 10, 196 (1977). Cm%iisKy , ( I . .J., PAUL, J. A., SH~TKTA, 1’. G., lstrophys. Spice Sci. 59. 73 (1978). C O X , 11. P., SVLTH, I%. bv , &trophy\. J. 189, 1, 105 (3974). Co\, L). P., TUC’KER, W’. H., Astrophys. J . 157, 1157 (1969). ( “ ~ w ~ I K , R.. VOGES, W., in: The Context and St<rttis of Ganimn-Rag-4strononiy. c d . R. ( i TIYLOR.

(’unim\Gs, A. C , STONE, E. C., VOGT, ll. E.. Pior. 13th Int. Covnic Rny Conf. (Den\er), To1 I .

I ~ A L L LRRO, A . i n : Stomir m d Molecula I’iocesses, ed. D. R. BATFS, Nrw Yolk; dt,tdcmic Press

D A I ~ G H C R T ~ , J K., HARTMAN, K. C , SCHMIDT, P. J., Astrophys. J. IHS, 493 (1976). IhDnExs, a. N., SCHLUPMANN, K., published i n Landolt-Bornstein (1971) DILWORTH, ( I . , i n : The Interstellar Medium, ctl K. PIXKIU, Dordrecht; Reidel, p. 69 (19731). l>oi)ns, D., STROXG, A. W., WOLFENI)ILC, A. W., WDOWCZYK, J., J. Phys. .I 8, 624 (1975) F’tzio. G. G., STECKLR, F. W., WRIGHT, J. P.. Astiophys. J. 113, 611 (1966). FLI.YULIIG. E., Y K I V ~ K O I W , H., Phys. RPV. 73, 449 (1948) FELTFZ, J. E . MORRISON, P., Phys Rev. Letters 10, 453 (1963) FELTRY, J. E., NORR~SON, P., Astrophys. J. 146, 686 (1966). F I C I ~ T I ~ , C E., H~RTXAX, R. C., KNIP’BEN, D. A., THOXPSON. 11. J., BIONAMI, C:. F., Oua~nmw, H.,

OZIL &I. E.. TUMER, T., Astropliys. J . 19S, 163 (1975). FICHTI~L, C. 16.. K V I F ~ E N , D. 4., Tsoxi~soz-, 1). J., RI(~NAMI, C . F., Crrcuxc. C. Y., .l\trophvs. J.

20% 211 (1976). F I ~ I I ~ E L . C E., KNIFBEN. 1). A, THOMi’cOiX, 1). J., i n : Rwent ddv.rnces in G~iinniCr-J<,iy Astro-

iioiny, eds. R. D. Wills and B. B&rrTnrc3#. ESA SP 124, p. 101 (1977).

ESRO SP-108, p. 229 (1974).

33i (1973); Vol. 1, 340 (1973a).

(1962).

FI\I\, L. A . Alstit>pllys. J . 206, 333 (1976) FOLLTX, J. W., Phys. Rcv. 72, 743 (1947). F L ~ R I ~ ~ R , P.. GILMAN, C., WonDmcxo\, C’ J., Proc. 14th Int. C‘osniir I t ~ y (’onf. (Prlimith). Val. 1 ,

( q ~ R C I \ MUNOZ, M., M ~ S O N , C . &I, SIMPSO\, J ( i \ \ \ L Z I , G . , ST~IOXI, G., Riv. Nnovo Cimento ( : I V L H L ~ R G , V I,.. SYROVATSKII, S. 1 , Tlic Origin of Cosniic Rags. Oxford; l’crp,imon Pies5 (1964). (;o~,i)cri IS , X. L., RIMATY, It., Fiw, I,. A. , Phys. Rev Lcttt~rs It, 1193 (1970). ( + O I < J ~ O X , 81 A.. B ~ R T O N . I!‘ B., Astrophys. J 208. 346 (1976). (:oi i m . R. J.. Phys. Rev. 185, 72 (19W).

( l o r LI). I t . , J . Astrophys. J. 196, 689 (1975). (;it t>ii,. 1” . Iliibcrtation, MPI f . Phvsik iind Astiophysik (1979). H a f i r 7 1 \ \ , 1t. C.,etal.,in: TheStruc t u t r b ,rnd thcConteiit oftheU,tldxJ;nndrralnctic Cjctnirnci Bays,

! I ~i t ra r ivx , c; . ;\IvLLI!,R, D., H I LPLF,R, W.. The Qriantnni Theory of Rdicition, London; Oxfold Prcass (1931). H F L \ ~ I : s , H. I<’.. KEEKE~, T. C., Astrophys. J. 228, 531 (1979). HFR\ISES, W . ct ‘il., Nature, 269, 494 (1977). Hruiwu, J. (’ . \I’hcre Are Thzy No\% 7 Cosmic Rays fiom Superno\ .re, Ph. I) thesii, Lo5 Aingc~lrr;

HTr,T.ts, A. Jx, Proc. 14th Int. Cosmic Ray Conf. (Muiiirh), vol. 2, 717 (1975). I s k i i r , C., et A, Proc. 13th Int. Cosmic Ray Conf., (Denver), Vol. 5 , 3073 (1973). . I 11 C*II, J . M., ROIIRLICH, F., The Throi ’i’ of Photons mii Electrons, C,imbridgcb; \tldisoir-\Veiley

J L UKIYS, E. B., Alstrophys. J. 210, 107 (1978). .JOI~LITJ, *J. R., Astrophys. J. ?Oh, 900 (1976).

. V C., l’hys. Rev. 167, 1150 (1968). , T. \V., Astiophys. ,J. 333, 796 (1979).

42.7 ( 1 976). -,. .J. 217, 8-59 (1977).

( ’ o ( LIJ. R. .J.. Physics 62, 555 (1972)

etl, E FrCIITEL and F. w. S T w i d R , SASA X-062-76-154, p. 12 (1976). 15, T., Phys. RN Letteri 38, 1368 (1977) .

Uni\Tc.rsit\ of Cdifornia (1974).

( 10.5.5).

J O K ~ T. I!‘., O’DELL, S I,., S T ~ I N , W. A, A\tiophFs. ,J. ISS. 333 (1974). JVTJI-Z. P. F., KNLMKEX, H. F., N,rture 272, G!)9 (1978). K ~ I ims, AT . Astrophys. J. 236. 99 (1980).

Gamma ILcy Astwnoiiiy ai:d t,he Origin of Cosni ic Itiiys 1 33

I.(WIFRhV, 1) 1.. BElCTbcII. D IL.? BlORRIS, 1). I., !?lr,3FEIRA, R. A. R.. l t % O , K. P., 1 1 1 . Recent i d - vanccs 111 C:amnia-R,iy Ahfronomy, edb. R. 1). WILLS a i d B. B \TTRICK. ESA h P 124, 1) 117 (1977); Astrophys. J. 826, 591 (1978).

hMB, R . C., \\’ORRILL, D. N., -4strophyh. J. ?31, L 121 (IB79). T, IMPTON, JI., MORGAN, B., B O ~ Y E I C , S., Astrophys. J. 206, 177 (1976). IIIYFR-H LSbELWiYDER, H. A., et nl. , preprint (197!)) MC(”ONNI.:LL, J , Qii,cntuni Particle Dynamics, Bmster ddi i i , North-Holland (1958). MCCRAY. It., S N O I ~ , I’. I)., J r . , Ann. Rev. Astron. Aslrophys. 17, 213 (1979). MCDON ~ L D , F. U., TRAIVOR, J. H., i n : Jupiter, ed. T. GEHRELS, Trrcsox; I’nivt~rsitv of Ailmiin

Press, p. 061 (1976). F., OSTRIKPR, J. P., Astiophys. J. 2lY, 148 (1977). . A., EIRL, J. A, Proc. 15th. hit. Cosmic Ray Conf. (Plovdiv), Vol. 1 , 3-57 (1877).

&LEYElI, P., In: Origin of Cosniic Rays, eds. J. 1,. Obhorne and A. \T. ~VOLFEUDALE, Dordrc( I r t ;

NUGLR, P. G . , I’roc. 14th lilt. Cosmic Rag Conf. (Miinith), Vol. 11, 3643 (1976). MONTMERLE, l’., Astrophys. J. 231, 95 (1979).

MULLSR, D., PRINCE, T., Proc. 15th Int. Cosmic Ray (’onf. (Plo\di%), Vol. 1, 360 (1‘377).

OSBORAF, J . !,., in: Origin of (’o~inic Rigs, eds. J. I,. Osbornc a ~ i d .I. W. ~VOLFCNDALE, Dordrecht;

1’ ICIIOLC Z Y K , A . G., Radio Astrophysicb, S,in Fi cjiicisco, F ~ r c n i , ~ n (1!)70).

P ~ u L , J . A., ct A , Xstron. A45tiopliys. 63, 1, 31 (1978). PB NZIAS, A. A, ~VILSON, K. LV., Sstrophj q . J. 142, 419 (1965). 1 3 ~ ~ ~ ~ h ~ ~ ~ ~ , C , Brcxai\ri, C:. F.. Astrori. Astropliyh. 54, 69 (1976); in: Recent Advances in Gamin,)-

PIVKIU, l i , Pioc. 15th J i l t . Cosm!c K,iy Conf. (Plovdiv) Vol. 10 139 (1977). PIVKIU, K , Sat i i ic 977, 17 (1979). PT(:ET, J. L , Sisc~ieit. F. I\’., +%ztiophys. J. 191, 323 (1974). I’L!~,I:T, J. I., STE( K i m , F. \\’., Rnxr)LKA?m, J. H., Astrophys. J. 206, 638 (1976). R ~ % ’ L I * , LL., 111: High Eneig) I’,lrticles and Quanta in Astrophysics, eds. F’. B. MCDONALD and

Reidcl, p. 233 (1975).

l\llnLLl:I<, D., ~ I I ’YER, P., AstropllyY. J. 1S6, 841 (1973).

1 I U b H O T Z h I , 1L F., Nnti<Ic 265, 228 (1977).

Iteidcl, p. 203 (1973).

PAGE, I). N., H ZIVfiIhTG, 8. LV., -1stIophys. J. 906, 1 (1976).

Ray A.,tioiiom), eds. R. D. \\-ILL\ m c ! R. BITTRICK, ESA SP 124, p. 125 (1977).

C. E. Frc HTEL, C’mibridgc; MlT Press, p. 122 (1974). K iMATY, , KOZLO\ SKY, B., LlNGTNFI:LTEH., R. E., Astrophys. J. SUPpl. 40, 487 (1979). Riunrour), J. C”., (b\, D. P., SMITH, U. W., Astiophys. J. ?04, 290 (1976). S tvrmow, 11. P., Suovo Cimenta 13, 12 (1959). SCAR51, L., et al., i n : Recent A ~ d v a ~ ~ o e s In Gamma-Ray Astronomy, cds. R. D. IVills and u. BAT-

SCHLICKRISER, K., Diploma them, University of Kiel (1074). S C I I L I C ~ ~ E I ~ L I ~ , K , Astrophys. J. 233, 294 (1979). SCTILICKET~ER, ti . , Astron. Astrophys., in press (1980a). SCHLICKEIWR, lL . , Astrophys. J. 236, 945 (1980b). SCHLICKEI~CR, K., THIELHEIM, K. O., Nature 261, 478 (1976). sCHLICKEIbER, s., TIIIELHEIRI, K. o., Astrophys. Sp‘lcc Srl. 47, 415 (1977a). HCHLICKEISER, li., THIELHL’IM, K. O., in: Recent Advances in Gamma-Ray Astronomy, eds. R. D.

TRICE, ESA SP 124, p. 3 (1977).

WILLS and B. BATTKT(~K, HSA SP 124, p. 139 (197713). 8CHLICKF,lbER, R., THIELHEIM, K. o., Moil. S o t Roy. L\StiOn. SOC. 16‘2, 103 (1978). SCOTT, J. S., X‘ctrrrc 233, 58 (1975). SHIRE, G , et al., X,rtiirr 2h2, 692 (1979).

W ~ K Y , C. J , in: Recent Advances in Garnmn-R<iy Astronomy, eds. R. D. WILLS and L<. KITTIITCK, ESA S? 124, 1). 131 (1977)

SIIUKLA, 1’. G . , PIUL, J., Astrophys. J. 20S, 893 (1976). SILK, J., Space Sci. Rev. 31, 671 (1970). SILVERBERG, K. B., Ol%ilWX, J. F., BALASUBRAHMA4NGAN, v. K., J. Geophys. Res. 78, 7166 (1973). SMITH, B. w., Astlophys. J . 211, 404 (1977). SOLOMON, P. hl., Physics today 26, 32 (1973). STRCKEIL, F. tV., Aistrophys. Space Sci. 6, 377 (1970).

134 REINHARD SCHLICKETSER

STWKER, P. W.. Cosmic Gamrn,i Rays, B.ilttruore; BInno Book Gorp. (1971). STECKER, F. IT., Astrophys. J. 1S3, 490 (1973). STECBER, F. IT.. Phys. Rev. Lrttrrs 33, 188 (1975). STECKCR, P. W., Astrophys. J. 219, GO (1977). KTECKCR, F. W., Bstrophys. J. 996, 919 (1979). STECKER, F. W.. PLJGET, J. L., STRONG, .4. JV., I ~ L ~ ~ D E K ~ M P , J. &I., A s t r o p b p J. 88, L 59 (1974). STRONG, A. W., WOLFFNDALE, A. W., BENNETT, I<., KILLS, R. D., Mon. Not. Roy. Astron. Soc.

STURROCK, P. A, A2strophys. J. 164, 529 (1971).

SW'ANENBUXG. B. N., et al., N<irtarc 975, 298 (1978). T A N ~ K A , Y., BLELKCR, J. A . &I., Space Sci. Rev. "7, 513 (1977). THOIIPSON, D. J.. FICIITEL, C. E., H A R T M ~ Y , R. C., KNIFFEN, D. L4., LAMB, R. C., Astrophyh. J.

WESEER, 14'. It., Pror. 13th Int. Cosmic R ty ('onf. (Denver), Vol. 5 , 3568 (1973). WEBBER, W. R., RoclisTRoH, J. &I,, J. (kophys. Kes. TA, 1 (1'373). WHITNORE, J , P h j s . Rep. 10, 273 (1974). WILLS. R. D., et nl., Pror. COSPAR Syinp. on Eon-Solar Gamma Rays (Bangalore), to be publi-

ZATSEPIN, V. T . Pror. 12th Int. Cosnilc Ray Conf. (Hobart) Vol. 5, 1720 (1971).

182, 751 (1978).

STURROCK, P d.. PETRObI i N , v., TURK, J . S., A4trophys. J. 196, 73 (1975)

913, 252 (1977).

s t i d 1980 in Advances in Sp'rce Exploratioii, PeigiLmon (1979).

gamma ray astronomy and the origin of cosmic rays

Documents