Gamma rays and the origin of cosmic rays

G A M M A RAYS AND T H E O R I G I N OF C O S M I C RAYS

D. J. V A N D E R W A L T and A. W. W O L F E N D A L E

Department of Physics, University of Durham, South Road, Durham DHI 3LE, U.K.

(Received 28 April, 1988)

I. Introduction

The cosmic radiation comprises a wide variety of particles and a minute flux of ),-rays. The charged particles are principally protons with about 10 ~ of heavier nuclei; electrons and positrons contribute about 3 ~o of the total. The ?,-radiation accounts of the order of 10 6 of the total. Neutrinos predominate in fact, by many orders of magnitude, these particles coming very largely from the Sun but their energies are mainly low, below about 20 MeV, their detection is extraordinarily difficult and, apart from the neutrinos detected from the recent supernova in the Large Magellanic Cloud, they have little relevance to cosmic rays 'proper' and will not be discussed here.

Although cosmic rays were first detected by Hess in 1912 in his heroic balloon flights, their origin and the manner in which they achieve their energies is still the subject of debate. The main problem destroying the possibility of an easy solution to the origin question is the existence of the Galactic magnetic field. This field is considerably tangled and of very uncertain topography and its strength is such that only at the very highest energies are particle trajectories approaching straightness. It is another example of Nature guarding her secrets carefully that just when straightness can be virtually guaranteed the flux of particles becomes so low that the problems of poor statistics start to dominate. Figures 1.1 and 1.2 show the energy spectra of the main components and from Figure 1.1 wilt be realised the considerable range of energies under consideration. Table I shows the corresponding energy densities.

Some general remarks can be made about the origin problem from the standpoint of the two different 'types' of particles - electrons and nuclei. Inspection of the radio synchrotron distribution over the sky, this radiation being caused by cosmic-ray electrons in the GeV region being deflected by magnetic fields, makes it apparent that the bulk of the radiation is coming from our own Galaxy, the extragalactic synchrotron flux being only a small fraction of the total. Many hot spots are seen in the synchrotron sky (Galactic H II regions, SNR, pulsars . . . . ) thereby giving a clue as to the sources of at least some of the electrons. Coupled with the fact that the 3K microwave background radiation - the relic of the big-bang - keeps out extragalactic electrons (at least of energy above some tens of MeV) we are able to conclude that cosmic-ray electrons are in the main of Galactic origin, with sources including those just listed.

The situation with nuclei is very different. No Galactic sources have been definitely identified (although there are strong clues - see later) and the vast majority could be

Space Science Reviews 47 (1988) 1-45. �9 1988 by Kluwer Academic Publishers.

" q -

QJ

it_. (/)

"7

'1=

-I--

r (3J

-4-- r -

I 1012

1 0 -6

- 1 8 -

10

ii 30 -

16 10 6

- / p

\1

I Extensive Qir showers

I

I

2 D. J. VAN DER WALT A N D A. W. WOLFENDALE

1018 Energy (eV)

Fig. 1.1. Energy spectrum of some of the more common components of the cosmic radiation (neutrinos excepted). In the shaded areas, the intensities are rather uncertain. Above 1014 eV, where extensive air showers are used to determine the energy spectrum, the mass composition is rather uncertain although a variety of techniques indicate that protons probably predominate above about 1016 eV. Note the flattening of the spectrum above a few times 1018 eV; this is suggestive of these highest energy particles originating

outside the Galaxy (after Wolfendale, 1983).

extragalactic. It is this distinction between a Galactic and an extragalactic origin that is the first target of those searching for 'the origin of cosmic rays'.

It might be thought that there would be some clues from energetics arguments. Wolfendale (1983) has considered these in detail. There are the well-known equalities of the cosmic-ray energy density (~0.5 eV cm-3) with the energy density associated with each of: magnetic fields, gas motion, and starlight. Apart from the last mentioned - which must surely be fortuitous - attractive origin models can be produced which give

G A M M A R A Y S A N D T H E O R I G I N O F C O S M I C R A Y S 3

"7 A

c - O laJ

u

D r -

> OJ

Z

"7 f,._ ttl

I

E "7

I/9

(11 u

-41-- f.._

EL

X

U_

Fig. 1.2.

0 I0

-I_ 10 ,

-2 10

10 -3

10 -z,

' ' I i ' I ' i

He

BE

-s l , i I i l I J \ , ~ N 10

10 100 1000 10000

K i n e t i c e n e r g y ( M e V / n u c t e o n )

Energy spectrum of the various atomic nuclei in the cosmic radiation for energies below 10 GeV nucl-] . The reduction below several hundred MeV nucl 1 is due to solar modulation. Recent studies (Chicago group, to be published) show that there are marked differences of spectral shape above

some tens of GeV nucl - '.

the equalities naturally. However, proceeding beyond the Galaxy, the 3K radiation has an energy density of 0.24 eV cm- 3, viz., virtually the same as that of cosmic rays (a factor of 2 difference is not significant) and the possibility of using energetic arguments to distinguish between the two possibilities, therefore, disappears.

It is true that if cosmic-ray nuclei were extragalactic (EG) and universal, with the local

4 D. .l. VAN DER WALT AND A. W. WOLFENDALE

T A B L E I

Energy densi t ies of the cosmic- ray componen t s nea r the Ear th

C o m p o n e n t E Energy densi ty (eV) (eV cm - 3 )

Pro tons and heavier nuclei Above 10 9 5 x 10 1 1012 2 • 10 -2

1015 10 4

1018 10-8

Elec t rons and pos i t rons Above 10 9 5 • 10 -3 10 l~ 1 x 10 3 1011 3 • 10 - 4

),-rays: diffuse backg round Above 10 7 1 x 10 -5 10 8 2 • 10 -6

energy density, the energy in cosmic rays would be second only to that in rest mass for

the Universe as a whole. However, this is not a compelling argument against and a better

argument favouring an EG origin would be the fact that protons are 30 times as common as the Galactic-born electrons.

Some progress has been made with the distinction between a G- and an EG-origin from studies of anisotropies in arrival directions (e.g., Kiraly et al., 1979) the principle

being that although the Galactic field does smear out arrival directions the smearing is

not quite complete. The main problems here are, however, that the anisotropies are very small (bI/I < 10-3 at most energies) and information only starts to be useful above

about 1012 eV because of the uncertain effects of solar modulation (the modulation

effects are, of course, interesting in their own right but they put paid to studies of

Galactic origin indicators). It should be stated here that the anisotropy work suggests that the particles above 10:2 eV - and perhaps as far as 10:8-1019 eV - are Galactic in

origin but the conclusions are not completely firm.

Insofar as the bulk of the cosmic-ray energy is carried by particles below several 10 ~~ eV this is a crucial energy range for origin studies. Interestingly, this is just where

the cosmic y-rays detected by satellites have a role to play; electrons and nuclei in the range 109-101~ eV interact with nuclei in the interstellar medium (ISM) to generate the

bulk of the y-rays in the range 35 - several 100 MeV, which is where cosmic ?,-ray data are the most precise.

In what follows we examine the information on cosmic-ray origin to be gained from cosmic ?,-ray studies.

2. Sources of Diffuse Cosmic y-rays (35-5000 MeV)

2.1. P R O D U C T I O N MECHANISMS

Ramana Murthy and Wolfendale (1986) have recently discussed ?,-ray production mechanisms in some detail. The main mechanisms for the energy range in question are

GAMMA RAYS AND THE ORIGIN OF COSMIC RAYS 5

electron-bremsstrahlung (and to a lesser extent electron Inverse Compton interactions

with starlight and 3K photons) and nucleus - ISM nucleus interactions leading to pion

production, from which n o mesons decay to two ),-rays.

Although we shall also be concerned with electron-induced ),-rays it is mainly the cosmic-ray nucleus-induced quanta in which we are interested - for the reasons given in Section 1 - and we concentrate on this aspect. Figure 2.1 gives the differential production rate for the various components making up the nucleus beam and the various

target nuclei in the ISM (p, ~, ...). The characteristic shape of the ),-ray spectrum, with

its peak at m.o c2/2 can be seen; the detection of this peak, as an indicator of nuclei in distant parts of the Galaxy, or further, has been sought for many years. Also apparent

in Figure 2.1 is the extent to which there is some doubt about the absolute production

rate of ),-rays, doubt that arises because of uncertainty in the local energy spectrum of

cosmic rays and conditioned largely by the difficulty in allowing for solar modulation effects.

In the case of electrons the situation at low energies is particularly severe. The point is that electrons of energy E e give ),-rays of energy roughly 0.4E e so that 100 MeV 7-rays come from 250 MeV electron parents (unlike proton parents which have E ~ 3 GeV) and the modulation caused by the Sun becomes very uncertain as one proceeds below 1 GeV.

The uncertainties in Figure 2.1 - and others - spill over into the important question

of the relative division of contributions between electrons and nuclei as parents of the

detected )~-rays. Figure 2.2 shows the situation, where we plot the fraction of 7-rays from

nuclei (termed 'protons' here - and in what follows) as a function of 7-ray energy for

the local situation. The effective energies for the energy bands covered by the two major satellite experiments to date, SAS II and COS B, are also shown in the figure (see the caption for details).

Inspection of Figure 2.2 shows that there is general agreement that above about 100 MeV protons predominate as parents but there is disagreement below. It should be noted that the division depends on position in the Galaxy in that it is conditioned by

the electron to proton ratio and this ratio is both expected to vary from place to place

and observed to do so. Figure 2.3 summarizes the situation for both inner Galaxy (R ~ 5 kpc) and outer Galaxy (R ~ 15 kpc). There is agreement that in the outer Galaxy

protons predominate for ).,-rays above 100 MeV but in the inner Galaxy Bloemen (1985) disagrees. However, all agree that for the highest COS B ),-ray band protons are the main progenitors of ),-rays everywhere.

Another way of representing the division of parents between electrons and nuclei is to show the energy spectra of ),-rays from the two components. Figure 2.4 shows such a division from the work of Bhat et al. (1986b).

2 . 2 . T H E ) , -RAY D A T A

As mentioned already, most of the data were recorded by the SAS II and COS B satellites. Table II summarizes the characteristics of these instruments and the data collected.

6 D . J . V A N D E R W A L T A N D A. W. W O L F E N D A L E

- 2 / + ~ ' ' I ' ' I ' '

10 ~ - - - �9 " . L ,

U /" B & S "~ 1 0 _ "

2 5 , /

/

o / p_ p ,

w 1626 , , m E

�9 , - - , , I I 1 \

I() 27 _.,..-II

Z 1-25 II

~,,. 0 - // ~,

- 2 7 , , I , , I , , 1 ,

10 10-3 162 10-1 10 o PHOTON ENERGY (GeV)

I I I I I

}CR-ISM

\\

\

I I ,

1 0 1

Fig. 2.1. Production spectrum of ),-rays for various cosmic-ray spectra (after Badhwar et al., 1981). 'p -p ' refers to cosmic-ray protons on hydrogen in the ISM and the remainder to all cosmic rays on all nuclei in the ISM. The extent to which different workers have made different estimates of the cosmic-ray spectrum is clear. On top of these variations are likely changes in absolute intensity of protons and heavier nuclei from

place to place in the Galaxy.

2.3. CONTRIBUTION TO THE DIFFUSE RADIATION FROM UNRESOLVED SOURCES

A major problem caused by the 7-ray detectors having such poor angular resolution is

the question of the extent to which an apparently diffuse radiation is truly diffuse (and

due to individual struck atomic nuclei in the ISM) rather than an assembly of discrete

sources, such as pulsars or other condensed objects. The situation is analogous to that

in Optical as t ronomy in the last century when Herschel and others worried about the


p/fofQ[ (%)

100

80-

60-

40-

20-

S C

1,1 I

S c C

I I

/ / Bt

I I I I I

10 20 50 100 200 500 1000

E~(MeV) Fig. 2.2. Relative contributions to the ),-ray flux of parent protons and electrons in the local cosmic radiation. G: Goned (1981), P: Pooh (1983), Bh: Bhat etal. (1986b), and BI: Bloemen etal. (1984a). S denotes the effective energy for the two energy bands in the SAS II experiment (35-100 MeV and > 100 MeV) and C the corresponding effective energies for the COS B energy bands (75-150, 150-300, and

> 300 MeV).

nature of 'nebulae'. We now know that some 'diffuse nebulae' are distant galaxies, i.e.,

composed very largely of discrete stars, whereas others consist of incandescent gas. The situation with ?,-rays is that a number of authors have worked from the (small) number

of identified discrete sources to estimate the fraction of ?,-rays coming from the unresolved sources; this fraction appears to be about 20% (e.g., Protheroe et aI., 1979). In fact, the fraction is a function of l and b, being largest in the inner Galaxy at small b and smallest at high latitudes. In the latter situation, where most sources would be nearby and more easily recognized, the fraction can be ignored.

8

plfofct[ (%)

100

80-

60-

40-

20-

0 10

Fig. 2.3.

D. J. VAN DER WALT AND A. W. WOLFENDALE

i I I t

Bh,(5,15)

B[

/ ~ t ( - 5) / / -

S S / (AC) -

I I [ I I

20 50 100 200 500 1000 E~(MeV)

As Figure 2.2 but for the outer Galaxy (SS: Sacher and Schonfelder, 1984, and '15': R ~ 15 kpc) and for the inner Galaxy ('5': R ~ 5 kpc).

3. L a r g e - S c a l e C o s m i c - R a y Intensi ty Gradients

3.1. GENERAL PRINCIPLES

Probably the best method of distinguishing between a Galact ic and an extragalactic origin

for cosmic rays is to search for the so-called cosmic-ray gradient on a large scale in the Galaxy. I f cosmic rays were extragalactic then one would expect the derived cosmic ray

intensity to be the same everywhere but if they were of Galact ic origin then a significant gradient should be present. In fact, the test is not foolproof in that although a Galactic origin can be proven, by detecting a gradient, it does not necessarily follow that the absence of a gradient leads to EG-origin. The reason is simply that cosmic rays couM

be produced in Galactic sources but diffuse so readily through the Galaxy as to give a near-uniform distribution of intensity. It is certain that cosmic rays do diffuse considerably so that, for a G-origin the gradient is not expected to be very large; the problem is therefore guaranteed to be difficult.

G A M M A RAYS AND THE ORIGIN OF COSMIC RAYS

' ' I ' ' I I

"r- > a /

Z "i-

f.i_

"T

~E 0

4 - -

- 2 8 - -

10

/ I

r

-29 L.

10 '

m

--- 163o O3

1631 10

I

, I , , I \ 100 1000

E ~ ( M e V ) Fig. 2.4. Gamma-ray emissivity showing the components adopted for protons and electrons in the work of Bhat et al. (1986b). The earlier Stephens and Badhwar (1981) estimate for protons is indicated by PSB.

The circles represent the COS B emissivities determined by Strong (1985).

TABLE II

Basic data for the 7-ray satellite experiment

Satellite SAS II COS B

Dates of Nov. 15. 1972 observation for 7months

Numbers of 7's 8000 detected

Energy range >35Mev (bands quoted: 35-100 and > 100MeV)

Angular resolution at 100 MeV (FWHM) 3 ~ at 200 MeV (HWHM) 1.8 c

Aug. 9, 1975 for 6 years

100000

> 50MeV (bands quoted: 75-150, 150-330, and > 300MeV)

3 ~

3 o

10 D. J. VAN DER WALT AND A. W. WOLFENDALE

Searches for a gradient using the y-ray data have been made for a few years now and Ramana Murthy and Wolfendale (1986) have given a summary of the history of searches. The basic problem has been the uncertainty in column densities of gas in the inner Galaxy, the mean cosmic-ray intensity along as line-of-sight being proportional to the measured ),-ray intensity divided by the total column density of target gas along that direction. Although the atomic hydrogen (HI) component is reasonably well understood, the column density of the molecular hydrogen component, N(H2), is subject to considerable argument. Indeed, one of the major contributions of y-ray astronomy to astronomy as a whole has been the demonstration that the early estimates of N(H2) by millimetre wave astronomers were far too high (Li et al., 1982; Lebrun et al.,

1982; Bhat et al., 1984b; Bloemen, 1985). It has been pointed out (e.g., Dodds et al., 1975) that the Galactic anti-centre is the

best place to look for the cosmic-ray gradient because H I predomir~ates and this has been done, as will be described, although there are several problems, including the low ),-ray fluxes present there.

3.2. THE RESULTS ON COSMIC-RAY GRADIENTS

Figure 3.1 shows the results of the COS B group (Bloemen et al., 1984) for the mean cosmic-ray intensity as a function of Galactocentric distance, R, in the outer Galaxy, where, as mentioned previously, the demonstration or otherwise of a radial gradient should be easiest. It will be noted that there is clear evidence of a gradient at the lower two energies - and this is in accord with earlier work, e.g., Issa et al. (1981) and with expectation for a Galactic origin for parent electrons but at the highest ),-ray energies the distribution is essentially flat. It is of course here, above 300 MeV, where protons predominate (e.g., Figure 2.3) and so the possibility of an EG origin has inevitably arisen. In fact, these results have aroused heated debate; for example Mayer et al. (1987) have made an alternative analysis of the same COS B data and arrived at a different conclusion, namely that there is a gradient for E~. > 300 MeV in the outer Galaxy specifically but that the mean CR intensity at R -~ 14 kpc is some 70~o of that locally. In fact this conclusion, as indeed all conclusions related to the outer Galaxy, need revising in view of the results to be described in Section 5 (a section that, identically, confirms the Galactic origin of at least many of the cosmic-ray protons).

Turning to the inner Galaxy the COS B group have presented the results shown in Figure 3.2 and their division of y-ray emissivity between protons and electrons is indicated. It will be noted that, contrary to the conclusions of Figure 3.1, there is now a small proton gradient (although in fact the latter is not significant).

The Durham group (Bhat et al., 1986b) have analysed the same COS B ),-ray data but with their own estimates of the distribution of the important molecular hydrogen component - and their results are as shown in Figure 3.3. Here there is a healthy gradient for both electrons and protons and an interesting aspect of this work is that an energy dependent gradient for both electrons and protons can be chosen such that both components fall on the same curve (Figure 3.4). These authors put forward a model involving production of cosmic rays in supernova remnants and diffusion of the particles

GAMb4A RAYS AND [ H E ORIGIN OF COSMIC RAYS II

1.5

Fig. 3.1.

1.0 , . . - , , , ,

~- t ._

0.5

"7- E o 0"0

"T"

r -

1.0 ' O

0.5

0-0

1.0

0-5

I z , I i I i I L I I '

70MeV- 150MeV

0

p

[ Sph - 2 - 1 -1 . . . . . . I . . . . . . Ib=B'gx10 cm s sr

, I J I I I I t t ~ 1 ,

150MeV-300MeV

- T - 0 1

- Ib=2.2xl ( j s I I I I

- Q ]"

_ 1 - Ib= 2.2x 1() s

i I ~ I

10

[

300MeV- 5GeV -

I [ , I i I I I -

15 20 --- R ( k p c )

Radial distribution of cosmic-ray emissivity in the outer Galaxy for the three COS B energy bands from the work of Bloemen et al. (1984).

out of the face of the Galactic disc (viz., preferentially along the z-direction) such that the diffusion coefficient is a function of both energy and R, the latter dependence arising

because of the disturbance of the ISM and attendant magnetic field caused by SNR.

Again, this model may need elaboration in view of the most recent results on spectral

changes as a function of position to be described later.

12 D. J. V A N D E R W A L T A N D A. W. W O L F E N D A L E

' ' ' l ' ' I I I I I I I I t I I

_ 70-150MeV_

2.0 - , , , ~

1.5

"T 1.0-

--r E 0

4 - - 0 " 5 -

- l -

r - 0"( [ I

O , .4-- O r -

.o cx 1'0 t O

0.5-

- I

I :D-

. . . . . . . . , _ _ , _ _

r . . . . ( ; . . . .

, , I , , , , , , , , , I , ' ' I ' ' " . . . . ' ' r ' I ' "

150-300HEY-

i

I I [ , I ! i i l I I I I I l I ' I [ , ' ' i i i i I I I I [ i

3 0 0 - 5 0 0 0 M e V .

Fig. 3.2.

1-0 - - . . ~ . . -~

o.s . . . . . . . . .

0.0 -I I I I I I I , | | I I I I I I I

0 5 I0 15 20 R(kpc)

Radial distribution of cosmic-ray emissivity in the Galaxy as a whole from the COS B group (Bloemen et al., 1986).

4. The Acceleration of Cosmic Rays in Supernova Remnants

4.1. ENERGETICS

There are two basic requirements which candidate sources of cosmic rays must meet in order to explain the observable characteristics of cosmic rays in the Galaxy. Firstly, the energy output of the sources in cosmic rays must be sufficient and secondly, the

G A M M A RAYS A N D T H E O R I G I N OF C O S M I C RAYS 13

A 2 "7

" - i 1 - A

"7 - 4 - -

"1-

2 -I-- O r - Q .

t'M I O

2

(b)

I I I I

(c)

I I I I

5 10 15 20 R(kpc)

Fig. 3.3. Radial distribution of cosmic-ray emissivity in the Galaxy as a whole from the Durham group (Bhat et al., 1986b). The data used are the COS B ),-ray intensities and the group's own estimate of the

distribution of molecular hydrogen in the Galaxy.

production spectrum must be such that after due allowance is made for energy losses

and energy-dependent escape from the Galaxy, the observed spectrum for cosmic rays

is recovered. Both these requirements seem now to be possible to be met in supernova explosions and supernova remnant shock waves. The possibility that supernovae are the sources of cosmic rays has been realised for a long time (e.g., Ginzburg and Syrovatskii, 1964) and follows from a simple calculation of the rate at which energy must be transferred to cosmic rays to maintain a steady state cosmic-ray population in the Galaxy. With an ambient energy density in cosmic rays of 0.5 eV c m - 3, a Galactic


100

10 .._i

L= 8(EI3OOMeV) ~

I 1 I I I I I

0 1000 10000

E(HeV) Fig. 3.4. The energy dependence of the cosmic-ray gradient parameter, L, against energy from an analysis of the data of Figures 2.2 and 2.3. The cosmic-ray intensity is taken to be proportional to exp - (R/L).

volume of 8 x 1067 c m 3 and a cosmic-ray lifetime of 2 x 107 years the energy input in

cosmic rays needed to maintain a steady state follows as ~ 104t ergs S 1. A supernova rate of 1 per 30 years, an average energy release of 1051 ergs and a 10% efficiency in

generating cosmic rays will be sufficient to provide the required energy input. Strong

stellar winds might also contribute, to the extent of about 20% (Abbott, 1982); thus,

although strong stellar winds may be of local importance they cannot meet the total

energy budget for cosmic rays in the Galaxy. The second attractive feature about supernova events in explaining the origin of

cosmic rays is the fact that charged particles may be accelerated by the SNR shock wave propagating into the interstellar medium. Ideally the cosmic-ray production spectrum in diffusive shock acceleration is e E - 2 which can explain the shape of the observed

cosmic-ray spectrum after allowance is made for energy losses and escape. In what follows, the basic idea of diffusive shock acceleration is discussed, after which

the theoretical results on the acceleration of cosmic rays in individual SNR are reviewed. Finally, the gamma-ray observations of interest to the problem of the acceleration of

cosmic rays in SNR's will be discussed.


4.2. T H E ACCELERATION OF CH A RG ED PARTICLES BY SHOCK WAVES IN

SCATTERING MEDIA

The topic of diffusive acceleration of charged particles by shock waves has been addressed in a number of review papers (e.g., Axford, 1981; Toptygin, 1980; Drury, 1983; Blandford and Eichler, 1987; Volk, 1987). Our purpose here is not to improve

on these papers but rather to compare theory and observations in order to make progress with the cosmic ray origin problem. Although the theory of the acceleration

of charged particles by shock waves in scattering media can be described in terms of the transport equation (e.g., Axford et al., 1977; Blandford and Ostriker, 1978), we will

here summarize the basic physics involved by following the microscopic analysis of Bell (1978).

Consider a plane shock wave propagating with a supersonic velocity u 1 through a plasma. In the frame in which the shock is stationary the upstream medium approaches

the shock front with a velocity u l, while behind the shock the downstream medium flows

away at a subsonic velocity u2. In both the upstream and downstream media there are scattering centres which isotropize the particle distributions. In the upstream medium

this is due to Alfv~n and hydromagnetic waves. In the downstream medium the

scattering is caused by the turbulence due to the shock. Due to the fact that the shock

speed is super Alfv6nic, particles are convected into the shock from the upstream medium. Once in the downstream medium a particle can either escape from the shock

by being convected away or be scattered back across the shock into the upstream medium. On each crossing of the shock a particle gains on average an amount of energy (4) (u 2 _ Ul)E due to the fact that the scattering centres on opposite sides of the shock front advance upon each other. Combining this with the probability (1 - 4u2/c ) for crossing the shock from downstream to upstream results in an energy spectrum E - "

far downstream of the shock, with /~ = (2u 2 + ul)/(u 1 -u2) . For a strong shock Ul/U2 = 4 which means that the hardest possible spectrum from this mechanism is G~E - 2 .

4.3. S H O C K ACCELERATION OF COSMIC RAYS IN SNR

The above mechanism is very attractive to apply to SNR shock waves. Shock waves in SNR have, however, a number of features which have to be taken into account when considering cosmic-ray acceleration. The analysis in the previous section applies to a plane steady shock with an infinite lifetime whereas shocks in SNR are usually near- spherical, non-steady shocks with a limited lifetime.

The acceleration of cosmic rays in SNR shocks has been studied by Moraal and Afford (1983), B ogdan and V61k (1983), Prishchep and Ptuskin (1981), and Lagage and Cesarsky (1983) to determine the effects of deviations from the plane steady case. Considering first the effect of the spherical nature of the shock, the solutions for the case of a plane shock will still apply if the diffusion scale length of the particles in the upsteam medium is less than the radius of the shock, i.e., D 1 < ulR where D 1 is the diffusion coefficient in the upstream medium. If this condition holds the shock will appear plane


to the particles. It is clear, however, that this condition sets an upper limit to the energy

to which cosmic rays can be accelerated in a spherical shock. Prishchep and Ptuskin (1981) argue that the corresponding condition, D 2 < u2R, may well be satisfied in the

downstream medium due to well developed turbulence, but that it will probably not be

satisfied in the upstream medium and that it will limit the efficiency of the acceleration process. Moraal and Axford (1983) set an upper limit of 3 x 1014 eV for the energy of

particles for which the shock will appear to be plane. Lagage and Cesarsky (1983) are somewhat more optimistic and state that curvature

effects should not be important up to an energy of the order of 1015 eV.

The effect of the finite lifetime of the shock can be investigated by noting that the

time-scale for the acceleration of particles with momentum p in a plane shock is given

by

~ a c c = 4- .

/.t I - - U 2

This means that the time needed to establish a power-law spectrum up to momentum

p from the injection of particles with momentum Pi is given by

P ;(o; O;)d, z a - + p ,

U 1 U 2 P t

The fact that r a is bounded from above by the dynamical shock time, R/u~, with R the

shock radius, means that an upper bound exists for the energy to which a particle can

be accelerated. Moraal and Axford (1983) found that the condition ra < R/u1 sets an upper limit of ~ 1014 eV to the maximum energy, i.e., approximately the same as the

maximum energy due to curvature effects. The numerical calculations of Moraal and Afford (1983) and Bogdan and VOlk

(1983) are made in the test particle approximation and, therefore, do not include nonlinear effects such as the scattering of cosmic rays by the hydromagnetic waves that are generated by themselves or the effect of cosmic rays on the shock itself. Lagage and Cesarsky (1983) included the effect of the generation of hydromagnetic waves and found

that the maximum energy to which cosmic rays can be accelerated is of the order of 1013 eV.

It is, therefore, clear, at least from a theoretical point of view, that although diffusive acceleration is a very attractive mechanism for cosmic-ray acceleration, its efficiency in SNR shocks is reduced due to the finite lifetime of the shock. The fact that the Mach number of the shock decreases with time is a further factor which affects the resulting cosmic-ray spectrum. In Figure 4.1 is shown how the Mach number and the resulting spectral index, q, changes with time as the SNR evolves. It is seen that the high-energy particles are produced predominantly in the very early stages of the SNR and that this lasts for only a small part of the total lifetime of the remnant. The calculations of both Moraal and Axford (1983) and Bogdan and VOlk (1983) show that the contribution of the early very strong shocks is not significant in the final spectrum. These calculations


3-0, , , , , 10

q(f)

2.9

2-8

2-7

2.6

2.5

2./+

2.3

2.2

I

I

l p/Po = 103

1

\

_ q ( f ) - - - M ( f ) _

\

9

8

7 M(f)

6

5

/+

3

2

2.1 I--/ -41

2.0 ~ 0 0-1 0.2 0-3 0-/+ 0.5

t/} Fig. 4.1. Plot of the time dependence of the Mach number of the shock (scale on the right-hand side of the figure) and the spectral index q. ~ is the time from the onset of the Sedov phase until the Mach number has dropped to 1. The fact that the spectral index decreases with time implies that the final spectrum is softer than the hardest possible spectrum that can be produced by shock acceleration. Very large energy gains, E/E o > 103, Occur only in the early stages of the Sedov phase. During the late stages the remnant processes a large volume of the ISM but is not effective in producing high-energy particles. Due to the finite life time and curvature of the shock the maximum energy attainable is about 1014 eV. (After Bogdan and

V61k, 1983.)

also show that the final spectrum is indeed a power law with spectral index

2.1 < q < 2.3.

Before turning to the observational side we need to ment ion the work of Blandford

and Cowie (1982). Although they studied primarily the radio emission from SNRs in

a cloudy interstellar medium they also made estimates of the gamma-ray surface

brightness of the giant radio loops which are of particular interest here. For the giant

radio loops they predict a surface brightness of ~ 7 x 10 . 6 cm -2 s - ~ s r - 1 which, as

will be seen later on, is quite close to that estimated from gamma-ray observations for

Loop I.


4.4. EXPERIMENTAL RESULTS ON THE OBSERVATION OF GAMMA RAYS FROM SNRs

The hypothesis that cosmic-ray protons are accelerated in SNRs can be proved (or disproved) only if it is possible to observe an enhancement of the cosmic-ray intensity as well as a spectrum harder than the ambient cosmic-ray spectrum in individual SNRs. This may not be easy to do since the majority of SNRs in the Galaxy have either a small angular diameter or are located close to or in the Galactic plane (Green's catalogue, 1984). The radio loops (see, e.g., Price, 1974) are, however, of larger angular diameter and are not located in the Galactic plane. The radio loops are probably very close SNR as their observed brightness and polarisation distributions are in rough agreement with results of models of SNR in the local magnetic field (Spoelstra, 1972, 1973). Berkhuizen (1973) has found that the observed Z - D relation for five of the radio loops is near to that of known SNRs. There are, however, also obstacles to the SNR origin of the loops and alternative explanations have been proposed (see, e.g., Price, 1974). A number of authors have nevertheless searched for an enhanced emission of gamma rays from some of the radio loops with very interesting results. Figure 4.2 shows the small circle geometry of Loop I, II, II, and IV.

90 b (deg) 80 --

30

0

-30

-60

-90 180

Fig. 4.2.

I I I i I I I I I

I I I I I I I I I

150 120 90 60 30 0 330 300 270

I I

I I 240 210 180

t (deg)

Small circle geometries of the radio loop features. The crosses indicate the ridge positions used by Berkhuizen et al. (1971) to determine the profile of each Loop.

4.5. PREVIOUS ANALYSES OF LOOP I

Bhat et al. (1985) and Lebrun and Paul (1985) investigated the possibility of an enhancement of the cosmic-ray intensity towards Loop I. Figure 4.3 shows the excess gamma- ray intensity as found by Bhat etal . (1985) from an analysis of the SAS 2 data. The gamma-ray excess, A/7, was obtained by assuming constant gamma-ray emissivities of


I /

/ - 6 0 ~ -20 o

2

, I; _60 ~ l _20 o

I

-1 AI~(16Scrn 2 s sr I)

eV]

I

0 ~ 20 ~ 4.0 ~ 60 ~ 80 ~ b

[E~ >100MeV' ]

~176 2o~ t b 6~176 8~176

Fig. 4.3. Gamma-ray intensity excess in Loop I as a function of latitude as found by Bhat et al . ( 1 9 8 5 ) . The excess M s = Ie , L - Ie, o where Le , L is the difference between the observed and expected intensities towards Loop I and Ie. o is the corresponding difference outside Loop I. The solid line gives the approximate

expectation for the case where the cosmic-ray intensity is uniform within the remnant.

3.7 x 10 - 2 6 and 2.6 • 10 26 atom-1 s -1 sr -1 for 35-100 MeV and > 100 MeV, re-

spectively, throughout the Galaxy. These emissivities were used together with the total gas column densities, to calculate the expected gamma-ray intensity from Loop I for a

particular latitude interval and the corresponding expected intensity outside Loop I for the same latitude interval. The excess A I , / i s then given by Ie, L - Ie, o where Ie, L is the difference between the observed and expected intensities towards the Loop and Ie, o the corresponding difference outside the Loop. Using the gamma-ray excess as shown in Figure 4.3 Bhat e t al. estimated the total energy in cosmic-ray electrons in the remnant to be about 1 x 1049 erg and for protons to be 1 x 1050 erg. These values are quite close to those expected from the calculations by Blandford and Cowie for a supernova with initial energy of 1051erg. The estimated >,-ray surface brightness of 7 x 10 - 6 c m - 2 s - 1 s r - 1 for E . /> 100 MeV predicted by the model calculations of Blandford and Cowie (1982) is also in good agreement with that found by Bhat et al.

20 D.J. VAN DER WALT AND A. W. WOLFENDALE

The analysis of Lebrun and Paul (1985) does not go quite as far as that of Bhat et al.

(1985). Using a maximum likelihood method, Lebrun and Paul estimate the emissivity and background intensity for the region of Loop I and for that outside Loop I. Their results indicate that the emissivity towards Loop I is larger by a factor of ~ 3 compared to that outside Loop I. For Ee > 100 MeV the emissivity towards Loop I is larger only by a factor of 1.2. Lebrun and Paul also calculated the excess intensity AI,. = L , obs - - Iv, exp and conclude that the excess is most conspicuous in the region which contains Loop I. Although both these analyses suggest an excess gamma-ray flux from Loop I, the situation is not quite as simple as this and will be discussed again

shortly.

4.6. O B S E R V A T I O N OF G A M M A RAYS F R OM LOOP III AND THE VELA SNR

These two supernova remnants were studied by Rogers and Wolfendale (1987). Obvi- ously, both of these remnants are of smaller angular diameter than Loop I which means low counting statistics. For Loop III, Rogers and Wolfendale found that a small excess in the gamma-ray intensity exists in the Loop and that it is present in all energy bands including E~ > 300 MeV for which protons predominate as the initiating particles. The cosmic-ray energy in the Loop is found to be about 25 ~o of that predicted by the Blandford and Cowie (1982) calculations.

For the Vela SNR, Rogers and Wolfendale searched for a gamma-ray 'halo' around Vela in order to avoid the pulsed emission from the pulsar. After allowing for gamma-ray

Wcr (erg) 2

5O I0

5

2

10 49

I I

/ +Ve,a 20 30 50 100

r(pc)

III

200

Fig. 4.4. Total cosmic-ray energy as estimated from gamma-ray observations for Loop I, Loop III, and the Vela SNR. The open circles are the estimates from Bhat et al. (1988) for Loop I and from Rogers and Wolfendale (1987) for Loop III and the Vela SNR. The full square is our new estimate for Loop I following a procedure somewhat different from that of Bhat et al. The solid line is the prediction by Blandford and

Cowie (1982).


emission due to the interaction of ambient cosmic rays with the interstellar gas, they

claim that a small excess is present.

The energetics for the three SNRs discussed, as found from gamma-ray observations, are as shown in Figure 4.4 together with the prediction from the model of Blandford and Cowie (1982). For all three SNRs studied the estimated energy in cosmic rays is somewhat smaller than predicted by theory. This may perhaps be not too surprising

when the numerical results of Moraal and Axford (1983) and Bogdan and V61k (1983) are taken into account. Apart from their demonstration of the existence of an upper limit

to the energy to which a particle can be accelerated, their predicted spectrum is also not

as hard as E 2 as assumed in the Blandford and Cowie (1982) calculations.

4.7. R E A N A L Y S I S O F L O O P I

In a recent paper Bloemen et al. (1987) contested the existence of an enhancement of

the cosmic-ray intensity towards the Loop I SNR as was claimed by Bhat et al. (1985). Bloemen et aI. tried to explain the difference between the observed and predicted gamma-ray intensity towards the inner Galaxy (310 ~ < I < 50 ~ at medium latitudes

(5 ~ < l < 30 ~ and noted that the excess intensity above the predicted value is approxi-

mately symmetric with respect to l = 0 ~ They rejected the claim by Bhat et aI. (1985)

of an enhanced emission from the Loop I region as such on the basis that if the excess

is due to Loop I it can be expected to be symmetric around l = 330 ~ and not around

l = 0 ~ Apart from this objection there is also the observation that the gamma-ray spectrum is significantly flatter towards the outer Galaxy than towards the inner Galaxy

and this affects the determination of the magnitude of the Loop I excess. This topic will

be discussed more extensively in the next section. We will now first establish the existence of an enhanced cosmic-ray intensity asso-

ciated with the Loop I SNR to address the objection of Bloemen et al. (1987). This will be done by using the COS B data for E.e > 300 MeV. The initiating particles of gamma

rays with E>. > 300 MeV are predominantly protons and, as we have remarked previ-

ously, these are the more significant particles from the cosmic-ray origin standpoint. Our

philosophy here is to investigate the longitudinal dependence of the gamma-ray emis-

sivity for the latitude range 10 ~ < b < 20 ~ . By doing this the effect of the local cosmic-

ray gradient is also included and it is then possible to see whether the emissivity in the Loop I region follows the general trend of the local cosmic-ray gradient. The total gas column density was determined by using the H I survey of Weaver and Williams (1973) and the Columbia CO survey by Dame et al. (1987). We also included the estimated column densities for H II by using the model of Lyne et aL (1985). The latitude range

used ensures that spill-over effects from the Galactic plane, due to the point spread function, do not occur and excludes also contamination due to strong point sources. This latitude range has also fairly good counting statistics and includes also the centre of Loop I. The result of our analysis is shown in Figure 4.5. The emissivities are plotted against cos/ which allows one to compare the emissivities at equal Galactocentric distances. The solid line is a least-squares fit of the emissivity as a function of cos l for all the points outside Loop I and represent, therefore, the local cosmic-ray gradient.


L J1

,i- E 0

E 0

o r -

' o

•

'l'll''l'llllll'''l_

1t �9 ..jr

1.5

1

0 . 5

m

m

m

I I I 0 " t Jll,, ll,Jllll 0 1 0

COS(L) 180 ~ 270 ~ 0 ~ 90 ~ 180 ~

Longifude (*) Fig. 4.5. Gamma-ray emissivity for E,, > 300 MeV as a function of longitude for 10 ~ < b < 20 ~ The total gas column densities used to derive the emissivities include H I, Hz, and an estimate of the column density of H II using the model of Lynn et al. (1985). The crosses are for the positions outside the boundaries of Loop I. The black squares are the positions inside Loop I and the black dots are the corresponding 408 MHz brightness temperatures normalized to the gamma-ray emissivity at I = 170 ~ The solid line is a least-squares fit of the emissivity as a function of cos/ of the points outside the Loop and represents the local cosmic-ray gradient. It is seen that the emissivities within the boundaries of Loop I do not follow the local gradient and are consistently higher than expected from the gradient. Since protons predominate as initiating particles for E.. > 300 MeV, this result supports the contention that there is an excess at all gamma-ray

energies.

A n u m b e r o f fea tures are immed ia t e ly appa ren t :

(1) A t the pos i t ion o f the N o r t h Po l a r Spur (l = 30~ where a s ignif icant enhance -

m e n t o f rad io emiss ion is o b s e r v e d (b lack circles), a significant e n h a n c e m e n t o f the

g a m m a - r a y emiss ivi ty as seen.

(2) A similar increase in emiss ivi ty is seen at l = 270 ~ i.e., on the edge o f L o o p I in

the four th quadran t .

(3) The d e p e n d e n c e o f the emiss iv i ty on cos I wi th in the L o o p I region is quite

different f rom that expec ted f r o m the local c o s m i c - r a y gradient . As a ma t t e r o f fact, it

is seen that for those pos i t ions in the first and four th q u a d r a n t s which are at equal

G a l a c t o c e n t r i c d i s t ances the emiss ivi t ies inside the L o o p I reg ion are cons i s ten t ly higher

GAIvIMA RAYS AND THE ORIGIN OF COSMIC RAYS 23

than those outside Loop I. This result is indeed significant since there is no reason why

the local gradient should be different in the first and fourth quadrants.

It can, therefore, be concluded that there is indeed an enhancement of the cosmic-ray intensity in the region covered by Loop I. Since there is no other simple explanation for

such an enhancement, this enhancement has to be ascribed to the Loop I SNR itself.

Having established the existence of an enhanced cosmic-ray intensity inside the Loop

we now turn to the lower energy gamma rays where electrons also contribute to the

emission. Due to the poor statistics of the SAS 2 data over small regions an analysis

similar to that just give for the COS B data cannot be made. The data have, therefore,

been combined for the latitude ranges - 20 ~ < b < - 10 ~ and 10 ~ < b < 80 ~ for the

three different longitude ranges: (1)260 ~ < l < 30~ (the L o o p I region),

(2) 30 o < l < 90 ~ (outside Loop I but still in the first quadrant), (3) 90 ~ < l < 260 ~ (the

outer Galaxy region). The reason for dividing the region outside Loop I in two separate

longitude ranges is due to the fact that towards the outer Galaxy the gamma-ray

spectrum is significantly flatter than for the Loop I region. For the longitude range

3 0 ~ l < 90 ~ it is found that the spectral index between 35 and 100MeV is not

significantly different from the Loop I region. Table III gives the emissivities in each

longitude range for the energy bands 35-100 MeV and > 100 MeV. The spectral index

for each longitude range is also given. The emissivities are in units of 10 26 a t o m - 1 s - 1 s r - 1.

T A B L E I I I

260 ~ < l < 30 ~ 30 c < 1 < 90 ~ 90 ~ < l < 260 ~

Ee (35-100 MeV) 4.9 + 0.65 3.94 _+ 0.78 2.25 _+ 0.69

E~. ( > 10 MeV) 3.07 + 0.23 2.62 _+ 0.32 2.54 + 0.26

Spectra l index 0.91 _+ 0.09 0.87 _+ 0.14 0.60 _+ 0.15

The emissivities for the longitude range 30 ~ < 1 < 90 ~ will now be used as the datum

level for comparison with the Loop I region. Apart from the fact that the spectral indices

are approximately the same, the average emissivities for this longitude range also include

the effect of the local gradient which is also present in the fourth quadrant where it is

included in the emissivities for the Loop I region. It will also be noted that the emissivity

values for 30 ~ < l < 90 ~ are approximately the same as those used by Bhat et al. (1985). Using these emissivities for the two energy bands we find that the excess gamma-ray

intensity from Loop I is 1.13 x 10 - s cm -2 s - 1 s r - l and 0.49 x 10 .5 cm -2 s - 1 s r -

for 35 MeV < E~ < 100 MeV and E~ > 100 MeV, respectively. The surface brightness

for E~, > 100 MeV is, therefore, in good agreement with the predicted value of 7 x 10 .6 cm -2 s - ~ s r - 1 as given by Blandford and Cowie (1982) for the giant radio

loops particularly when it is realised that our b-range only covers a fraction of the total. The total energy in cosmic-ray electrons in the remnant is calculated as follows. The expected gamma-ray intensity for 35-100 MeV towards Loop I is


4.6 • 10 -5 cm -2 s - ~ s r - ~ (using the emissivity for the datum region, 30 ~ < l < 90~

The fraction of line-of-sight that includes the Loop is 0.44. Also, it can be expected that

the average gas density inside the Loop is less than that outside. Using a mean gas

density inside the Loop of 0.4 c m - 3 and of 1 cm - 3 for outside the Loop, the expected

intensity due to the Loop would have been 0.8 x 10 - 5 c m - 2 s - 1 sr 1 for the 'normal'

cosmic-ray intensity; this latter is, therefore, enhanced by a factor 1.4 inside the loop.

The contribution of electrons to the total intensity for this energy band is 60~ (Bhat

et al. , 1984). Combining this with the energy density of 2.3 • 10 - 2 eV cm - 3 for inter-

stellar electrons with energy > 100 MeV (Strong and Wolfendale, 1978) the energy of

electrons in Loop I contributing to excess emission in the 35-100 MeV energy band is

found to be 6 x 1048 erg. For the higher energy band the energy in electrons is found

to be 1.3 x 1048 erg. The total energy in electrons is, therefore, 7.3 x 1048 erg. A similar

calculation for protons gives a total energy of 1.6 x 1050 erg.

It will be noted that these values are somewhat smaller than those given by Bhat et al.

(1985). This is due to the fact that the excess intensity was calculated in the present case

only using the emissivities for 30 ~ < l < 90 ~ . The calculation for the excess intensity by

Bhat et al. also included the longitude range 90 ~ < l < 260 ~ for which the spectrum is

significantly flatter. The rather steep cosmic-ray gradient in the outer Galaxy for the

A

v,.. oO

"-i-tn

'E O

-4-- t::l

oO t - O

O r -

Fig. 4.6.

-26 10

1()2710

I i i ' '

I I I

I00

E (MeV) 1000

Integral gamma-ray emissivity as a function of energy for Loop I. For Ee > 35 MeV and E~, > 100 MeV the SAS 2 data were used and for E > 300 MeV the COS B data.


low-energy particles will certainly enhance the apparent excess if this region is included in the datum region. The gamma-ray emissivity as a function of energy is shown in Figure 4.6. The spectrum is only slightly flatter than that for the longitude range 30 ~ < l < 90 ~ It is in qualitative agreement with the spectrum found by Bhat etal .

(1985) in the sense that a power-law fit extends from the lowest to the highest energies. To summarize, we conclude that there is indeed positive evidence for an enhancement

of the cosmic-ray intensity inside Loop I. This enhancement is seen not only at low energies but also at the higher energies. Although the energies estimated to reside in electrons and protons are somewhat lower than expected from a 10% efficiency for the conversion of the total measurement energy in a SNR (of initial energy 10 sl erg) into

cosmic rays, the results are not discouraging. Further work in this direction will indeed be important to establish the role of shock acceleration of cosmic rays in supernova remnants.

5. Variations of the r-Ray Spectral Index Across the Galaxy

5.1. DIFFERENCES AT LOW ENERGY RELATED TO THE ELECTRON/PROTON RATIO

It will be apparent from what has been said already that the low-energy spectral index of the ),-ray intensity is related to the e/p ratio - specifically, the steeper the spectrum below, say, 200 MeV, the bigger the e/p ratio.

The early studies of the y-ray spectrum (e.g., Stecker, 1969a, b; Clark et al., 1968; Fichtel et al., 1972; and Strong et al., 1973) were mainly directed towards answering rather general questions about the origin of the y-rays and their division between the Galactic and extragalactic components. Hartman et al. (1976) made an analysis of the longitudinal variation of the ~ spectral index in the Galactic plane using SAS II data but the relatively large uncertainties precluded firm conclusions about spectral index variations.

Issa et al. (1981) showed, from an analysis of both SAS II and COS B data that the ),-ray emissivity per hydrogen atom falls off with increasing energy more rapidly for molecular gas than atomic gas; thus, insofar as the ratio of molecular to atomic gas is higher in the inner Galaxy than in the outer, there is evidence for a dependence of spectral shape on Galactocentric radius. The investigations of Mayer-Hasselwander et al. (1982) gave a different result, however. In this later work the COS B 'colour-index' (i.e., the ratio I;. (70 < E~ < 150 MeV)/(I~,(150 MeV < Ey < 5000 MeV)) was determined as a function of longitude but no significant change was detected. However, a later analysis by Mayer-Hasselwander (1983), using a better estimate for the background correction showed that the y-ray spectrum is indeed steeper ('softer') towards the inner Galaxy (i.e., the e/p ratio is higher there) Riley et al. (1984) and Riley and Wolfendale (1984) found essentially the same result as Issa et al., viz., a steeper ),-ray spectrum associated with molecular hydrogen, in the inner Galaxy region. Bloemen et al. (1984, 1986) have also concluded that the e/p ratio is higher in the inner Galaxy.


All the above is consistent with the conclusions given in Section 3 concerning large- scale gradients, viz., that the radial gradients are steeper at lower energies.

5.2. D I F F E R E N C E S A T H I G H E R E N E R G I E S A S S O C I A T E D W I T H T H E P R O T O N

C O M P O N E N T

5.2.1. General Remarks

The previous analysis has referred to the relative numbers of electrons and protons contributing to the ~,-ray flux and there is general agreement that the e/p ratio is somewhat higher in the inner Galaxy - a not altogether unexpected result.

Of greater interest is the situation at higher "l-ray energies, where protons predominate, the question being: does the energy spectrum of protons vary in spectral shape (as well as intensity - see Section 3) from place to place in the Galaxy? There have been interesting developments here, recently, as will be described.

Although there had been some suspicions for some time, the first published results appear to be those of Bloemen (1987) and Bloemen et al. (1987) now to be described.

5.2.2. Latitude Dependence of the High-Energy 7-Ray Spectrum: Bloemen (1987) and Bloemen et al. (1987)

In the first paper, Bloemen (1987) showed that the ratio of the inner Galaxy intensity to that in the outer Galaxy fell with increasing energy, as shown in Figure 5.1. The latitude range referred to in the figure is I bl < 30 ~ so that a significant fraction of the intensity comes from regions away from the Galactic plane. An important result of the investigations was a clear demonstration that the result is rather insensitive to changes in the 7-ray background intensity (a previous source of worry when this phenomenon was first noticed by the Durham group in 1986).

It is immediately apparent from Figure 5.1 that there must be something unusual about the latitude distribution of the 7-ray intensity at high energy in that in the Galactic plane the ratio of inner to outer intensity cannot fall below about 2.5, the ratio of the average gas column densities in these two directions - and this woud occur (viz., ratio ~ 2.5) if the cosmic-ray proton intensity were constant, independent of R.

The unusual latitude dependence is revealed in Figure 5.2. In the next section we will discuss our own analysis of this problem but continue here with the interpretation placed

on the results by Bloemen et al. (1987). These workers put forward the interesting possibility that the latitude dependence of

the gamma-ray spectrum is due to propagational and energy loss effects of the type discussed by Lerche and Schlickeiser (1982). In this model cosmic-ray nucleons are produced in the Galactic plane and propagate through diffusion and convection (due to a Galactic wind). The mode of propagation which is dominant is determined by the time-scales for diffusion and convection, the time-scale for diffusion being given by L2/D(z, p) and that for convection being given by L/V(z) where L is a characteristic length of the system and V(z) is the wind speed (considering a one-dimensional model). In a similar way the importance of different energy loss processes depends on the


>- 10 X

. . .J <I: LD

i i i I---

O

r I , 1 Z Z I---'4

O I-- <

">o

Fig. 5.1.

I I l I I I I I I I I I I I

I I I I I

I I I I I l I I

I I I

R

m

1 - -

13

BACKI]ROUND USED:

�9 BEST ESTIMATE

[ ] +99% UNCERTAINTY

O -99~176 UNCERTAINTY

I I I I I I I 1 1 1 I 1

0"I ENERGY

lllJ 1

(SeV)

\ -04 --E

I I I I I I

10

Ratio between the gamma-ray spectra towards the inner and outer Galaxy from the work of Bloemen (1987). The broken line indicates the best power-law fit above 300 MeV. The figure also illustrates

that the result is rather insensitive to changes in the gamma-ray background intensity.

time-scales for the different processes. The loss mechanism with the smallest time-scale is the dominant mechanism. For protons energy losses are due to ionization

and adiabatic deceleration with time-scales ~i~p3/zn(z), Z = 1.5x 10~1Q 2 (eV c 1)3 cm 3 s - l and ZA ~ 3/(dV/dz), respectively. (Q is the charge of the particle).

From these expressions one finds that ionization losses dominate when

P < Pc • (3gn(z)/(dV/dz)) w3. Similarly, convection will be the dominant mode of propa-

gation when z; < rD, i.e., whenp <PD = [zV(z)/(Do d(z))] l:a, where we have assumed, following Lerche and Schlickeiser, that D(p, z) = pa 2(z)Do" It is found, therefore, that

for Pc < P < PD adiabatic deceleration will be the dominant momentum loss mechanism while convection will be the dominant mode of propagation. Due to the energy depen-

dence of the diffusion coefficient, particles with p ~ PD will be convected away by the

wind leading to a flattening of the spectrum. The z-dependence of PD will cause the flattening to move to higher energies with increasing z.

Whether the flattening of the proton spectrum as predicted by this model can explain the observed flattening of the gamma-ray spectrum depends on at least two conditions. Firstly, the flattening should occur inside the gas layer so that it will be observable with gamma rays (which are produced by interactions with the gas). Secondly, the spectral indices predicted by the model are asymptotic values. This means that the value ofpD

28 D. J. V A N D E R W A L T A N D A. W. V ' , ' O L F E N D A L E

A

y -

O O GO

I

O O

L ~

I

Z O O c O

(D

1.1+

1.2

1.0

- ' ' ' ' I ' ' ' ' I ' ' ' J

........ 310~ < t< 50" 90 ~ < t < 270 ~

08

0"6 ~ -

0-4 - - ~ .... 2 ...... ~

0.2 I" .... * ..... : ? .....

n l - , , , , I , , , , I , , , , k/

0 10 20 30

I tQtitud0l (*)

Fig. 5.2. Latitude dependence of the ratio of the gamma-ray intensity between 800 MeV and 6 GeV and the intensity between 300 and 800 MeV as found by Bloemen et al. (1987). At the highest latitudes the spectrum towards the outer Galaxy is significantly flatter than towards the inner Galaxy. The observed flattening with latitude for the outer Galaxy is explained by Bloemen et al. as being due to a Galactic wind. Towards the inner Galaxy the spectrum shows a slight steepening with latitude which cannot be easily

explained by the Galactic wind model.

should be large enough so that the spectrum in the 1 -10 GeV energy range is signifi-

cantly different from that above PD" If this is not the case, spectral changes along the

line-of-sight may not be observable due to averaging. Therefore, PD >> 10 GeV c - 1. The

effects of these conditions on the possibility of observing the flattening can be investi-

gated by assuming specific functional forms for V(z) and d(z). Following Lerche and

Schlickeiser (1982) we take V(z )=3V1 z or V ( z ) = 3 V l z o ( l _ e ~,,zo), with

z o = 180 pc, as possible descriptions of the dependence of the wind speed on Galactic

height. In the case V(z)= 3Vz the windspeed can increase without bound. For V(z) = 3Vlzo(1 - e -z:z~ an upper limit of 2 x 10 11 s - 1 can be set to the value of V 1 by demanding that V(z = co) = 3Vlz o < c. In Figure 5.3 the dependence o fpD on z is shown for three cases. Curve 1 is for V(z) = 3Vlz and d(z) = 1, i.e., the diffusion

coefficient is independent of z. For curves2 and3 we have used V(z) = 3Vlzo(1 - e -z/z~ and D(z,p) = Dopa(1 + btanhz/z o) which represents a

rather slow increase of D with z. For curve 2 b = 1 and for curve 3 b = 10. In all three cases VI = 1 • 10 - 14 s - l . It is seen that the model will easily explain the observed

flattening in the gamma-ray spectrum in the case of curve 1 and perhaps also for curve 2. However, allowing the diffusion coefficient to increase by only an order of magnitude


> oJ

E

r- OJ E 0

4 10

10 3

10 2

101

10~

10 10

I I I I I I I 1 [ I zl I I I I I

=_--

/ , /

/ / "

. 2 / -

/ /

/ i

/2

.F f

/ /

, : , / /

/

/

100 1000

Z(pc) Fig. 5.3. Momentum, PD, at which convection and diffusion time-scales are equal as a function of height above the Galactic plane. (1) V(z) = 3Viz and d(z) = 1. (2) V(z) = 3Vlzo(1 - e -z,'z~ and d ( z ) = l+tanhz/z o. (3) V ( z )=3Vl zo (1 -e z'~~ and d ( z ) = 1 + lOtanhz/z o. For these three cases V~ = 1 x 10-14 s - 1. (4) Is the same as (3) but with VI = 1 • 10-13 s - ~. Although PD >> 10 GeV c - ~ for

(1) at z = 180 pc, this is not the case for (2) and (3). This means that the effects of convection dominated propagation will not be observable with y-rays with E~. > 300 MeV in cases(2) and (3).

from z = 0 to z = m has as a consequence that the flattening will not be observable

with gamma rays. It is clear that the rate of increase of the diffusion coefficient with

z is very important. The dependence of V 1 on z if the value ofpD = 100 GeV c - 1 is

shown in Figure 5.4. It is seen that for Case 3 (V(z)= 3 V l z o ( 1 - e z..'--0),

d(z) = 1 + 10 tanhz/zo)V 1 has to have a value of the order of 10-13 s 1 so that the

flattening will be seen with gamma rays with E > 300 MeV. Curve 4 in Figure 4.2 shows

the corresponding dependence ofpD on z with V 1 = 1 • 10- 13 s -

The observed difference in spectral indices between I bl = 2.5 ~ and 22.5 ~ is 0.4 and

is in agreement with the predicted difference of 0.36 if a = 0.6. The difference of 0.36

is based on the asymptotic spectral indices predicted by the model. The variation ofpD along the line-of-sight may, however, reduce this difference in practice.

It will be clear from what has been said that the Galactic wind model can explain the

observed flattening of the 7-ray spectrum towards the outer Galaxy, this result being

taken alone. There are problems, however. As Bloemen et al. remark, and as can be seen

in Figure 5.2, there is a slight steepening of the ),-ray spectrum as one proceeds to higher


"i- I/} i . r l

5" 0

X

10"

10 3

10 2

101

10 0

_= I I I I I I I I [ I

\ 3

-

" I I I I I I I I [

100 i I I I

0

i i i l i 1 ~

m

I I I I I

1000

Z(pc) Fig. 5.4. V~ as a function of height above the Galactic plane for the case when PD = 100 GeV c- 1 V(z)

and d(z) are the same for (1), (2), and (3) as in Figure 5.3. The figure shows that a lower limit is set to one value of V~ so that the cosmic-ray spectrum is significantly flatter below 100 GeV c-~ than above 100 GeV c- ~ and that this occurs already within the gas layer. If this flattening starts only outside the gas layer, it will not be observable with gamma rays. The figure shows also that the lower limit of V~ depends on the wind model as well as on the rate of increase of the diffusion coefficient with height above the Galactic

plane.

lat i tudes towards the inner Ga laxy rather than a reduct ion and this is upsetting. Bloemen

et al. need to assume that the Sun is in a special posi t ion in the sense that as one

proceeds inwards the Galac t ic wind character is t ics change in such a way that the height

at which the proton flattening occurs is outs ide the gas layer and thereby unobservable

in the y-ray data. Our own possible reason for the ' specia l posi t ion ' will be discussed

later. Another worry concerns the wel l -known higher y-ray emissivity towards the G C at

'high lat i tudes ' . We have, earlier (Sect ion 4), following Bhat et al. (1986a, b), invoked

accelerat ion of cosmic rays in the Loop I S N R as being resposible but Bloemen et al.

are not convinced. There leaves the problem, then, of why the low-energy pro ton

intensity is so much higher. Bloemen et al. propose that the column densi ty of ionized

gas (H t[) has been previously grossly underes t imated and that when this is included the

average cosmic- ray intensity inferred from the 7-ray results falls. This interesting idea

will be considered further later.

Before leaving the analysis of Bloemen et al. reference should be made to their


treatment of the low-energy ),-rays - those generated by electrons. They draw attention

to the similarity of the dependence of the spectral index on latitude for both ),-rays and

radio synchrotron radiation (a topic also considered in the next section). The argument advanced is the same as that for protons, viz., that a Galactic wind is responsible, blowing more efficiently in the outer Galaxy. The problem in the inner Galaxy is

side-stepped to some extent in that there are few radio data available in inner Galaxy directions from which spectral shapes may be determined.

5.2.3. The Model o f Rogers et al. (1988)

As mentioned already, the flattening of the spectrum at 'high' Galactic latitudes in the outer Galaxy had been noticed by the Durham group. Rogers et aL (1988) have made

an independent analysis of the COS B (and SAS II) data and found rather similar, but

not identical results to those of Bloemen etal. (1987). They have also made an in-

dependent study of the reasons for the flattening and put forward a different model. It

is too early to say yet which (if either) of the two models is correct. In fact, as will be discussed in the next section it is conceivable that a model which owes something to

both treatments is correct.

Insofar as this topic is one of considerable contemporary interest we examine both aspects of the work of Rogers et aL, viz., their derivation of the ),-ray and cosmic-ray spectra and the interpretation of the results.

Figure 5.5 shows the integral exponent of the ),-ray spectrum at 'high' energies,

resulting from the assumption of a power-law spectrum between E~ = 300 and 800 MeV

(viz., by comparing the measured fluxes above 300 MeV and above 800 MeV). Restrict-

ing attention to the comparison between the Galactic centre direction (defined here as

310: < 1 < 50 ~ ) and the anti-centre direction (90 ~ < l < 270 ~ it will be noted that the

sense of the difference is similar to that found by Bloemen et al. (Figure 5.2) although the two results are not identical. Such differences as occur are presumably due to a

disparity in the actual latitude ranges considered in the two treatments and somewhat different background corrections and are not to be regarded as serious.

It is interesting - and probably important - to note that there is a similar trend, and of similar magnitude for the difference in 1' (between GC and AC) for the SAS II results.

That is, electrons are showing a similar behaviour. For reasons to be discussed shortly, Rogers et al. put forward the hypothesis that the

spectral variations are due to a spiral arm effect, specifically that the proton and electron particle spectra are flatter in the spiral arms than in the interarm regions. For this reason

an analysis was made of the spectrum in a further direction, that along the local spiral

arm: 60 ~ < I < 90 ~ It can be seen in Figure 5.5 that there seems to be the same behaviour as before, i.e., that the ),-ray spectrum is steeper in the GC region than in the spiral arm region.

The philosophy of the model advanced by Rogers et al. can be appreciated by reference to Figure 5.6. If the diagram is correct, and inevitably there are arguments as to the position of the solar system with respect to the spiral arm, its height above the Galactic plane and the z-extent of the spiral arm, then the reason for suggesting a flatter


1-4

1.2

1.0

0.8

0 .6-

1"0-

0 8 -

A~ 06

0.t,

0.2

i 0 0140" 30* 0*

1.4

1-2

1-0

COS B

10' 20* Ibl

GC-AC ( COS" B)

0 " 8 -

0-6-

0.4-

I I I

10" 20* 30* Ibl

08

06

GC-AC

O' ~ I

0.2-

0 0*

( SAS II )

I I I

10" 2O* 3O* Ibl

~ SA

I I I

020" 10 ~ 20* 30 ~ - 020* 30 ~ Ibl

018 ! i

0-6-

0-4-

0 .2-

0 0 -

GC-SA (COS B)

10" 20" Ibl

Fig. 5.5. The latitude dependence of the integral exponents of the gamma-ray spectrum as found by Rogers et al. (1988) . The exponents were derived from the measured intensities above 300 MeV and above 800 MeV using the COS B data. GC denotes the Galactic center direction (310 ~ < l < 50~), AC the anti-centre direction (90 ~ < l < 270~ and SA the spiral arm direction (60 ~ < l < 90~ Rogers et al. interpreted the latitude dependence of the spectral index towards the outer Galaxy in terms of a flatter spectrum for the

parent cosmic rays inside the Orion arm than outside the arm.

s p e c t r u m in the a r m c a n be u n d e r s t o o d : as I bl i nc reases , the f rac t ion o f the p a t h t h ro u g h

the H I gas w h i c h is c o n t a i n e d wi th in the a r m inc reases . F o r example , at I bl = 25 ~

t o w a r d s the Ga lac t i c an t i -cen t re , near ly ha l f t he 7-rays ( f rom H I) ar ise f r o m in t e rac t ions

b= 2

5"

3 -z

(kpc

)

b=16

~ %

. 2

o

b=lO

b=25

'

o

b=16

o

b=lO

I .

I I

I I

I I

~ |

~

I ~

I I

I

9 8

7 6

5 4

3 ~

1 S ~/-~j 1

2~-~

3 /+

5 Sa

giffa

rius

Orio

n Pe

rseu

s d

(kpc

) e

,--

G,C

. A.

IZ.

Fig.

5.6

. ll

tusl

rati

on o

f th

e ge

omet

ry a

ssu

med

by

Rog

ers

et a

l.

(19~

8).

/'he

Sun

is

loca

ted

on t

he i

nsid

e ed

ge o

f th

e O

rion

arm

as

indi

cate

d by

the

dis

trib

utio

n of

sp

iral

tra

cers

in

the

vici

nity

&th

e S

un. T

he b

lack

dot

s in

dica

te t

he m

edia

n di

stan

ces

alon

g th

e li

ne-o

f-si

ght o

ver

whi

ch g

amm

a ra

ys a

re p

rodu

ced.

Th

e cr

osse

s in

dica

te

the

corr

espo

ndin

g di

stan

ces

for

the

radi

o em

issi

on. F

or b

= 2

5 ~

alm

ost

500/

,, of

the

line

-of-

sigh

t is

wit

hin

the

Ori

on a

rm w

hen

vie

win

g to

war

ds t

he a

nti-

cent

re d

irec

tion

. T

owar

ds t

he i

nner

Gal

axy

only

the

int

erar

m r

egio

n is

sam

pled

by

gam

ma

rays

.

O

t~

�9

O

34 D. J. VAN D E R W A L T A N D A. W. W O L F E N D A L E

within the arm. Towards the Galactic centre, on the other hand, the 7-rays are derived entirely, for I bl > 6 ~ from interactions in the tenuous gas in the interarm region. Figure 5.5 shows the form expected for the difference in exponent between GC and AC versus latitude; it will be noted that there is rough agreement with observation.

Rogers et al. have also examined the situation with the slope of the radio spectrum, and its relationship or otherwise to the slope of the ),-ray spectrum. They argue that although there is a difference in slope between GC and AC in the same sense as for ~,-rays (Figure 5.7), the b-dependence of the difference is not the same. The reason advanced for the disparity is the rather obvious one that the synchrotron radiation is sensitive to the particle (electron) spectrum averaged over a much bigger region of space (see Figure 5.7). Thus, it is not surprising that the two forms of 7 versus I bl are different.

S

0.8

0.7

0.6

(a) 408/820MHz

B

SA(60 <i<90 )

.50 ~ i a 0 5* 10"

-- ~_.~GE(30*<i<60 ~

As <t< 210 ) I I I I

15" 20" 25* 30"

Ibl

S

0"9 -

0"8--

0 7 -

0 6 -

(b) 408/1~20MHz

*< [< 60" )

~ ' J ~ S A ( 6 0 " < t< 90")

AC(90"< L< 210" ) 0.50 . ~ I i i ~ I

5" 10" 15" 20" 25" 30 ~

Ibl

Fig. 5.7. Latitude dependence of the spectral index for radio observations. GC, AC, and SA denotes the same longitude ranges as given in Figure 5.5. When comparing radio and gamma-ray data it should be remembered that whereas the gamma-rays emission are produced dominantly in the gas layer, the radio

emission comes also from the halo.

GAMMA RAYS .AND THE ORIGIN OF COSMIC RAYS 35

We consider that the radio results do not allow us to distinguish between the models

for explaining the ?,-ray results.

The model of Rogers et al. has the attractive feature that it is consistent with the usual

view that SNR - which were, of course, more frequent in spiral arms than elsewhere - generate cosmic-ray spectra which have a differential exponent 7 ~ 2, unlike the

ambient cosmic-ray spectrum which has ~, ~ 2.6. The higher exponent is conventionally assumed to result from diffusive losses out of the Galaxy, the diffusion coefficient

increasing with particle energy as ~ E ~ A bonus is the view, recently put forward by

Jokipii and Ko (1987), that SNR are more efficient in stronger magnetic fields, the point being that the mean field is higher in the arm than elsewhere.

q//,r~

-25 10

-26 10

' I ' ' I (Q) a~ o

0 _

-27 , , I , , I 1 0 10 100 1000

E~(MeV) Fig. 5.8. Energy dependence of the integral gamma-ray emissivity for the inner (IN) and outer (OUT) Galaxy for three different latitude bands. The emissivities were calculated by using only the H I column densities. The 35 and 100 MeV points were obtained by using the SAS II data and COS B data for the 300 and 800 MeV points. The excess in emissivity towards the inner Galaxy is more pronounced at the lower

latitudes (units of q,'47r: a tom-~ s - 1 s r -1) .


q//+rl:

-25 10

-26 10

i i I i I I

.T ( b ) 12~ < l b l < 2 0 ~

OUT

,jIN

1 6 2 7 , , I , , [ 10 100 1000

E~( MeV ) Fig. 5.8b.

There is a problem with the explanation of Rogers et al., however, and this concerns

the absolute magnitude of the y-ray emissivity spectrum (derived by dividing the measured 7-ray intensity by the column density of gas). Figure 5.8 shows the result.

There is a clear excess of emissivity at the lower y-ray energies over the whole latitude range for the inner Galaxy compared with the outer Galaxy. Clearly, if we are postulating a greater efficiency of cosmic-ray acceleration in the spiral arm then we would expect

a higher~ emissivity here. A number of possibilities spring to mind. The first is that raised by Bloemen et al., concerning ionized gas (H II). The idea stems

from the pulsar observations (Lyric et al., 1985) which indicate that the scale height for ionized gas may well be one or more kpc and that there is a radial gradient (density falling with increasing R). We have endeavoured to make what we consider to be an upper limit to the column density of HH as a function of l and b by adopting z~/2 of 2 kpc and a sharp cut off in a(H I0 at R = 12 kpc, and the effect of including this gas


I I0-2s I-

i

q/4n:

10 -26

' ' 1 ' ' I (C) 2 0 ~ < 3 0 ~

IN

/ OUT

- 2 7 , , I , , I

10 10 100 1000

E~(MeV) Fig. 5.8c.

in the analysis yields the emissivity spectra shown in Figure 5.9. It will be noted that the low-energy difference is still present although now much smaller.

The second possibility concerns the excess in the Loop I SNR which occupies a rather large fraction of the inner Galaxy (Section 4). In fact, if the Loop I contribution is subtracted there still appears to be an excess in the inner Galaxy direction (see Figure 5.10), although it is true that the excess is considerably reduced.

Another possibility is that in the inner Galaxy direction we are deriving particles (both electrons and protons) which have leaked out of the next spiral arm (at R ~ 8 kpc). Whilst this idea is not impossible it appears rather unlikely in that we would expect a steeper gradient in the Galactic plane than appears to be the case (see Section 3).

Concluding this section, it might be possible to explain the differences in absolute intensities by combining all the effects just referred to but the price paid seems rather high.


-25 10

q/4.n:

-26 I0

B

-27 10

10

' ' I ' ' I

{g.} 8~ ~

OUT

IN

, , I , , 1

100 1000

E~(MeV)

Fig. 5.9. As Figure 5.8 but now an upper limit for the column density o f H II has been included to calculate the emissivities. The HII column density was calculated from the model of Lyne et al. (1985).

5.2.4. A Composite Model to Explain the Spectral Variations

It still seems to us that the most distinctive feature of the solar system's position is its

situation on the inner edge of a spiral arm. A composite model presents itself in the following way: cosmic rays are accelerated by SNR (both by way of strong single shocks and by passage through many weak shocks) and these are most common in spiral arms. However, the same energy source which accelerates the particles also causes a Galactic wind and this blows more strongly in the arms than elsewhere. It is appreciated that the diffusion coefficient may well be smaller in the arms but it is postulated that on balance the wind wins. The reduction in low-energy emissivity values in the outer Galaxy would then follow. In one sense the model is in the spirit of Wolfendale's suggestion (Wolfendale, 1986), referred to by Bloemen (1987) and used earlier in connection with the large-scale gradient, that the trend in cosmic-ray lifetime with increasing Galactocen-


10 -25

q/4n:

-26 10

' ' I ' ' I

( b ) 20~ Ibl < 30 ~ -

IN

10-27 I I I ' I I 10 100 1000

E~(MeV) Fig. 5.9b.

tric distance is important. We are now suggesting that the lifetime is dependent on both

R and energy.

6. Gamma Rays from Discrete Sources and Giant Molecular Clouds

6.1. G A M M A RAYS F R O M P U L S A R S

Ever since the discovery of pulsars (Hewish et al., 1968) and the identification that pulsars are rapidly rotating, strongly magnetized neutron stars (Gold, 1968) it was realized that they may accelerate cosmic rays to high energies. The fact that gamma rays with energies up to 1012 eV are observed from isolated pulsars, and that the gamma rays are pulsed, implies that highly relativistic particles are associated with them. For isolated pulsars the gamma-ray emission is most likely to be due to leptons radiating in the strong magnetic field of the object. Although protons can also be, and presumably are,


-25 10

q/4n:

-26 I0

m

-27 10 10

' I ' ' I 0 0

8 < Ibl< 12

, , 1 , , I 1 0 0 1 0 0 0

E~(MeV) Fig. 5.10. As Figures 5.8 and 5.9. In this case the excess emissivity due to the Loop I SNR as found in Section 4.7 has been subtracted. Only the lower latitude band is shown here. There still appears to be an

excess in the inner Galaxy direction although it is considerably reduced with respect to Figure 5.8(a).

accelerated to very high energies in the magnetosphere of the pulsar, they will not radiate

gamma rays in the same way as the leptons, due to their larger mass to charge ratio. The presence of high-energy protons, or ions, will become apparent only if some form

of target material is present with which the protons can interact to produce gamma rays

through n~ A full discussion of this aspect of gamma-ray astrophysics is beyond

the scope of this paper and the reader is referred to Ramana Murthy and Wolfendale

(1986) where it is discussed at great length.

Concerning the production of gamma rays by relativistic electrons in isolated pulsars, it must be noted that although the basic mechanisms are reasonably well understood, the differences in spectral shape for gamma rays for different pulsars indicate that the

situation is not simple at all. Since a complete review of this topic is beyond the scope


of this paper, we will only outline the model of Cheng et al. (1986a) to illustrate the complexity of the processes involved in the pulsar magnetosphere.

Cheng et al. assumes that global current flow patterns exist in the outer parts of the magnetosphere. They show that such flow patterns give rise to large regions in the magnetosphere that are charge depleted. Those regions are called the 'outer gaps'. Deep inside the gap the potential drop along the magnetic field lines are of the order of 10 ~s V. A number of processes give rise to the creation ofe +/e- pairs in the gap which are then accelerated in opposite directions. Not only do the e +/e - pairs give rise to gamma rays through curvature radiation or inverse Compton scattering, but they also control the growth of the gap. The e +/e - pairs are produced by 'primary' gamma rays (i.e., gamma rays due to curvature radiation from leptons pulled out of the crust of the neutron star and which are accelerated along the magnetic field lines) either by direct pair production or by photon-photon interactions inside the outer gap. For the Vela pulsar, Cheng et al.

(1986b) argue that the primary e +/e- pairs are produced through the interaction of primary gamma rays and infra-red photons. The primary e +/e - pairs are accelerated to extreme relativistic energies which give rise to secondary gamma rays through inverse Comptons scattering with the infra-red photons in the gap. The secondary gamma rays are energetic enough to produce secondary e +/e- pairs again through interaction with the infra-red photons. The secondary e +/e - pairs lose energy by synchrotron radiation

of gamma rays and X-rays. A third generation of low-energy e +/e pairs is produced from the interaction of secondary gamma rays and the X-rays. The low-energy e +/e - pairs radiate infra-red photons through synchrotron radiation and it are these photons which interact with the primary gamma rays to produce the primary e +/e pairs.

For the Crab pulsar a different sequence of events is proposed. In this case the primary e +/e- pairs produce secondary gamma rays in the gap through curvature radiation. Secondary e +/e - pairs are produced through the interaction of the secondary gamma rays with X-rays that are produced outside the gap. Tertiary gamma rays are then produced as a result of inverse Compton scattering between the secondary e +/e - pairs and the X-rays. Cheng et al. have shown that the spectra of the Vela and Crab pulsars can be explained in this way over the entire range from the optical wavelengths up to gamma rays.

Concerning the usual assumption that electrons from the pulsar are responsible for the ),-rays, it must be remarked that the energy spectrum of 7-rays from the Vela pulsar, which is significantly flatter than that from the Crab pulsar (Hermsen, 1980), is rather similar to that of the ~r~ Thus, we either have a chance result or this is an unusual distribution of target gas near the pulsar such that protons are the source of the parent ~~ (A possibility that also arises is that the energetic protons from the pulsar interact with the radiation field to produce ~~ and thus ),-rays.) Such a situation is not impossible in that for Cygnus X-3, where 7-rays have been recorded up to l0 is eV, protons are usually assumed to be primarily responsible, although of course, the periodicity is much longer (4.8 hours in stead of milliseconds).

We will not pursue this topic any further here but will rather move on to address only briefly the subject of gamma-ray production in giant molecular clouds which is also currently of interest.

42 D.J. VAN DER WALT AND A. W. WOLFENDALE

6.2. G A M M A - R A Y S O U R C E S IN G I A N T M O L E C U L A R C L O U D S

Insofar as giant molecular clouds (GMC) represent 'condensations' of gaseous matter, in which large amounts of gravitational potential energy have been released and, furthermore, they contain within them young and active stars, they are potential sources of cosmic rays.

As mentioned already, the 2CG COS B catalogue of 'sources' contain some which certainly represent GMC irradiated by cosmic rays. When the catalogue was released initially (Hermsen, 1980) the COS B workers considered that most of the sources were discrete but, following the arguments of Li and Wolfendale (1981) and later papers, it became increasingly accepted that some (probably about half) represented irradiated molecular gas. Indeed, the study of ~,-rays has become an important tool in studying the distribution of molecular gas in the Galaxy (e.g., by Bloemen et al., 1984; Bhat et al.,

1984; Houston and Wolfendale, 1985; Wolfendale, 1988). However, there are problems, which are becoming increasingly severe, because of the realisation that there are cosmic- ray intensity changes from place to place in the Galaxy, as mentioned in the previous sections.

The problem with identifying cosmic-ray sources within GMC arises from the poor angular resolution of the 7-ray detectors so far employed. The result is that only rarely can anything other than the average cosmic-ray intensity within a cloud be determined. Immediately, then, there is the problem of the datum cosmic-ray emissivity to take, viz., the average value outside the cloud and this is now seen to be somewhat variable. If attention is directed to the work of Issa and Wolfendale (1981b) in which a variety of local clouds were examined and cosmic-ray enhancement factors were estimated, it is probably true that some GMC can be rather definitely claimed to have significant enhancements and thereby represent clouds containing, or having nearby, cosmic-ray sources. The most outstanding are probably Cygnus and Eta Carinae. Concerning models for cosmic-ray sources, Montmerle (1981) has given what appears to be a valid one, involving particles acceleration by stellar winds and confinement by resonant Alfv6n wave scattering.

Turning to closer GMC, the two clouds in Orion are a good case to consider. Both Bloemen etal. (1984b) and Houston and Wolfendale (1985) considered them inert and simply penetrated by the ambient cosmic-ray flux and derived values for X (= N ( H z ) / W c o ) as follows: 2.6 + 1.2 and 1.85 + 0.5, resectively. The difference, which is clearly not significant, is due to the adoption of different datum cosmic-ray emissivities. More recently, Richardson and Wolfendale (1988) have adopted a different view. Both by virtue of taking a datum emissivity from different regions than hitherto and by considering the latest stellar extinction data to give a better estimate of the cloud mass and thereby the value of X (1.5) they make a case for there being an enhanced cosmic-ray intensity in the cloud than outside. They argue that the cosmic-ray spectrum within the clouds is steeper than that outside and put forward models for explanation. The mechanism advanced by Morrill (1982), Morrill et al. (1984), involving the convection of low-energy electrons from outside the clouds into the clouds, is a strong


contender to explain the facts, although the presence of electron sources within the clouds or the propagation of a large supernova shock from outside cannot be ruled out. Richardson and Wolfendale argue that some other local clouds may well be in the same situation.

It is clear that the whole question of the interrelation of cosmic rays and GMC is in an interesting state.

7. Summary and Conclusions

It has been pointed out that cosmic ),-rays have something to say about the origin of cosmic-ray particles. Although the statistical precision of the data and the directional accuracy of the satellite-borne detectors operated so far have been poor, useful results have been achieved already.

It is the reviewers' view that the situation at present concerning cosmic-ray origin is as follows:

(i) Cosmic-ray protons below 10 GeV or so, which produce the majority of ),-rays in the region 300-5000 MeV, are produced mainly in our Galaxy. The evidence against an extragalactic origin seems strong; there would then be consistency with the conclusions that the particles above 3 x 1011 eV (up to 1019 eV) are also mainly Galactic,

an observation that comes from anisotropy measurements. (ii) The recent observations of changes of spectral shape of the ~,-ray spectrum with

changes of longitude and latitude add weight to the idea of Galactic origin. The details are not clear but a composite model involving supernova remnant acceleration preferentially in Galactic spiral arms and spectral modification by Galactic winds looks promising. The changes appear to relate to both electrons and protons.

(iii) There is still evidence for an excess cosmic-ray intensity in the nearby Loop I SNR and the magnitude of the excess is of the order of that expected in terms of contemporary shock acceleration theory, again both electrons and protons are involved.

(iv) There is weak but finite evidence for an excess cosmic-ray intensity in some local giant molecular clouds, the increase in intensity being greatest for those particles producing 7-rays of energy below about 150 MeV, presumably electrons.

Acknowledgements

We are grateful to our colleagues, K. M. Richardson, J. L. Osborne, J. Wdowczyk, and M. J. Rogers for helpful suggestions.

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Gamma rays and the origin of cosmic rays