29
RIVISTA DEL NUOVO CIMENT() VOL. 4, x. 4 1981 Discrete Sources of Cosmic Gamma-Rays. P.A. ]{ILEY and A. V~'. '~VOLFENI)AL],'~ Department o/ Physic.~ ~, I'nirersity o/ l}urlmm - Durham, U.K. (ricevuto il 11; I)i{.tqnbrc 1980) 1 1. I ntroduetion. 2 2. ~ Point~) sources of gamma-r~diati{m and the, it identification. 2" 1. Source e,~taiogues. 2"2. Identittcation of sources. 7 3. The contribution of discrete som'{'cs to the galatic emissivity. 7 3"1. Method of analysis. 8 3"2. The logN-log S plot. 13 3"3. The local surface emissivity in gamma-rays. 15 3"4. The contribution of sources to the emissivity of the Galaxy. 17 3"5. The contribution of pulsars to the gamma-ray emissivity. 20 4. Molecular clouds as discrete gamma-ray sources. 20 4"1. Speciiie molecular-cloud sources. 23 4"2. (',ontribugion from the molceulnx clouds in g~q~era, l. 24 5. 't'he rtLdial w~riation of the gal~(;ti(: gamma-r:ty emissivity. 27 6. Conclusions. 1. - Introduction. The SAS 2 and COS B satellites have produced detailed measurements of tile ltux oi~ g~mmla-rays of cncrgies grcater than 35 McV over '~ large part of the sky. The most strikint~ feature of the gamma-ray sky is the gMaetie plane; /.ha majority of gamma-rays in this energy r:mge come from latitudes b <; 10 +'. This ttux of galactic gamma-rays provides ~L tool for measuring the distribution of eosmie-r%y electrons and nucleons in the Galaxy, sinc(~ cosmic rays arc exI)cctcd to produce a gamma-ray flux through bremsstrahlung ~md =o i)roduetio n and to a lesser extent, through inverse Comptou interactions of electrons on the r~uli~tioJt tieids. Following the SAS 2 mission several 'it- tempts were made at fitting the observed longitude distribution of the flux with models of the galactic distribution of cosmic rays and gas [1-9]. The most important ('onclusion tha,l emerged was that there is evidence for a gra- dient of cosmic-r-t,y intensity in the Galaxy fred particularly significant was

Discrete sources of cosmic gamma-rays

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Page 1: Discrete sources of cosmic gamma-rays

R I V I S T A D E L NUOVO CIMENT() VOL. 4, x . 4 1981

Discrete Sources of Cosmic Gamma-Rays.

P . A . ]{ILEY a n d A. V~'. '~VOLFENI)AL],'~

Department o/ Physic.~ ~, I 'nirersi ty o/ l}urlmm - Durham, U . K .

(ricevuto il 11; I)i{.tqnbrc 1980)

1 1. I ntroduetion. 2 2. ~ Point~) sources of gamma-r~diati{m and the, i t identification.

2" 1. Source e,~taiogues. 2"2. Identit tcation of sources.

7 3. The contribution of discrete som'{'cs to the galatic emissivity. 7 3"1. Method of analysis. 8 3"2. The logN-log S plot. 13 3"3. The local surface emissivi ty in gamma-rays. 15 3"4. The contribution of sources to the emissivi ty of the Galaxy. 17 3"5. The contribution of pulsars to the gamma-ray emissivity. 20 4. Molecular clouds as discrete gamma-ray sources. 20 4"1. Speciiie molecular-cloud sources. 23 4"2. (',ontribugion from the molceulnx clouds in g~q~era, l. 24 5. 't 'he rtLdial w~riation of the gal~(;ti(: gamma-r:ty emissivity. 27 6. Conclusions.

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

The SAS 2 a n d COS B sa te l l i t es have p r o d u c e d d e t a i l e d m e a s u r e m e n t s

of t i le l tux oi~ g~mmla- rays of cncrgies g r ca t e r t h a n 35 McV over '~ la rge p a r t

of t h e sky . The mos t strikint~ f e a t u r e of t he g a m m a - r a y sky is t h e gMaet ie

p l a n e ; /.ha m a j o r i t y of g a m m a - r a y s in th is ene rgy r :mge come f rom l a t i t u d e s

b <; 10 +'. This t tux of ga lac t i c g a m m a - r a y s p rov ides ~L tool for m e a s u r i n g t h e

d i s t r i b u t i o n of eosmie-r%y e lec t rons a n d nuc leons in t h e G a l a xy , sinc(~ cosmic

r ays arc exI)cc tcd to p r o d u c e a g a m m a - r a y f lux t h r o u g h b r e m s s t r a h l u n g ~md

=o i ) rodue t io n a n d to a lesser extent, t h r o u g h inverse C o m p t o u i n t e r a c t i ons of

e l ec t rons on the r~uli~tioJt t ieids. Fo l lowing the SAS 2 miss ion seve ra l ' i t -

t e m p t s were m a d e a t f i t t i ng the o b s e r v e d l ong i tude d i s t r i b u t i o n of t he f lux

wi th mode l s of the ga l ac t i c d i s t r i b u t i o n of cosmic r a y s a n d gas [1-9]. T h e

m o s t i m p o r t a n t ( 'onclusion tha,l emerged was t h a t t h e r e is ev idence for a gra-

d i e n t of cosmic-r-t,y i n t e n s i t y in t he G a l a x y fred p a r t i c u l a r l y s igni f icant was

Page 2: Discrete sources of cosmic gamma-rays

2 r . A, P~ILF, Y Ftll(l A. ~,V. ~VOLFENI)ALE

the conclusion of Dodds et al. [5] and later workers, that the (l +10) GeV proton flux fell with increasing distance f rom the Sun towards the galactic anticentre.

The reason for the interest is th'~t ,~ gradient points strongly towards a galactic

origin of the p'~rticlcs in quest ioll.

Some of the flux is known to com~ not f rom cosmic-ray interact ions with

the interstellar medium, however, bu t f rom discrete, sources of gamma- rays .

By ,~ <~ d i sc re te , source we mean any locMized region of emission not due to

the irradiation of interstella,r gas by the a,mbient cosmic-ray flux which wu'ies

slowly with galactic, position. Thus the te rm <~ discrete source, >> m a y include not only starlike objects sneh a.~ pulsars, bu t more extended regions of emis-

sions due, for ex'mq)le, 1o locMized cosmic-ray acccler'~tion in the vicini ty of

gas clouds (el. [10, 11]). The increased da ta sample produced by the COS B

mission increased the number of known discr(;te sources and rq,ised 1he pos-

sibility tha t "~ large fraction of the flux is due to such som'ces. A knowledge

of the distr ibution of discrete sources ,md~ if possible, of their ident i ty is

thus very impor tan t for :my s tudy of the distribtHian of cosmic rays using

gamma- ray data. In this paper an es t imate of the contributiolt of discrete sources l,o the, to ta l

gam|na-r '~y emissivity of the G:~l:~xy is a t t empted . In sect. 2 the da ta on dis-

crete sources are reviewed and some possible identifications of the sources

are discusscd. In sect. 3 the local surface emissivity due to discrete sources

is es t imated and compa, rcd to the total surface emissivi ty locally. By using a model of the source distribution in the Galaxy, an es t imate of the luminosi ty of the Galaxy due to sources is made. The contr ibution made by pulsars is

also discussed. In sect. 4 evidence suggesting t ha t some of the discrete sources

are giant molecul~u' ch)uds is considered. Finally, a possible breakdown of

the galactic luminosity in gamma-r 'u l ia t ion into components due to eosn| ie-ray

interactions in molecular and "~tomic hydrogen and a eomt>onent due to t ru ly

discrete sources is given.

2. - {{ P o i n t - sources of gamma-radiat ion and their identification.

2"1. S o ~ r c e c a l a l o g u e s . - Discrete sources of g~unma-mdiat ion have, been

sought using 1)oth spatial and tempora l analysis of tile da ta on gamm'~-ray

arriw~l directions and times. A local enhancement of the flux consistent with

the, poini, spread function of the telescope may be taken as evidence for a dis- crete som'ee, if the probabi l i ty of such an enhancement being produced by

statist ical fluctuations is sma,ll. Evidence for g '~mma-ray emission f rom pulsars has been sought by test ing the data for pulsations at the pulsar period. Fur- thermore, if a sp~,,,tial elfl ' ,ancement of the flux is found, reguhu' t.ime var ia t ions

in the tlux provide evidencc tha t the source is comi)aet and not a diffuse source too smM1 to be resolved by the telescope. I)uc to the low ra te of g a m m a - r a y s

Page 3: Discrete sources of cosmic gamma-rays

])[S(ll~,],;'l'[,', S~I;I~(['I",S 01; ('()SMI(' (~AM)JA-IU~YS 3

f r o m m~y s (mree , h o w e v e r ~ s u c h i imi~V "m~lys i s is p o s s i b l e in o n l y n f e w e~ses ,

so t h M sp : f l i a l :ma lys i~ r e m a i n s l h e prin(, ipa, l m e t h o d of f inding" s o u r c e s i n

~he dt~tq,.

10ore. d i s e r e l e sou | ' ( ' es w(q'e f o | | m l 1)y su~'h ;m ~ma,lysis u s i n g d,~t,~ ~ ' ~ t h e r e d

b y the. S A S " te leseOl)e . Thre(~ oI' l h e s e w e r e ident;ifie.d wit;h obje<;~s k n o w n in

o t h e r p ' u ' t s of l h e eleei ,rom:~g|wti(~ s i )e(~trum b y t iming" ~malys is . T h e s e were,

t h e puls:~rs I 'S]~ 0531 ] - 2 1 ( t h e ( ' ra ,b ]) | | ls:~r), I ' S R 0 8 3 3 - - 1 5 ( t h e Ve l~ P u l s a r )

, rod i h e v:~,ri:~,bh, X-r:l,y sour( ' e , ~ 'y~ 'nus N-3. T h e f o m ' t h sonree~ m u n e d

'I'AI~LI;: I. - ~,'eeoml (![)S I~ ,atalogue (t[e~m.*e~ Ihesi.~', 19S0).

Sour(.(~ / h Er ro r H u x Rem:u'ks

dius ~.m 2~

2 ( ! ( ; 0 0 ( i - 0 o 6.7 - - 0.5 1.() 2.4

2C(H)10-- 31 1o.5 - - 3 1 . 5 1.5 1.2

2('(~()13 [ 00 13.7 0.6 l.O 1.0

2('(~036 I I)l ;~Ii.5 1.5 I.U 1.9

2('(11054 I 01 54.2 1.7 1.() 1.3

2(~(;065 { 00 (i5.7 (L0 0.8 1.2

2(?(~075 I-00 75.t) u.0 1.(~ 1.3 (.ottld be ext, ended fea tu re , O[]|(~1' s | r l l~ ' ( l l l 'P is p r e s e n l , 2('(~078 I 1)1 7S.0 1.5 1.i) 2.5

2(I(',095 [ 04 95.5 4.2 1.5 I.]

2('(1121 I 04 121.i) 4.0 1.() 1.0

2(~(~135 [ 01 I:~5.0 1.5 1.I) I.n

2(!(.~184 - 05 184.5 - 5.s 0.4 3.7 1'14R0531 I 21, a l s o s e e n b y S A S 2

2( ' ( ;195 ! (~ 1.95.l .1.5 i l l 4.S also seen b y SAS 2, possible v~trial,ion w i th 59 s pe r iod

2C(~218-- 0o 21S.5 - - O.5 1.:~ I,~)

2CG235 ~)l 235.5 .-- 1.0 1.5 1.0

2C(~26S - - 02 2~;:~.(i --- 2.5 u.3 13.2 1 'SR0833 - - 45, also seen b y SAS 2

2 C G 2 8 4 - 00 284.3 - - ().5 1.u 2.7 , 'ouhl be, e x t e n d e d f ea tu re

2C(~288 O0 2,~.3 0.7 1.;; 1.6

2C(1289 f 64 289.'; 64.6 0.8 0.6 3C273

2CG31] O1 311.5 - I.'3 l.O 2.1

2CG333 I- 01 333.5 1.0 1.1) 3.8

20(]342 02 342.9 - - 2.5 1.0 2.0

2C(1353 ] 16 35:;.3 l(;.i) 1.5 l . I ff Oph iucus : ~

2(!G356.1 oo 356.5 0.3 l.O 2.6 poss ib ly w~riablc

2CG 359 -01} 359.5 o.7 2.0 l.g

Page 4: Discrete sources of cosmic gamma-rays

4 P. A, FzlLEY ~l ld A. W, ~,VOLF]~,NDALE

5' 195 + 5~ could not be identified with any known object, though it too was

found to be variable, pulsating with a period of 59 s [112].

Tile COS B satellite, with its longer obserw~tional period, has crumbled many

more ((point ~) sources to be identified. The latest catalogue from the COS B

collaboration [13] contains 25 sources found by analysis of the data gathered

between August 1975 and December 1978. Earlier catalogues [14-16] con-

tain some sources not listcd in the latest catalogue. Some of these earlier

sources were later found to be inconsistent with a point source, being too broad,

while others did not produce a significant enllaneement by l;he standards used

to compile the latest catalogue. Table I lists the 25 sources of Hermsen 's

catalogue. T'~ble ] I lists sources from previous catalogues and tile reasons for

their exclusion from theft of Hernlseu.

T A B L E I 1 . -- Other reported sources.

Source 1 b Flux Remarks

80.0 0.7 4.4 ~ 1.l Cygnus X-3 source [12]. SAS 2 reported 4.8h period. Source not observed by C,0S B; see subsect. 2.2 for discussion

106.0 1,5 1.0 reported in [16]

176.0 --7.0 1.8 reported in [14, 16], enhancement not significant above 100MeV

189.0 1.0 1.4 Reported by IIEI~MSE~ et al. [14, 16], not consistent with point sourcc

295.5 0.5 1.3 [16] (*)

321.0 -- 1.2 1.3 []6] (*)

3 2 7 . 5 - - 0 . 5 2 .2 [16] (*)

(*) The sources ~t 295.5, 321.0 and 327.5 did not p roduce a s ignif icant exc~ss accord ing to the cri ter ia used by HFICMSE~" in p roduc ing the la tes t CO,~ B ca ta logue [13].

HERMSEN defines a ganHna-ray source as a significant excess above the local

background which has a spatial distribution consistent with the point spread

function of thc telescope and points out that , ill general, a t ruly pointlike

object and a feature of about (1--2) degrees ill extent are not distinguishable.

For source, s within t 5 ~ of the galactic plane he defines ~,n excess to be significant

if the probability tha t it is produced by tr random fluctuation of the background

is less than l0 -6 (corresponding to a deviation of more than 4.75 st ,mdard

deviations). The prob,~bility tha t the catalogue contains one spurious source

is estimated by HERMSEN to bc < 2 '~o. The catalogue is not complete. HERMSEN finds evidence for ,~ddition't.1

sources in the galt~etie plane froln l '~ ,-~ 79 ~ to 1 ~ ~ 84 ~ and concludes tha t there

Page 5: Discrete sources of cosmic gamma-rays

DISCRETE SOUI~,CES (IF 1!()$3[1C GAMMA-IIAYS

is evidence | ha t o11t~ of nlol'e o[ thelll ma, y 1)e variabh;. WILLS et al. [16], whose

catalogue contains 4 sources addit ional to Hcrmscn ' s , claim tha t their catalogue

is complete down to ~ min imum flux of 1.3.10 -~ photons cm --~ s -~ (E > 100 MeV) in the region 90" < / -~ 300 ~ -- 1 5 " < b < 15 ~ HEIr claims completeness

down 1o this flux only for l he region 9 0 " < / < 2 7 0 ~ , - - ] 5 ~ ~ [13].

2"2. I d e n t i / i c , tio,~ o] sourc~.s. - ()nly two g a m m a - r a y sources in the, second

C()SB catalogue have been identified with known objects with complete

ccr ta in |y viz. :2CG184--05 with PSR0531 t 21 and 2 C G 2 6 3 - - 0 2 with

PSI~ 0833--45 ]17, 18]. Thcse have been identified because the gunlmn-radiat ioh

pulses with the same period as the r:~dio sigmd from them. To a lesser degree of

certainty, the som'('(~ 2C(~ 289 J-64 h~s been i(h'utitied with thc quasar 3C273 on liile 1):~sis of sp:~ial (.oin(qdenee :~ll(l spcelml evidence. Iti h~s hcen suggestied

t]la, t 21~G 135-[-01 is a.lso ~sso(,i:~t(,d uibh a. qua,sar: QSO 0241-t 622 [19], bu t

n3ore re, c(Hl|, eviden(~e suggests tirol it is more likely to be a, ssociated in some

wa,y with l, he variable r'~,dio-souree GT ()236~ 610 [13, 211]. The source

CG 353@16 is thought to be associ:~tcd with the 0-()phiucus dark cloud. This

cloud had been proposed as a potent ia l sour(,e by BLACl( and F i z I o in 1973 [21],

but with a ltux much less lih~m eventual ly foun(I. I s s i et al. [22] argue tha t the

mass of the cloud coml)lex is much gre~ter thalt had hcan t, hought hi ther to

a,ml conclude Om,t the, g~lllll|~b-i'a,y flllx front the cloud east be explained by cosmic-ray intcraetions with the g:rs using' the loc:d value of the cosmic-ray

intensity. I~|()IIFIIA~ e ta l . I l l I, however, a,(h)pt a smaller mass for the gas,

(~o lwhlde ~]l~l, lJ al l in('reased cosmic-ray ][[1X is n e c e s s : ~ r y l~ud propose ~ model

involving the aceelcra, tion of costal(, rays in 1he vieinit,y o[ l~he cloud by an old supernova shock wave--lhe~ North Polar Spur (Loop 1). Other workers

too require an enhanced cosmic-r;~y tlux 123]. The source observed by SAS 2 in the vicinity of Cygnus X-3 is part icularly

interesting. I t s large intensity and 4.8 h period made, its reali ty and as-

sociation wilh (!y~nus X-3 almost terra.in. The intensity mc:~sured by SAS 2 in(ticates a luminosil, y in g a m m a - r a y s over 30 l,imes tlt:~l of the Crab pulsar

(PStr 0531-~21), a.nd yet, it, w~s not; observed by the COS B satellite, a l though HJ~l~s~,;~; finds eviden(.e for a stru(,lure ~dditional to thalJ due to 2CG 075-[ 00

and 21!G 07S@01 in its vicinity. KxrvFl~y [12] points out tha t the SAS 2 observ:~tion was made about 6 months :filer the series of very large radio out-

bursts were seen from Cygnus X-3 and ~hat the 1~()S B observations were made

at a t ime when the X-ra, ys fr()m the ol).iect were rei)orted to be in a very low

state, Some confirmation for the variabili ty of (!ygnus X-3 at higher energies

(> 1() t: eV)( :omes f rom measurements using the a tmospher ic (~erenkov thee-

nique (A. A. STI'it 'ANIAN, i)riv~te communi(,ation). () ther id(,ntiiic~tions of individttal sour('~,~ h~ve been m~ule, bu t none has

yet received univers'fl acceptance. For extra,pie, PROTHEROE et al. [24] present

e'r favouring '2C(I 075 ~-00 and 21'(I 078 ~-01 (table I) being due to eosnfie-

Page 6: Discrete sources of cosmic gamma-rays

{i I ' . A. I r g i l d A. 1V. x, YOLFI~;NDAI,I,;

ray irradiation el the gas clouds in t!ygnus. Tha t there are extended sources

due to the cosmic-ray irradiation of large cloud complexes seems ineontra-

vert ible [25, 26], but the nm nbe r of sources in table I I due to clouds of smaller

angular size is not yet clever. Wha.t is clear is tha t no simple identif ication of

sources with a single class of objects (.an be made.

The lat i tude distribution el sources indic:~l,es t ha t they arc young objects,

lying close to the galactic plane. The mean vahtc of Ibl for sources withiu 10 '~

of the pla,ne is ~ 1.5 ~ indicating th:tt R/z.-~ 40, /r being tile distance of the

source f rom the Sun and z its distance f rom the galacl, ic plane. Tile inevi table

widening of the lat i tude distr ibution due to the poor angula,r resolution of the

instrumenl~ m a y mean t~hat % be t te r es t imate is closer to R/z ,~ 6t). I f the

Crab puls'~r source 2CG 18.~-- 05 has a luminosi ty typica l of the sources, then

their mean distance f rom the Sun would be .~ 3 kpe, giving z .~ 50 pc, similar

to t ha t for moleenlar clou(ls and H I [ regions.

Following the suggestion of Strong 127] tha t g a m m a - r a y sources may

be associated with giant H I I regions, a sla~tistical test wa.s c ' |rried out to see

whether any evidence of sueh objects forming ~ class of g a m m a sources could be found. The second (~OS B source, catalogne w~s compared with the Sharpless

( 'ataloguc of H I I regions (a northerndlemisI)here survey)[28] and with the ) l{odgcrs, ( , amibe l l and Whi teoak (RCW) catalogue (% southcxn-hemisphere

survey) [29]. The con|p~rrison involved counting the mmlber of t I I I regions

within 2 ~ of a g a m m a - r a y source and comparing this number with the ex- pected number of ehmlee associations. To es t imate the latter, the gt~mlna-l'ay

source co-ordinates were ~'aried by displacing t hem in longitude, in steps of

:l", f rom A / - - - - - 2 0 ~ to -~-20 ~ mul counting the associated number of H I [

regions ill each case.

Tile Sh~rptess c~t~logue covers the g~fl:mtic plane in the longitude range

l (350 + 0 - 2 4 0 ) ~ and the IgCW eatMogue covers it in the range I (240 : -0- -40) ~ To obtain a cat~floguc covering the whole galactic plane, we have used the

Sharpless catalogue, the more complete of the two, where possible, supple-

ment ing it)using the Ir ca, talogue in the region 1 (24t) ~ ~50) ~ In looking

for associations betwcca the I l I I regions and g a m m a - r a y sources, we have

used only H I I regions with ,regular diameters between 5' and 100' and the 21

g~mmla-ray sources which have not yet been identified with known objects

(i.e. we have used the second COS B catalogue less the sources 2CG 184- -05 ,

2CG 263--02, 2CG 289-[-64, 2CG 353@16). Tile expected number of chance

associations is 25, while the :~ctual num ber of H I I regions within 2 ~ of a gamma- r~y source is 35, two standa.rd deviations ~bove the expected number . Those g a m m a - r a y som'ces which contr ibute most to the excess are 2CG 006-}-00,

2CG 013@00, 2CG 284- -00 and 2CG 359--00 . I f the smal ler-diameter H I I re- glens arc also included, the expected | m m b e r of ch~mcc coincidences increases to

30.8 and the number of actual coincidences to 50, 3.5 s tandard deviations larger

tha.n the expected vMue.

Page 7: Discrete sources of cosmic gamma-rays

I ) I ,~(~IgETE S()( rTLCES (')F {:OS51I(~ G X M ~ [ A - l l X Y : ~ 7

Thus it wouhi alq~ea.r theft. I herc is some correlat ion be tween the posit ions

of g a m m a - r a y sourc(~s and those of HI I regions. The result is only ma.rginally

significant and due main ly to ,! el! ~hc 21 sour(~es lcs ted, bu t a.dds weight to

the conje(~lur(~ t h a t ga.nm~a-r:/y sour, 'es art, y o u n g object;s a, nd hence likely

to 1)c found in the vi(,inity of o ther young" ol)jeets, such a.s I t l I regions a.nd

moleeuhtr ('louds. This is also sugvesl(,d by the mc~m height of sources a.bove

lhe ga.la('l.ie plane a.s dis('ussed c~a'lier.

The fa.ct lha t the lwo sources to have been posit~ively identif ied are bo th

pulsars suggests t ha t ma.nv other sources may a.lso be l)ulsars (see ref. [3011 ). Most

y-ra.y soure('s do not ('onta, in a, I(no~;n pulsa.r within lhci r error radius, however .

Fur thcrmor( ' , while the gamma-ra .y sources seem |o have a. scale he ight of a.bout

50 l)e, l)ulsa.rs have a scale hei~'ht of about 350 pc [31 ]. I t appet~rs tha.t pulsars

art, born ne:lr l o the vala('tic l)lam', Iml., I)cc:lusc of their high velocities (the,

lne~m v(,locily 1)crpendieula.r to lhc l)l:mc has been est, imalcd as 100 kms 1)

and lifelime of :d)out 5"106 ye~/rs [31[, spend mos|~ of their life, much fu r the r

f rom it . Thus, it' :/l:lrv(, 1)roportiou of so(4r(.cs (~rc I)uls~lrs, t hen t h e y a.rc y o u n g

pulsars which have no t ye t m o v e d f:~r f rom their birt, hplac(~. The surface densi ty

of pulsars near the Sin1 e,stimalc(l 1)y MANClIESTER is Of the order of 500 kI)c -~

(this refers 1o lmlsa.rs ~hosc 1)c~ml direction alh)ws 1,hem to be seen f rom l)hc

Earl.h). I f only lhose 10 ~ yca.rs old or younger could 1)e seen as gamma.-ray

sources~ then they wouhl 1)reduce :~, sm't'~/cc densi ty of :~l)out~ 1 ga.lllln~l source

per ki)c ~. This dens i ty is sullicieul: lo Cxl)l~/iu the number of surces seen,

provided t h e y ha, re simila~r htttfiuosilics to I'S1L 0531 [-')I and I ) S g 0 8 3 3 - - 4 5 .

The object iou to this i(lenlifi('alion of sour(,es w i t h young' ( ~ l0 ~ y(:a.rs) pulsars

is lha.t only two l)ulsa.rs ha, r e been l'ouwl to 1)e :~ssociatc(l with s o u r c e s - -

wherca.s ma, ny olhers would ha.re been cxl)c(q(!(1. A possible expla.natiol~ is t he reduced sensi t ivi ty of some oil the nldiol)ulsa.r surve,ys to shor t -per iod

pulsa.tions (<~ 0.3 s for the, Molongolo and ,lodrell ba, nk surw',ys). 8in('e y o u n g

pulsa.rs are expel,led Io h:tve shorl~ l)eriods, they ma.y have, been misse,d in such

searches [32] a.nd ~v~ must ro~':trd the siiu:~lion :~.s still somewha.t open.

3. - T he c o n t r i b u t i o n o f d iscrete sources to the g a l a c t i c e m i s s i v i t y .

3"1. M e t h o d of a ~ a l y s i s . - Despite our iguora.nce of tlle iden t i ty of nlost

of the discrctc sourc('s in ~hc second (:OS B c~/ta.logue, we :~re a.ble to m:~ke

some est im~tcs of ~heir d is t r ibut ion ill the vicinity of the Sun a.nd their eon-

t r ibu t ion 1o the local cmissivi ty of the (L~laxy il~ ga.mma.-rays. A me thod

which has been used to make such :m c~t:ima.lc is the use of a 1)lo~ of log N vs.

log N, N being the n u m b e r of sources with :~o llux vret~ter t h a n S [33, 33,]. I n

this section we exa.nfine this me thod in detai l and develop it to estima.te the,

surface cmissivi ly of the Ga laxy n('~u" l.hc Sun due to discre,te sources.

Page 8: Discrete sources of cosmic gamma-rays

8 P . A . I ~ I L E Y and A . VV. W ( ) L F E . N D A L E

3"2. The log N-log S plot. - We wish to derive an expression relat ing the

number of sources observed to have fluxes between set limits and the densi ty

and luminosity of sources. We use the observat ion t h a t sources are on the

average much far ther f rom the Sun than they are f rom the galactic plane to

derive such an expression.

Suppose t ha t the density of g a m m a - r a y sources in the Galaxy m a y be

decomposed into the product of two functions

~(1, r, z) 6(l, r)h(z),

where I is the galactic longitude, r is the distance f rom the Sun along the galact ic

plane and z is the distance above the plane. The function ~(1, r) gives the sur-

face density of sources and h(z) the dependence of source density on distance

f rom the plane. Tim function h(z) is normalized so tha t

co

f h(z) dz : - 1 c~

and we assume tha t h(z)= h(--z). Suppose, further , t ha t the spec t rum of

source luminosities is the same throughout the Galaxy and is given by ,~(L).

By means of this notat ion, the number of sources, in the la t i tude range Ib] < 0,

the longitude interval A1 and with a flux S or greater, is given by

c~ oo

(3.1) N(> ~') = f fa(1, r) ~(4z~r ~ S)4~, '3H(r sin 0)dr dS AI, o s

i where It(z) = j (z) dz. z

The dependence of N on S may be seen more clearly, if the change of va- riable L = 4:~r2S is made, regarding L as a funct ion of r. Then

(3.2)

o o ~

I f the surface density is roughly constant for values of r----~/L/~4S for

which LI(L)/S 2 is nonnegligible, and H ( ~ L / 4 ~ ] s i n 0 ) = 1 under the same

conditions, then

L~ (3.3) ;v(> ,~) ~ 8~s A~.

In this case N ~: 1/S and an es t imate of f ,a m a y be made by using the num-

ber of sources producing a flux of S or more. The plot of l ogN- log S m a y

Page 9: Discrete sources of cosmic gamma-rays

thus be used as a test of the constancy of the surface density for sources. Care mus t be exercised in doing so, however, since, if the luminosi ty spec t rum 2(L)

is fairly fiat, then it m a y happen tha t N oc 1IS even though the surface density

of sources is not constant .

10 ~

b)

A

100

" - I I I I I I I , I

\

- I

I I I I I I I I

10 ~

I I I I I 1 I I ] f

100 10 ~ x l O -6 100

' ' ' ' ' ' ' I

DISC]{ETE SORUCES OF COSMIC GAMiMA-RAYS

f lux photons (E>100 MeV)(cm -2 s -1)

10 -6

Fig. 3.1. - a) log N-log S plot for the ~nticentre region (60~ l ~ 300~ b) log N-log S plot for the centre region ( - - 6 0 ~ ~-60~

Figures 3.1a) and b) show log N-log S plots for the 25 sources in the second COS B catalogue. The da ta have been divided by longitude into the centre

(-- 60o ~ l ~ ~- 60 ~ ~nd ant icentre (60 ~ <: l ~ 300 ~ regions. I t is seen tha t ,

while the ~ntieentre sources are consistent with the N zc 1/S relationship,

the centre sources are not. This not only indicates tha t the source surface density is not constant towards the central region, but tha t the source luminosity

spec t rum is too steep, ~t least above a certain luminosity, to flatten the log N-log S curve to one roughly consistent with N oc 1/S. We can thus con-

clude t ha t the source surface density in the ant icentre region is approx imate ly

constant out to the limit of source visibility.

Using the 7 sources in the ant icentre region with fluxes S ~ 1.3.10 -6 cm -~ s-~

we m a y derive the surface emissivity due to sources, i.e. La, obtaining the value

/~a - - (5,5 • 2.1).10 -5 photons (E > 100 MoV) cm -~ s - t .

In so far as the density of sources will va ry over the Galaxy, N ( > S) will va ry with I. One method of incorporat ing bo th the / -dependence and the infor-

mat ion available in the log N-log S plot is to plot the sources on a polar graph

Page 10: Discrete sources of cosmic gamma-rays

10 e . A . R IL]~Y ~I1(:1 A. W . W O L F ~ E N D A L E

of S -~ vs. I. If all sources had the same luminosity L, then S -~ would be pro-

port ional to the source distance

and the graph would reveal the distribution of sources in the vicini ty of the Sun. (Of course, unless L is known, the actual distance scale remains hidden.) Although not all sources have the same luminosity, this plot is still useful in tha t the number of sources per unit area of the plot is proport ional to Lr the

surface emissivity due to sources, bu t now it is an average of the surface emis-

sivity in the direction being considered. This m ay be seen by using eq. (3.2) to calculate the expected number of sources with flux between $1 and S~ and

then transforming variables from S to t ~ S-~. We arrive at the result

t2 r

(3.4, 4zcN(tl, t 2 ) = f f t L 2 ( L ) ( r ( V ~ t ) H ( V Z 4 ~ t s i n O ) d L d t A l . t l 0

The area encompassed by the limits tl and t~ and the longitude range A1 is

so dividing both sides by A t

t2

A t ~ Aloft d t ,

t t

we obtain

4u N(tl , t~) At

t2 O0

t O/d dt t ~ 0

ta

f t dt t l

The r ight-hand side is a weighted average of La in the direction I. Fur- thermore, the larger the values of tl and t2, and hence the smaller the flux values

$1 and S~, the fur ther f rom the Sun this average applies. In fig. 3.2 a plot of S -~ vs. 1 is shown. F rom this plot it is obvious tha t the

surface density of sources increases towards the galactic centre, provided tha t

the luminosi ty spectrum of sources is constant th roughout the Galaxy. In using fig. 3.2 to make quant i ta t ive estimates of the surface emissivity, the in- completeness of the sample must be borne in mind. Following our earlier dis- cussion about the lower limit to S, we use sources with a flux of :l.3.10 -~ pho- tons cm -2 s -1 (E ~ 100 MeV) or greater to est imate the emissivity due to sources. Even this higher limit to S will produce an underest imate of the emissivity in the region towards the galactic centre, however. To carry out the analysis

Page 11: Discrete sources of cosmic gamma-rays

D I S C R E T E S O U R C E S O F C O S M I C ( ~ A M M A - R A Y S

2 2 0 ~ ] 8 0 ~ 140 ~

11

2 7 0 ~ 90 ~

3 2 0 0 0 o 4 0 ~

Fig. 3.2. - Plot of S " ~'s. 1 for the 22 sources of the second COS B catalogue which have ]b[ < 10 ~

of the surface emiss iv i ty due to sources, we divide the S-~ vs. 1 plot in to 6

regions as shown in fig. 3.2. The gr~ph is d iv ided in to two flux regions:

( 1 . 3 . 1 0 - 6 ~ . 6 . ] 0 -6) pho tons cm -2 s -~ (the far region) a n d > 2 .6 .10 -6 pho-

t o n s . c m J - s ~ (the n e~r region), and three long i tude regions: 11~ (-- 60 - - ~- 60) ~

(the cen t re region), 1H (60--120) ~ a n d {240--300) ~ ( the local region), a n d

1 ~I (120--240) ~ (the an t i cen t r e region). Eueh of these six regions has the same

are~, so t ha t , if t he surfucc dens i ty of sources were c o n s t a n t w i th in the l imi t

of v is ib i l i ty of sources, t h e n lhe u m n b e r of sources in euch region would be

the sume, or nt leust cons i s ten t w i th in s t~t is t ical f luc tuut ions . T~ble I I I shows

the n u m b e r s of sourc, es in each ~rea.

TABLE II I . - The number o] sources i~ each o] the 6 regions used in the analysis.

S > 2.6.10-6 1.3.10 -6 < S < 2.6.10 .6 {near) (far)

centre 2 6

local 2 3

anticentre 2 0

Page 12: Discrete sources of cosmic gamma-rays

1,2 P . A . R I L E Y and A. w . ~VOLFENDALE

Only sources with b '~ < 10 ~ have been used. The enhancement in the far-

centre region is seen, al though the number of sources in it is only about 3

s tandard deviations above the mean of the remaining regions. To calculate

the local value of L we use the three <~ near ~> regions and the far local region.

Using the formula

@ L > - - A t '

we arrive at the value

@L} = (7.0 • 2.3). 10 -s photons (E > 100 MeV) cm-"- s -~ .

Had we used all 6 regions, the result would have been only a little different

(<La> -~ (7.8~:2.0).10 -~ cm-~s ~) because the excess in the far-centre region

is counteracted by the deficit in the far-anticentre region.

I n order to check tha t this analysis gives a reliable estimate of <aL>, we

have tested it on models of the Galaxy produced by Monte Carlo simulations.

Sources were distributed throughout the model galaxy with a distribution

similar to tha t given by KODAIRA [35] for supernova remnants and their

huninosity sampled from a power law distribution 2(L) pc L r. I n some simul~-

tions, sources were located in spiral arms, using the Georgelin model [36], while in

others they were spread uniformly around the disk. I t was found tha t the

analysis used in this section gives reliable estimates of <aL> except when the

luminosity spectrum 2(L) is too flat, i.e. when the exponent y < 3. The log N-

log S distribution for sources in the centre region in this case (i.e. y ~ 3) was

flatter t han tha t for the COS B data. I t was found tha t the steepness of the

log N-log S distribution could be reproduced only when the luminosity spectrum

became very steep above a luminosity of (1+3) .10 a9 photons s -1 and when

a substantial fraction of the sources was located in spiral arms. On the basis

of these tests we conclude tha t our method of analysis should produce a re-

liable estimate of <L@.

A further point of note regarding the distribution of sources on the S-~

vs. 1 plot is the number of sources with fluxes between 1.0.10 -6 and 1.3.10 -6

photons cm -2 s -1 in the local and anticentre regions. I f the density of sources

were constant in these regions, one would expect about �89 the number of sources

with fluxes greater than 1.3.10 -6 photons cm -2 s -l. In fact, there are 6 sources

whose measured flux is between 1.0 and 1.3.10 -6 photons cm -2 s -~, one with

a flux of 1.3-10 -6 cm -2 s -~ and 6 with fluxes greater than 1.3.10 -6 cm--" s -~.

This excess of sources may par t ly be explained by the possible 30 ~o error in

the flux measurements, sources with a flux of less than 1.0.10 -Gcm -~ s -~ being

measured to have this minimum detectable flux due to statistical fluctuations.

I t may also arise from pure noise. Such phenomena do not appear to be able

to explain the whole of the discrepancy, however, so tha t there is some evidence

Page 13: Discrete sources of cosmic gamma-rays

D I S C R E T E S O U R C E S OF COSMIC G A M S [ A - R A Y S 13

for ~ density enhancement at the l imit of source visibil i ty in the range 1H (60--140) ~ This could be explained if g a m m a - r a y sources lay main ly in

the Georgelin spiral pa t t e rn [36]. The enhancement in source density towards

the galactic centre would then be due mainly to the Sagit tarius-Cariua a r m

about 2 kpc f rom the Sun, while the slight enhancement at :~ lower flux level

in the direction l ~r (60--140) ~ would be due to the effects of the Perseus arm.

As discussed earlier, the presence of the Sagit tarius-Carina a rm is also suggested

by the results of the Monte Carlo simulation we h,~ve performed.

3"3. Thc local sur/acc emissivi ty in gamma-rays. - We have obtained a value for (aL} t.he loc:~l surfi~ce emissivit.y of the. Galaxy due to discrete sources

of gamma-rays . We now turn to the problem of calculating the local surface

emissivi ty of the Galaxy due 1o both discrete alld diffuse sources (i.e. cosmic-

r ay -gas interactions). We att(~mpt to determine this i~l two ways: f rom the

var ia t ion of the galunla-ray tlux with lat i tude above b n = l0 ~ and f rom the

var ia t ion of the flux with longitude for b" < 10%

]in ~ model of the Galaxy in which the surface emissivity s is constant ,

independent of R, the flux us :r function of lat i tude is

~ O~

where 5'o is the isotropic (extragalactic) component . Although this equat ion

breaks down at low lati tudes, because s is not constgnt with R, at high lat i tudes

it holds so long :~s ~ does not va ry too rgl)idly near the Sun. If, for exampl%

the sc,%lc, height of the volume emissivity were 100 pc, then only regions within 1 kpc of the Sun wouht contr ibute significantly to the flux at B~titudes b ~r > 10%

Figure 3.3 shows a graph of S(b) ~:s. cosec Ibl fol' bo th nor thern and southern

galactic lati tudes derived f rom the tabul:~ted (tat:~ of SAS 2 presented by FlCrt-

TEI~ et al. [37]. The southern-hemisphere data are less complete t han the north-

ern ones, due to the poorer coverage of t ha t hemisphere by the SAS 2 experi- ment . Dat:~ for the regions l '~ ( - - 9 0 - - t- 90) ~ altd l" (90--270) ~ and for pos- it ive and neg~tive lati tudes ~re showu sep~ral)ely. The effect of the Gould's Belt is evident for the regions l (-- 90 " 90) ~,, b > 0" and 1 (90--270) ~ , b < 0 ~ In

calculating the surfac,~ emissivity~ we have used only dat:~ f rom the other two

regions, which should not be affected by emiss io l / f rom Gould's Belt. F[CItTEL

et al. [38] have produced ~ similar fit 1:o the da ta in order to calculate the

isotropie flux So, and arrive at similar values to those presented here. The

surfacc emissivity estim,~t(~d f rom the data is

~" (2.5 :t 0A).10 ' phototls cm ~ s -L (E > 100 ~IeV),

the error shown being 1 s tandard deviation.

Page 14: Discrete sources of cosmic gamma-rays

14 P . A, R I L E Y and A. XV, ~VOLF:ENDAL]~]

i

7 E

t., Lu v

o

o

x l 0 -s

ol l

"/ /o

J Y ~

~ 0

/ o / /

/ /

/ ~ II /

/= / . /

i

/

[ I ~ I i I i l 0 1 3 4 5 6 7

cosec Ibl

Fig. 3.3. - Variation of gamma-ray flux with latitude for [b[ > l0 ~ The tabulated data of Fichtel et al. [37] have been used to derive the fluxes. The effect of the Gould Belt is evident for the regions l ~ ( - - 9 0 - - + 90) ~ , b > 0 ~ and /=(90--270) ~ b < 0 ~ o/=(270--90) ~176 . / = ( 2 7 0 § ~176 a /=(90--270) ~176 �9 /=(90--270) ~ b<O.

I t is also possible to arrive a t an es t imate of the local surface emiss ivi ty

f rom an examinat ion of the longitude dependence of the low-lat i tude flux. I f i t is assumed t h a t the emissivi ty s depends only on the distance f rom the centre of the galaxy R, then the longitude distr ibution can be unfolded to give the

var ia t ion of e with R. Such unfoldings have been per formed previously b y

STRONG [39] and CARAVEO and PAVL [40]. We have repeated the unfolding

using a different me thod to t h a t of these authors. The Galaxy has been divided

into 10 radial bins out to 15 kpc f rom the centre and the surface emissivi ty

of each bin chosen to give the least-squares fit to the line flux calculated

between lati tudes of - -10 ~ and -~ 10 ~ Figures 3.4a) and b) show unfoldings of

the line flux for the hemispheres l (0--180) ~ and 1 (180--360) ~ The SAS2 da ta t abu la ted b y FICHTEL have been used for this unfolding. The values for the local surface emissivity are (1 .7• -4 photons cm -2 s -1 (l H (0--180) ~ and

(1.9=L0.3).10 -4 photons cm -2 s -1 (l H (180--360)~ bo th somewhat lower t han

the value obtained by the previous method. The advantage of the es t imate based on the lat i tude dependence of the

flux is t ha t the assumptions upon which it is based are more likely to be realized

Page 15: Discrete sources of cosmic gamma-rays

DISCRETE SOURCES OF COSMIC GAMMA-RAYS 1 ~

151 xlO- ~" ~E

~10 o

A t~

o 5

e~

~ 0

xlO -4

a)

i

[

4. 8 12 16 gaLctctocentric rczoLius(kpc)

I I

8

b)

,I

I

16

Fig. 3 .4 . - a)RadiM variation or the gMactic emissivity in gamma-rays above E = 1 0 0 M e V derived from unfolding the line flux (Ibt<10 ~ for /~-(0-180)~ b) r~dial variation of the gMactic emissivity in gamma-rays above E = 100MeV derived from unfolding the line flux (Ibl < 10 ~ for /==(180-360) ~

than those upon which the unfolding is based. I t has the disadvantage tha t

it provides an estimate of the mean surface emissivity of the Galaxy within

about 1 kpc of the Sun, whereas the estimate of the surface emissivity due to

sources, with which we want to compare it, is an average taken over a larger

area. The unfolding result, on the other hand, is more liable to inaccuracies

through departures from the assumed symmet ry of the Galaxy, but has the

advantage of being based on data coming from a similar area of the Galaxy

as tha t used in the source analysis. As ,~ mean value, based on the results of

both methods, we take e = (2.04-0.3) .]0 -4 era-"-s -1.

3"4. The contribution o/ sources to the emissivi ty o] the Galaxy. - Using the

results for the local values of <La} and e, we may estimate the fraction of the

local emissivity contributed by discrete sources. Using <aL}----(7.04-2.3).

�9 10 -6 photons cm -2 s -1 and e ~ (2.0=[=0.3).10 -4 photons cm -2 s -1 (both refer-

ring to photons of energy above 100 MeV), we obtain the local contribution

of sources as 0.35~:0.15. Because the sources in the second COS B catalogue

all lie near the Sun on a galactic scale, the distribution of discrete sources in

the Galaxy as a whole cannot be determined from them and so the total emis-

sivity of the Galaxy due to such sources cannot be estimated from the cata-

logued sources alone. Since the latitude distribution of sources is typical of

Page 16: Discrete sources of cosmic gamma-rays

t ha t of very young objects, however, we may reasonably suppose tha t t hey have a similar radial distribution to such objects and hence estimate their

contribution to the to ta l emissivity of the Galaxy in gamma-rays. As examples of (< young >> objects in the Galaxy we take molecular hydrogen,

supernova remnants and pulsars. The radial distribution of molecular hydrogen has been est imated by GORDON and BURTON [41], t ha t of supernova remnants by KODAIRA [35] and tha t of pulsars by MANCHESTER [31]. These are shown

in fig. 3.5. The three distributions are similar, having a pronounced peak

12 6 9 b)

2 x 1 0 3

t .J i

i

I 0

I

"~ 10 3

7"-" 9 o {3_

.~ 6

o

2 3

12 16

16 [ , . A . R I L E Y a n d A . w . ~ V O L F E N D & L : E

114 I B ' 1'2 ' 1'6 gaZactocentric radius(kpc)

M

4. 8 12 16 galactocentnic cadius(kpc)

Fig. 3.5. - Radial variation of the distribution of young galactic objects: a) molecular hydrogen: after GORDON and BURTON [41] ( ) and BLITZ and SHU [42] ( - - - - - - ) ; b) supernova remnants: after KODAIRA [35]; C) pulsars: after MANCHESTER [31].

Page 17: Discrete sources of cosmic gamma-rays

DISCR:ETE S OURCES OF COSMIC r 17

between 4 and 6 kpc from the galactic centre. The peak is more prominent in the H. distribution, bu t this may be due to an over-estimate of the H~ density in the inner Galaxy due to the galactic metallicity gradient not being taken into account by GORDON an(l BURTO]N. BLITZ and Srrc [42] show that , when the metallicity gradient is included, a flatter distribution of H2 results. Using

these radial distributions, we can relate the total number of objects in the

Galaxy to the surface density at the solar circle (i.e. at 10 kpc from the galactic centre). For the distribution of pulsars and SNICs the total number in the Galaxy is about 800 a t , where ~<~ is the surface density (in kpc -2) at the solar

circle. For Gordon and Burton 's H2 distribution the figure is about 1000 ~o' For the reasons discussed above, we will regard the figure derived from the H~ distribution ~s an over-estimate and adopt 800 as an estimate of the ratio of the total number of gamma-r~l,y sources iu the Galaxy to their density

(kpe 2) in the solar neighbourhood. Using this figure to calculate the total emissivity due to point sources of gamma-r,~ys, we arrive at the result L

source = (5.3~:1.8).104~ photons s --1 (E > 100 MeV). The total emissivity of the Galaxy derived from the unfolding described earlier is

L~ ~ (14.5 ~: 1 ) '10 ~' photons s ~ (E > 100 5IeV),

so tha t about 37 % of the total galactic emissity in gamma-rays may be ascribed to discrete sources.

The contribution of discrete sources to the detected flux of gamma-rays depends upon the longitude and latitude. At low latitudes (e.g. b H < 5 ~ more

than 37 ~o of the gamma-ray flux is probably due to discrete sources, while at higher latitudes the proport ion is likely to be less than 37 %.

3"5. The contribution el pulsars to the gamma-ray emissivi ty . - The discovery of pulsed gamma-radiat ion from l)SR 053 lq-2 l and PSR 0833-- 42 suggested tha t other pulsars would also be gamma enfitters. A search using the arrival times of gamma-rays requires precis(; knowledge of the pulsar period and its derivative which in practice means radio observations el the pulsars contem- porary with the gamma-ray observations. An examination of data from the SAS 2 experiment for pulsed emission from 75 radiopulsars gave tenta t ive positive results for the pulsars PSR 1818-- 04 and PSR 1747-- 46 (and,

of course, for PSR 0531~-21 and PSIr 0833-- 42) [43]. An examination of the COS B data failed to confirm PSR 1 8 1 8 - - 0 4 as a gamma emitter,

bu t produced positive results for two other pulsars - -PSR 1 7 4 2 - - 3 0 and

PSR 1822- -09117] . These remain lenla t ive identifications, however, and

pulsars PSR 0531-}-21 and ] 'SR 0833- -42 l'en|~in the only confirmed gannna- ray pulsars.

Buccm,sRI ct al. [44], on lhc basis of 1t1(, ltux from PSR 0 8 3 3 - - 4 5 ,rod PSR 0531-}-23 and the claimed fluxes from I'SR 1747 -- 46 and PSR 1822 -- 09,

Page 18: Discrete sources of cosmic gamma-rays

18 r . A. R I L E Y and A. 1V. ~VOLFENDALE

deduce that the efficiency with which pulsars convert their rotational energy loss to gamma-radiation increases with the age of the pulsar. They present evidence for a similar effect for the radioefficiency of the pulsar. The efficiency in both cases appears to vary as ~ oc T ~, with a _~ 1.5, ~ being the characteristic age of the pulsar calculated from its period and period derivative. More re- cently AYAsT.I and OGE~)IA~ [45] have produced a model of gamma-ray production by pulsars based on the (( outer gap ~ model of Cheng ct al. [46]. I t predicts that for young pulsars ~ ~. There are, nevertheless, some ob- jections to this model. The same method of cMculation of the expected flux as Buccm~RI ct al. used in determining the efficiency of gamma-ray pulsars predicts thut the pulsar PSI~ 1929+10 should be about 8 times as bright as PSR 0531+21. Its galactic co-ordinates are l '~= 47.4, b U = - 3.9 and so it should have been easily detected. The high-latitude pulsar PSI~ 0950+08 should produce a similar flux to PSR 0531+21, but it has not been observed either, although this may be explained by its being near the edge of the area viewed by the COS B satellite and in a low-exposm'e region of the area scanned by SAS 2. The pulsar PSIr 1642--03 would have been expected to produce a flux some 80% that of PSR 0531+21, yet it was not seen either. These three and some of the other pulsars listed by :BUCCItERI et al. should have produced enough flux to be detected using spatial analysis alone if all, or at least a siza- ble fraction of, pulsars followed the proposed trend in gamma-ray efficiency. I t would appear then that most pulsars produce considerably less gamma- radiation than would be suggested by a study of PSI~ 0531+21 and PSR 0833- 42.

In the absence of any other data we shM1 derive limits on the contribution of pulsars to the galactic emissivity by a comparison with radiodata. MA]NCttESTER [31] has derived the radioluminosity distribution of pulsars from the second Molongolo pulsar survey. This distribution may be approx- imated as

( Z ) -~ ~ = 1 . 8 5 , 0 . 1 < L < 1 0 O m J y ( k p c ) ~, N ( L ) = A 100 ' where [ ~ = 2 . 1 , 1 0 0 < L < 1 0 5 m J y ( k p c ) '2.

The mean luminosity is thus Ldoom~z = 2.33 mJy (kpc) 2. The luminosity of

PSR 0531+21 is 1920 mJy (kpc) ~-, so that

L = 1.16'10-3Lo531.

The effective lmninosity (i.e. ignoring beaming effects) of PSR 0531+21 in gamma-rays is 1.44-103~ photons s -1 ( E > 100 MeV) (assuming a distance of 2 kpc). If the mean gamma-ray luminosity of pulsars is the same fraction of the luminosity of PSI% 0531+21 as is the mean radioluminosity, then we would have

i S . = 2 . 1 " 1 0 3 6 S - ~ .

Page 19: Discrete sources of cosmic gamma-rays

DISCRETE SOURCES OF COSMIC GAMMA-RAYS 19

MANCHESTER est imates the totM n u m b e r of potent ia l ly observable puls~rs ill

the G~l~xy ~s N~ = (4.2 =~1.6).105, so the g~mm,~-r~y luminosi ty of the G~l~xy

due to puls~rs, in the above model, is ~bout 9.10 ~ photons (E ~ 100 MeV) s -1,

or ~bout 60 % of the to ta l emissivity. (Using the effective luminosi ty ,~nd the

number of potent ial ly observable sources ~utom~tic~lly includes the effects

of beaming of the puls~r emission.) The ~v~il~ble d~t~ suggest, however, t h a t

the ~ssumption t ha t the g~mm~-r~y luminosity is proport ional to the r~dio

luminosity, using PSR 0531+21 ~s ~ normalizat ion point , produces ~n over-

es t imate of Lv. Figure 3.6 shows ~ plot of the r~dio fluxes (400 MHz) ~md

g~mm~-r~y fluxes of ~he 15 puls~rs with r~dio fluxes ~ 200 m J y ~nd b ~ 20 ~

listed by MANCHESTER ~nd TAVLO~ [32] (*). I t is clear f rom this gr~ph tha t

those puls~rs whose r~dio fluxes predict, in this model, ~ g~mm~-r~y flux

obse rwb le by the COS B exper iment in gener,fi produce ~ much lower flux

th~n expected, p robab ly less th~n 20 o//o of the expected flux.

We would thus conclude tha t , ~lthough young bright puls~rs Inlay contr ibute

15

lu. )

7 E

g A Lu

o

o. 5

t~ E E

-6

0 1.0 2.0 3.0 rc~c~io flux (Jy)

Fig. 3 . 6 . - Comparison between the radio (400~lltz) and gamma ( E > 100MeV) fluxes of puls~rs with ~ radioflux of 200 mJy or greater. Pulsars used are from the list of Manchester and Taylor [32]. Some of the pulsars between 200 and 400 mJy have been omitted but lie in the same region of the graph as the other in that flux range.

(*) The flux limits for gamma-ray~ are e.~timated using the background flux at the position of the pulsar and the fact that no point source has been reported consistent with that position.

Page 20: Discrete sources of cosmic gamma-rays

2 0 P. A. Ir and A. W. ~VOLF:ENDALE

significantly to the g a m m a - r a y luminosity, older pulsars do not cont r ibu te

more t han about 10~o of the to ta l g a m m a - r a y luminosi ty above 100 MeV.

The contr ibution of young, br ight pulsars will have been included in the es t imate

based on the 25 g a m m a - r a y sources in the second COS B catalogue discussed earlier.

4. - M o l e c u l a r c l o u d s a s d i scre te g a m m a - r a y s o u r c e s .

4"1. Speci]ic molecular-cloud sources. - I n the previous section an es t imate

of the contr ibut ion of discrete, i.e. starlike, sources to both the emissivi ty

locally and the to ta l galactic emissivi ty has been made. I n the in t roduct ion

it was pointed out tha t the main purpose of such an es t imate is in the context

of a s tudy of the distr ibution of cosmic rays in the Galaxy using gamma-

radiat ion as a probe. The point of the es t imate of the contr ibution of discrete

sources to the emissivi ty is t ha t it tells us how much of the flux can be at-

t r ibuted to such sources and how much to cosmic-ray interact ions with the

interstellar medium. The poor angular resolution of g a m m a - r a y telescopes complicates the problem still further, however. Because ~ source of angular

ex ten t less t han about 2 ~ would appear as a (( point )) source, it is not known

how m a n y of the sources in the COS B catalogue are t ru ly starlike and how

m a n y are due to small diffuse cnhancements of the flux. The vari '~bility of

some of the sources leaves no doubt as to their compact nature. Other sources will be diffuse, however. The 9-Ophiucus dark cloud, for example, is one such

source. PROTHEROE et al. [24] have presented arguments showing tha t the

bulk of the g a m m a - r a y flux in the vicini ty of 2CG078-~01 can be explained

as being a consequence of the interactions of cosmic rays with the gas in the cloud complexes of the Cygnus X regions. Fur thermore , I~IERMSEN, in his discussion of possible identifications for the g a m m a - r a y sources in the second COS B catalogue [13], points out t ha t the g a m m a - r a y intensi ty distr ibution

in the vicini ty of 2 C G 2 8 4 - 00 and 2 C G 2 8 8 - 00 resembles the dis tr ibut ion

of the radio cont inuum emission, which also m a y be t aken as an indication

of ~ diffuse product ion mechanism of the gamma-rays .

To invest igate the possibility t ha t molecular clouds appear as discrete

sources of gamma-rays , we have compared the g a m m a - r a y flux f rom several

massive clouds with t h a t expected on the basis of cosmic-ray interactions.

Most of our da ta have come f rom the survey b y BLITZ [47] and STARK and BLITZ [48], but to this has been added da ta on ~-Oph (cf. our recent work [22]) on Cygnus X [49] and on the galactic centre region [50]. The masses and dis- t .mces of the six clouds studied are plot ted in fig. 4.1, together with lines showing

the mass required to produce a flux of 10 -6 em -2 s -~ at the E a r t h under the

assumpt ion of various values for the emissivity. The local value (corresponding

to F ---- 1 on the graph) has been t aken to be q/4z (Ey > 100 MeV) = 2.2.

Page 21: Discrete sources of cosmic gamma-rays

D I S C R E T E SOURCiES OF COSMIC (~AMMA-RAYS 21

10 ~ G C 0

7 F = I / / / / lo

l o ~ [ / J , I , ~ I 10 -1 10 0 101

distance(kpc)

Fig. 4 . 1 . - .~[asscs and distances of the six molecular-cloud coinplexcs discussed in the text . The lines show the mass required to producc flux of l0 -6 cm 2s ~ at the Ear th under the assumption tha t the cosmic-ray intensi ty in the cloud is F times the local v~luc (taken as q/4u(E., :-- 100 McV) ~ 2.2.10-2c' s 1 (H atom) 1).

�9 10 -2G (H a tom) ' s -1 sr -1 a c c o r d i n g to our d e t a i l e d ana lys i s [22]. This va lue of q

shou ld be :~ppropr ia te for c louds w i t h i n a b o u t I k p c of t h e Sun, b u t f u r t h e r

af ie ld s igni f icant di f ferences m a y well occur due to c o s m i c - r a y g rad ien t s . As

m a y be seen f rom fig. 1.1, a t l eas t five of t he se c loud complexes shou ld be seen

in g a m m a - r a y s , if t i le g a m m a - r a y e m i s s i v i t y in t h e i r v i c i n i t y is c o m p a r a b l e

to t h e loca l v a l u e or la rger . The f lux of g a m m a - r a y s f r o m t h e 6 c loud com-

I)lexes ha~ been e s t i m a t e d us ing d a t a f rom t h e SAS 2 ~md COS B s~tcl l i tes .

The d~ t a f rom SAS 2 are t hose t a b u l a t e d b y FICHTEL et al. [37] a n d those f rom

COS B a re t h e f luxes g iven in t h e l a t e s t source ca t a logue [13, 16] t o g e t h e r

w i th t h e f lux con tou r s of M a y e r - t l a s s e l w a n d e r et al. [51].

W e shal l now discuss in de ta i l our f lux e s t i m a t e s for each of these c louds

a n d also t h e mass a n d d i s t ance es t i in~tes we h :we used.

~-Oph. The COS B ca t a logue quotes :t f lux of 1 . 1 - 1 0 - 6 c m -~ s - t for t h e

~-Oph source. The u p p e r l imi t on t i l e f lux e s t i m a t e d f rom t h e SAS 2 d a t a

is 0 .7-10 -6 cm J- s 1 (at t h e 1 s.d. level) , however . T h e COS B f lux is a c c u r a t e

to w i th in a b o u t 30(}~). W e havc , the re fo re , used :b f lux of 0 .75.10 -6 em--~ s -~

as an e s t i m a t e of t h e f lux a b o v e 100 MeV. The mass of t h e o-Oph c loud is

d i scussed in [22].

/ ' e r OB2. This c loud is s i t u a t e d in t he reg ion of l ~ 160 ~ a n d b ~ - - 1 7 ~

This r eg ion is ou t s ide t h e a rea covered b y the COS B co l l tour m a p a n d on t h e

edge of t h a t covered b y t h e source ca t :dogue , so t h a t our f lux e s t i m a t e is b a s e d

on t h e SAS 2 d a t a a lone. T h e f lux e s t i m a t e for t h e ene rgy r ange Ev > 100 MeV

is (1.4=]=0.7).10 s c i n - 2 s 1 while no m e a s u r a b l e f lux excess a b o v e t h e back -

Page 22: Discrete sources of cosmic gamma-rays

22 r . A. R I L E Y and A. W. "WOLFENDALE

ground appears for 35 < Ev < 100 MeV. STARK and BLITZ [48] give the dis-

tance to the cloud as 350 pc and its mass, based on CO observations, as 4.10 * M o.

Ori OB1. This complex is situated in the region l 202 ~ to 217 ~ b - - 1 4 ~

to -- 22 ~ once again outside the range of the COS B data used here. For this

cloud there is a measurable excess in both energy ranges, the fluxes

being (1 .710.8) .10 -6 cm-" s -1 (35 < Ey < 100 MeV) and (1.0=]=0.5).10 -6 cm-" s -1

(Ey > 100 MeV). STARK and BLITZ [48] quote the distance to Ori OB1 as

450 pc and its mass as 2 .105Mo. A COS B observation of the Orion complex

has recently been made. CARAVEO et al. [52] conclude tha t the flux from the

cloud is consistent with it having a mass of (1.2=L0.4).105Mo and being per-

meated by a cosmic-ray flux giving an emissivity of qy/4n =- (3.4 ~=0.5). �9 10 -~-G (H atom) -1 s -1 sr -1, with the assumption tha t the cloud is 500 pc distant.

This would correspond to q/4z ---- 2.5.10 -6 (H atom) -1 s -~ sr -~ using the mass

and distance estimates given by STAI~K and BI~ITZ, or 1.1 times the local value

of qvl4z assumed here.

M o n O B 1 . The cloud is situated at 1_~200 ~ , b_~2 ~ . There is no C O S B

source at this position, nor is a significant excess seen in the SAS 2 data. An

upper limit to the flux of ~ 1 . 1 0 -6 cm -~ s -~ for energies above 100MeV is

indicated. STARK and BLITZ [48] give the distance to Mort OB1 as 800 pc and

its mass as 1 .105Mo . Only an upper limit can be set on the emiss iv i ty- -a

value ~ 4 • the local value.

Cygnus X. - The cloud complex marked (( Cyg-X ~> in fig. 4.1 comprises many

clouds in the general direction of 1 ~ 80 ~ b ~ 0 ~ In an earlier paper [24] we

examined this region in some detail using COS B data (E v > 100 MeV) and

comparing the lati tude and longitude dependence of the flux with tha t expected

from cosmic-ray interactions with atomic and molecular hydrogen. The con-

tr ibution to the gas density from molecular hydrogen was taken from the survey

by CO~G [49] which gives almost complete coverage of the region 75 ~ < 1 < 85 ~

Ib] < 4 ~ The contribution from atomic hydrogen was obtained from the

digitized 21 cm data of Weaver and Williams (1973, private communication).

Examinat ion of the data shows tha t the source 2CG078-~01 can be explained

as being due to cosmic-ray interactions, if the y-ray emissivity of the gas clouds

is q/4u ~ 3.4.10 -26 (H atom) -1 s -1 sr -~, i.e. about 1.5 times the local value.

The flux front 2CG078~-01 is quoted by HERSmEN aS 2.5"10 -~ cm -2 s -~ [13].

With a mass of 106 M o and a distance of 1.3 kpe, the flux expected from it

using the local value of qy is 1.6.10 -6 cm -2 s -~. Thus, if the flux reported for

2CG078~01_ can be equated with tha t from the molecular-hydrogen complex,

the value of q in the Cygnus complex is estimated as being about 1.6 times

the local value, in agreement with our earlier work.

Galactic centre. There is much evidence for a ring of molecular clouds

round the galactic centre subtending an angle of radius _~ 1.5 ~ at the Sun

Page 23: Discrete sources of cosmic gamma-rays

DISCRETE SOURClgS OF COSMIC (~AMMA-RAYS 2 3

(e.g. see [53]). The mass is uncertain, bu t here we adopt the range (~--10).

�9 107 M o quoted b y SCOVlLLE et al. [50] and t rea t this as a conventional cloud

complex pene t ra ted b y the ambien t cosmic-ray flux (Mthough we are mindful

of the m a n y problems in this region the likelihood of genuine discrete sources,

excess radiat ion density causing enhanced inverse Conlpton emission, etc.).

The COS B source 2CG 3 5 9 - - 0 0 produces a flux of 1.8.10 -6 cm-~s ~ (E v >

> 100 MeV). I f this is identified with the flux f rom the ring of gas at the centre,

t hen the emissivity of the gas is (0.9~0.5) t imes the local vMue of qv"

10

F

10

Per" 0B2 @-Oph

h

Non OB1

T

10 -~ 10 ~ 101 dlstance(kpc)

GC

I

Fig. 4.2. - The cosmic-ray intensities required to produce the observed flux from the six molecular-cloud complexes discussed in the text. The intensity is shown relative to the local value: "< E,t(35-:-100) .Me\ r, o E v-> 100 MeV.

The value of q/4a has been calculated f rom the flux mass and distance est imates for each of the six clouds considered above and is p lot ted in fig. 4.2

as a funct ion of distance f rom the Sun. As can be seen f rom the figure, the emissivities required to explain the g a m m a - r a y flux f rom the clouds is con-

sistent with the local value to within a factor of 2, and this is regarded as a

sat isfactory feature. I t is worth noting t h a t all the nearby clouds which should

have been seen have been seen, and this suggests t ha t irradiated clouds form

a significant fract ion of the so-called sources.

4"2. Contribution lrom the molecular clouds in general. - Molecular clouds

are not a local feature, of course, and recent studies have shown tha t giant

clouds are the dominant component of the ISM, most of the molecular hydrogen being contMned in cloud complexes of average mass greater t han 10~Mo.

Giant-molecular-cloud complexes thus represent a class of objects which are

Page 24: Discrete sources of cosmic gamma-rays

2 ~ I ' , A. R I L E Y a n d A. 1V. W O L F E N D A L E

the most massive in the Galaxy (see, for example, [54] and other papers in the same volume). We have initiated a s tudy to investigate the amount

of s t ructure such clouds would produce in the gamma-ray flux from the Galaxy as a whole, and in part icular the number of apparent discrete sources tha t could be explained by them. The s tudy involves a Monte Carlo simu- lation of their distribution in the Galaxy from which a map of gamma-ray intensities is produced. The intensi ty map is then analysed for sources in the same way as the COS B data. ]0~ull details and results of this s tudy will be re- por ted at a later date. I ' rel iminary results indicate tha t the la t i tude and fhlx distribution of sources expected on the basis of the molecular-cloud hypothesis

are numerically consistent with the actual distributions, if the Gordon and

Bur ton mass estimates are correct. As mentioned later, we think it likely tha t

the GB densities are too high by a factor 2 and thus we arc led to believe tha t about 50 % of the discrete sources are irradiated clouds, the rest being pulsars,

SNR, extragalact ic objects, etc. I t is relevant to point out at this stage that , if genuine discrete sources were

found in regions of star formation quite frequently, then the nearby Orion region would be a likely place. However, as discussed, thc gamma-radia t ion from Orion is quite consistent with the cosmic-ray irradiation hypothesis alone.

5. - The radial variation of the galactic gamma-ray emissivity.

Our initial interest in the contribution of discrete sources to the gamma-ray luminosity of the Galaxy arose from the desire to use the gamma-ray data to determine the cosmic-ray distribution in the Galaxy. Since the distr ibution of discrete sources is not known and cannot be deduced from the data present ly available, f inn conclusions regarding the radial dependence of the cosmic-ray flux in the inner par t of the Galaxy still elude us. Making the reasonable as- sumption tha t discrete sources of gamma-rays are distr ibuted in the same way

as such young objects as SNR, however, we can obtained some indications as

to the variation of the flux. The first step is to derive the radial distribution of gamma-ray emissivity.

We have adopted the average from the (0--180) ~ longitude ranges for the

SAS I I da ta (E~. > (35--100) MeV and Ey > 100 MeV)) and the COS B data

(Ey > 70 MeV). The longitude range was chosen to approximate tha t for which

the molecular gas is known (albeit approximately) and the averaging has been im~de in order to improw; the statistical precision. Figure 5.1 shows this average emissivity distribution.

The derivation of cosmic-ray intensi ty requires data on the large-scale gas distribution in the ISM and here we have used the densities f rom the work of Blitz and Shu [42] ra ther t han from GORDON and BURTON, because of the allowance in the former work for a metall icity gradient in the Galaxy (this

Page 25: Discrete sources of cosmic gamma-rays

DISCRETE SOURCES oF C()S3II(3 GAMMA-RAYS 2,~

affeels the abundance ratio n((:O)/,~(l:l.,). The Blitz and Shu densities locally

(R_~ 10 kpe) are less than ha.lf the Gordon and Burton values. Some con-

firlnation comes from the formaldehyde results of Few et al. [55], which lead

to H2 densities simil,~r to those of Blitz and Shu.

6 , ; , ; ;

~4

r

I 1

~2

I I I

0 12 16

t

1

t [ L _ _ _ _ t t i i 4. 8

g,~lactocentP[c radius (kpc)

Fig. 5. l. -- 'I'll(; radial ([i81ribuLioll of gl)~llllllll-l'~lV emis~ivit,y in the Ga,la, xy. The distr ibu- t ion shown is the average of dis t r ibut ions der ived from the SA~q 2 d~ta ((aS -100) McV and > 1 0 0 M e g ) 'utd tim U()S H da ta ( > 7 0 M e V ) , using the longi tudimd range I (0 : 180) ~ in e~ch ease.

Figure 5.2 sho~vs the radial distribution of cosmic-ray intensity if we as-

sume that all the diserele sources are irradiated clouds. Figure 5.3 gives the

same quant i ty for the lnore reasonable :~ssumption that only 50 ~ of tile sources are irradiated elouds. To l a.ke out the genuine som'ees, we have a ss|||ned l haL

their radial distril)ul,ion is lhe same as lhat of SNt{ aeeor(iing to KODAIRA [35J;

here the SNI{ density peaks at R -- 5 kI)(' , where it is about 2.3 times the local

value. Such an assumption does not mean tha t SNR a, re definitely y-r:~y sources,

because ma,ny other likely objects (c.ff. gia, nt t11I regions) have similar radial distributions.

Figure 5.3 is probably the most reasonabh, radial distribution of cosmic-ray

llux at present, i t relates to the longitude range (0--180) ~ "rod corresi)onds

to y-rays largely in the range (35+250)MeV. The mixture of electrons and

protons responsible is probably ~ 6 0 : 4 0 .

The existence of gradients is elearly marked, I)~u'tieula, rly towa, rds the anti-

cent.re, where the assumptions involved are most likely to be valid. The low

value at R ~ 9 kI)e (slightly negative!) is striking; it is present in the emis-

sivity distribution :rod ])resuma, bly comes from long path lengths (at l "~ 65")

Page 26: Discrete sources of cosmic gamma-rays

2 6 P . A . R I L E Y a I l d A. ~V. "WOLFENDALE

12

PI_ e3

7~

~8

o

tlj

"6 4 Q 0 c)

"~_

x l 0 - 26

m

I++ +

i i I 8

ga to tc tocetc ic c a d f u s ( k p c )

I

16

Fig. 5.2. - The radial distribution of cosmic-ray intensity derived from the emissivity distribution of fig. 5.1 and the HI and l[ 2 densities of Gordon and Burton as moditied by BLITZ and SHtr [42]. I t has been assumed tlmt all discrete sources arc irradiated clouds.

t h r o u g h the i n t e r a r m region b e t w e e n the S~gittm.ius and Or ion armS. I t 'is

m o r e p r o n o u n c e d in t he eosmie- ray i n t ens i t y p lo t because of t h e s u b t r a c t i o n

of an ave rage discrete source flux a, l t hough this is eounterbM~meed to solne

12

I

7

'T

~ 8 _T_

n~ ,TZ. o 'Z LU "-~4-

ra -

03

0

i I

I I 4

-l++ 4-

I I

8 galczctocentric cadfus ( k p c )

I I

t 12 16

Fig. 5.3. - The radial distribution of cosmic-ray intensity derived in the same way as that shown in fig. 5.2, but under the assumption that only 50% of the discrete sources are irradiated clouds, the rest being starlike sources distributed in the same way a SNRs.

Page 27: Discrete sources of cosmic gamma-rays

I)ISCI~ET1~ S O I ~ I i C E S ()F (!I~S3IIC GAM3tA-R, AYS 27

extent by the fa,(.l t ha t we have divi(h,(l l)y l he averaged gas density. 11 is unlikely tha,t a more aeeurate l;re~tment would remove the min imum and this

too is to be regarded as providing fur ther evidence for an intensi ty gradient.

6 . - C o n c l u s i o n s .

The la, lesl c:~lalogue of a,pparenlly dism'ete gamma-ra, y sources produced

by the ( !OBB ('ollaboration contains ',)5 sources. ()m' calculations show tha t

the sour('es ( 'onlvibule (35~15)~ of lhe h)eal gamma-ra, y eulissivity of the Galaxy and, if they ave distrit)uled similarly lo young galactic obje, ets, a, simila, r

])roporlion of the tola.1 g a m m a - r a y lure|nosily of lhe Galaxy. Two of the COS B

sources have been |dent | t ied with compact objects (i.e. PSIr 0531 ~-21 and

PSI{ 0833- - 15), while el, bra's m~y be simila, l' lo the (~yg X-3 source detected

by the SAS '2 teles(!ol)e (e.g. 2('(} 135+01) . l'voba.bly about half of the sources,

however, are due to small but; tm~ssive (.louds o[' gas irradiated by the ambient

eosmic-ra, y ilux and the fv~mtion of the flux from gelmine diserele sources is

probably only a,1)out 20 ('' /O '

There ~l'e ~ nlllll|)el' of oth('l ' ~Ul~dyses ~v]|io|| h~ve 1)een l|l~([e reeently and ~vhi(,h add ~veighl 1o our ('on(.lusion tha t lit(' ( 'ontril)ution of .a'enuine (lis(q'ele

sere'cos is small. These ('a,u 1)e itemized as follows:

i) The long`iluale dist:vibulion of g'~m|n|:>ra, ys is slv(mgly eom'elal,ed ~vil, h

that, of the radi(~syn(,hroiv(m llux. Speciti('ally, the high-energy COS B tlux

(E v ;> 3110 MeV)uom'elates \ev3 well with lhe radio llux at .108 MHz (()SB()I~.NE

el a/.~ l|riva~le ( 'ommmli('alion) a.ft,ev lhe small identified peaks from discrete,

r~u|iosources have beell vemove([. Now it is well known thq, t the bulk of 1,he

synehrotron flux is not due to discrete sour( 'es- -but due 1 o smoothly dis tr ibuted

electrons moving in the g:da,(qie lna.gneli(' l i eh l - -and thus there is the strong suggestion lha t the 1)ulk of the ~a, mnm,-~'ay flux is also of ( 'ontinuum orig'in.

it) A i|lll||l)(q' of wol'k(q.s ha.v(, eXa, l|iilied I he eo|'vela, tiou of l he ga, n|ma-va, y ltux (modili(,d only I).v lhe subtva(,li|m of gam|na,-ra, ys from known dis('vete

objecls) with the cohmm dens|tics of g`as in a tomic ~md molecular form. Most recent is our own work [56J giving eviden('e for a loeal g`rt~dient in cosmic-ray

intensi ty which is close to tha t indiea,le|l ill rio.. 5.2. Now, although the 1)asie

g a m m a - r a y data are the same in the two a, nalyses ([561 and the present work),

the. t r ea tmen t of gas and geometry i s very different, i t is dill|cult to th ink

of a distr ibution of discrete sources whi('h wouhl allow the deriw~tion of similar

g'vadients.

ll, elm'nill- ' to lhe relevan('e of lhe gtmlma-vay resulls to the | l istribulion ' 1 of (:estate-ray intensity in the (,a a.xy there is still quite strong evidence (fig'. 5.3)

for gradients, such a.s wouhl vesull f rom a. g'alaetie origin for the mixtm'e of

electrons and nuclei resl)onsible fro' the bulk of the ltux.

Page 28: Discrete sources of cosmic gamma-rays

2~] P. A. RILI.;Y nnd A. W. V'7OLF]".NDAL]'~

RE FE RE NCE S

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Astron. Sot., 182, 751 (1978). [10] T. MONa'_~U,;I~L~: Astrophys. J., 231, 95 (1979). [11] (;. E. MORF~LI., H. J. VOLK, .~I. FOIgMAN, G. F. BI(;NAMI, P. A. CAltAVEO and

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