LETTERE AL NUOV0 CIMENT0 VOL. 5, N. 16 16 Dicembre 1972

Unorthodox Ideas Concerning the Origin of Cosmic Radiation.

K. SITT~

Department o/ Physics, University o/ Freiburg . Freiburg i. Br. Laboratorio di Cosmo-Geo/isiea del C.2f.R. - Torino

(ricevuto il 24 0 t toh re 1972)

When pulsars were discovered a few years ago, hopes rose high tha t the s tudy of these strange objects would also provide the solution to the puzzle of cosmic-ray origin. Their huge kinetic energy of rotat ion, shed in the form of electromagnetic-dipole ra- diation, suffices to replenish to the 1041 erg/s of escape losses of cosmic-ray energy. Moreover, i t seemed for a while tha t since under favourable conditions part icle energies around 10 ~0 eV could be a t ta ined b y pulsar acceleration, extragalactic sources need not be involved even to account for the most energetic EAS primaries. Acceleration by pulsar fields appeared to be uniquely and completely responsible for the presence of cosmic rays.

La te r developments cast doubts on these comprehensive claims. The absence of an appreciable anisotropy in the arr ival directions of EAS primaries at energies above I0 ~7 eV suggests either extragalact ic origin, or dominance of heavy nuclei (~.2). Equally, a t tempts to establish a correlation between EAS arr ival directions and pulsar positions have not been convincingly successful. While SUGA (8) repor ted positive evidence, OSBORNV- and WOT.F~NDAL~ (4) concluded from their analysis of a larger body of da ta tha t no significant correlation exists. Thus the claim for uniqueness of the pulsar sources must be abandoned.

In addit ion, also the claim for completeness cannot be upheld against objections which apply independent ly of the specific acceleration features. They were first discus- sed in a different context (5), bu t are most easily summarized in relation to a recent paper of 0STRIKER and GUNN (s). There they consider the processes by which the grav- i ta t ional collapse of the core which produces a pulsar can lead to a supernova (SN) explosion. This is ascribed to the fact t ha t the electromagnetic-dipole radiat ion which sets in immediate ly with the collapse is absorbed by the still inward falling envelope material . Thus the fall is arrested, and reversed into expulsion of the $1~ shell. In the case of the Crab, for instance, the kinetic energy of the ejected shell amounts to about 104Serg. Considerably more than t ha t must have been absorbed by the envelope

(x) S. KARAKULA, J. L. OSBORNE, "E~. ROBERTS and W. TKACZYK: Journ. Phys., A S , 904 (1972). (3) J . L . OSBORNE, E. BOBERTS and A. W. WOLFENDALE: I I I European SYmposium on Cosmic Rays (Paris , 1972). (') K. SuaA: INS R e p o r t No. 188, Un ive r s i ty of Tokyo (1972). (4) J . L . OSBORNE and A. W. WOLFENDALE : in 3rd European gymposium on Cosmic Rays (Par i s , 1972). (5) K. SITTE: Nuovo Cimento, 7 B, 110 (1972); K. SITTE, L. BRIATORE and M. DARDO: NUOVO Cimento, 10 B, 498 (1972). (e) J. P. OSTRIKER and J . E. GUNN: Asirophys. Journ., 164, L 95 (1971).

1033

1034 K. SITTE

init ial ly, since radiat ion and adiabat ic losses will have taken their share. I t is irrele- vant whether par t of the dipole radia t ion has been used to accelerate charged particles. A spherical shell of mass M 8, expanding with a velocity v, remains pract ical ly opaque to relat ivist ic part icles for a t ime Ta:

(1) T a ~ (3MJ4~rAv2)�89 ,

where A is the a t tenuat ion mean free pa th of the particles, about 100 g/cm ~ for protons. Using the conservative values M~ = 0.1M 0 and v = 790 km/s (the init ial velocity esti- ma ted for the Crab Nebula), one has To ~0.88.107 s ~100 d. Only after tha t t ime pulsar can become an effective producer of cosmic rays.

But par t ic le acceleration by pulsar fields up to energies around 1030 eV is possible only in the very earliest phase immediate ly after the collapse, if a t all. A t t > Ta the maximum energy still a t ta inable will be lower by about two orders of magnitude. Hence, even if the pulsar mechanism can provide particles of the highest energies found in cosmic radiat ion, pulsars stil l cannot be the source of t ha t component. Quite apar t from the anisotropy argument we are led to demand another source for the ul tra- energetic EAS primaries, and to abandon the uniqueness claim of the pulsar theory.

l~oreover, during tha t period of absorption the pulsar has already emit ted the larger pa r t of the energy given to the dipole radiat ion. Fo r the model adopted by GUNN and OSTRIK~.R (7), and applying their approximate solution for the t ime dependence of the angular velocity,

(2) co ~-- co0.(1 + t / T a ) ~ , Tg ~ 0.16 d ,

one finds t ha t Iess than 40% of the part icles accelerated by the dipole radiat ion can emerge from a shell with a mass and velocity as l isted above. The correct fraction is l ike ly to be much smaller since the approximat ion used tends to underest imate the emission in the early phase, and the parameters used tend to underest imate the dura- t ion of the phase of absorption.

In short, the conclusion is t ha t by whatever mechanism and with whatever efficiency t h e dipole radia t ion energy is t ransferred to relativist ic particles, most of i t ends up as kinetic energy of the $I~ shell, and only a small fraction contributes to the inter- stel lar cosmic radiat ion. Tha t leaves i t very doubtful whether this fraction can still satisfy the energy balance requirement. More l ikely cosmic-ray production by pulsars falls short of t ha t requirement, and other sources must supplement it. Hence the claim for completeness of pulsar origin appears untenable as well. Certainly we must look for extragalact ic sources to account for the most energetic primaries, and probably we must look for addi t ional or a l ternat ive sources also for the low-energy component.

In a renewed search for possible sources one is well advised not to dismiss offhand unconventional views on cosmic-ray origin. Here we shall briefly examine two of them: the assumption of extragalact ic origin of the entire cosmic radiat ion, and the ~ cosmic- r ay big bang ~) theory.

Extragalac t ic origin of the bulk of cosmic radiat ion is usually discounted for two reasons. Firs t ly , i t is argued tha t a ~ universal ~) radiat ion with an energy density around 1 eV/cm a as found in the Galaxy would comprise an unduly large fraction of the total rest energy of the Universe, and no process can be envisaged b y which t ha t much could be transferred to energetic particles. Secondly, experimental evidence shows tha t the densi ty of intergalact ic electrons is lower by two or three orders of magni tude than tha t

(~) J . E . G u ~ and J. P. OSTRIKER: Phys. Rev. Left., 22, 728 (1969); Acta Phys. Hung. 8uppL, 29, 69 (1970).

U N O R T H O D O X I D E A S C O N C E R N I N G T H E O R I G I N O F C O S M I C R A D I A T I O N 1 0 ~ 5

established for galactic electrons. Since i t is unl ikely t ha t the rat io between the nu- cleonic and the electronic components is drast ical ly different in galaxies and in recta- galactic space, a similarly lower to ta l intergalactic cosmic-radiation densi ty is indicated.

But these arguments are not well grounded. Le t us suppose, for the moment, t ha t cosmic-ray part icles do emerge from some extragalact ic sources, and propagate through intergalact ic space, filling i t to a densi ty 0m- If these part icles reach the halo of a galaxy, their previous pract ical ly undefleeted motion becomes diffusive, their propagation slowed down by scattering collisions, and their density augmented by accumulation. Consider, for simplicity, a spherical halo of radius Rh in which the particles diffuse for a t ime T h. Then the s teady-state condition gives us an ~( init ial ,) halo density

(3) 0 Q~ = e.," ( 3 / 8 . ) . (cTJRh).

Note tha t if Rh ~ 15 kpe, T h ~ 108 y, 0~/~ ~ 250, a very substantial increase. Bu t comparison must be made between qm and the disk density 0d of cosmic rays

which will differ from Q~ because halo part icles cannot freely enter the disk. Unlike the halo, the disk has a magnetic field H~ which is essentially regular, with its lines of force more or less paral lel to the equatorial plane. Assume tha t the orderly field is broken up by irregulari t ies of mean dimension ro in average distances 20, and tha t the disk is a cyl inder of radius Rh and height Z o. Halo part icles entering its upper or lower surface will be reflected by the disk field unless they chance to strike an irregular- i ty. This gives them (at low part icle energies) an ent ry probabi l i ty p, of the order

(4) p~ ~ ro/Ao,

and taking the halo flux as source for an (~ ini t ial ,> disk flux 0 ~ yields from the equi- l ibr ium condition

(5) o 0a ----- e ~ (Pd4n) "(cTa/Zo),

0 0 where T is the disk lifetime. I t is seen tha t , if Ta is of the order of l0 s y, Qa/~h>> 1, which shows tha t certainly extragalact ic origin is compatible with a metagalactic energy densi ty smaller than its galactic equivalent by several orders of magnitude. More specifically, a res t r ic ted-random-walk model (8) would give

(6) Td ~ (Zo/ro) ~" (~olc)

so tha t (5) leads to

0 0 (7) ~/0h ~ Zo/4~ro >> 1 .

(We have used the notat ion 0 ~ and 0 ~ because the proper equilibrium densities 0h and 0~ will differ from them. Especial ly 0h will be bui l t up by part icles leaving the disk, and a small re-entrant halo flux will replenish ~o. The full expressions need not be given here explicit ly since the change in Qa is obviously not significant (p, << 1 !), and therefore a t any ra te Oa/qm>> 1.)

In order to show tha t the assumption of extragalact ic origin is not in conflict with empirical facts, we still have to examine its predictions concerning the (~ a g e , of cosmic- ray particles. Recall, here, t ha t there are two ways to define this quant i ty (9). On the

(8) K. SITTE: Left. Nuovo Cimonto, $, 483 (1972). ( ' ) M.M. SHAPIRO,* Rapporteur paper, Proceedings o/the X I I International Conference on CosmicRays (Hobart, 1971).

1036 K. SITT]~

one hand, the well-known estimates Th ~ 10Sy and T~ ~ 10Sy merely imply tha t the particles must have t ravel led for those periods in one or the other of the galactic regions. Their proper basis is the evidence derived from the composition analysis, t ha t on the average the part icles have t raversed not more than about 5 g/era ~" of mat ter . On the other hand a direct l ifetime measurement by (~ radioact ive clocking ~ is possible - - u p to a point. I t s result is the t ime of flight of a secondary nucleus like xoBe which originated in the Galaxy wherever the primordial radiat ion came from. Hence this measurement brings us reliable information about the mode of galactic propagat ion - - d o m i n a n t residence in disk or h a l o - - b u t no conclusive evidence on the source region. F o r the amount of ma t te r t raversed in intergalact ic space is cer ta inly small even during a (~ universal )~ cosmic-ray lifetime T H ~ 1 /H ( H = Hubble constant) , and the number n of (~ collisions ~ of a cosmic-ray part icle wi th a ga laxy

(8) n = 2 ~ q . A a . c T "

( ~ d q ~ 2 ~B h -~ (~ cross-section ,~, N a = ~ concentration ~ of galaxies) is also small compared with unity. On the average, part icles incident on the Ear thwi l l not havepassed through another ga laxy before, and the pa th length given by the composition analysis refers to the diffusion of the part icles in our Galaxy.

Radioact ive clocking m ay give a decisive argument against extragalact ic origin if a short l ifetime indicat ing strong dominance of disk propagat ion is affirmed. Fo r extragalact ic origin this would imply ei ther the absence of a halo, or the existence of condit ions in the halo which permit a very fast diffusion. But in the absence of a halo the disk, reflecting extragalact ic primaries, would fill up only to a densi ty

(9) Qa = era" (Pd4z) "(eTdlZo),

probably not sufficiently in excess of the metagalaetie density. Similarly a very short T~ in an existent halo would not allow a sufficient bui ldup there, as (3) shows. A t present , though, the (~ clocking ,~ da ta do not seem to demand this conclusion. Therefore we have no compelling reasons to rule out a pr ior i all theories of extragalact ic origin for the bulk of cosmic radiat ion, not only for i ts ultra-energetic component.

One meets a similar si tuation on re-examinat ion of the (~ cosmic-ray big bang ,~ theory, proposed a few years ago b y W~BB~R (10), and b y DURGAPRASAD (~1), and all bu t abandoned in the meantime. This theory assumed tha t all cosmic-ray particles were accelerated to their present energies in one single, catastrophic act, perhaps an explosion in the galactic centre which also formed the halo. (The possibil i ty of such catastrophes was investigated, for instance, by BURBIDGE and I-IoYL]~ (1~-).)

The main advantage of the ~( big bang ~ theory is tha t i t yields quite na tura l ly a shorter pa th length for nonrelativist ic than for more energetic part icles: v T instead of cT , if T is the t ime elapsed since the (~ bang ,. Tha t would improve the agreement between calculated and observed low-energy compositions (s.~x). The difficulties of the theory come from the observations on cosmic-ray-induced radioactivit ies, especially in meteorites, which have demonstra ted constancy within a factor of about 2 of the in tensi ty of cosmic radiat ion over a period of the order of 109y (e.g. (13,~4).) This places

(1o) W. R. WEBBER'. Bull. Am. Phys., Soe., 12, 591 (1967). (11) N. DUR(]APRASAD: Journ. Geophys. Res., 72, 965 (1967). (la) G. R. BURBIDGE and F. HObbLE: .Astro~hys. Journ., 138, 57 (1963). (1*) j . GEISS" Proceedings of the V I I I InJernati(mal Con]erence on Cosmic Rays, Vol. 3 (Jaipur, 1963), p. 434. (~,) M. H o ~ A and J. R. ARNOLD: ttan~buch der Physik, Vol. 46[2 (Heidelberg, Berlin, 1965).

U N O R T H O D O X IDEAS CONCERNING THE ORIGIN OF COSMIC R A D I A T I O N 1037

the (~ big bang ~) at a t ime at least 109 y ago, and imposes two demands: firstly, the ab- sence of appreciable leakage from the Galaxy, i.e. a near-perfect t rapping mechanism, and, secondly, a propagat ion mode allowing the part icles to spend most of their t ime in some outer regions of low gas densi ty so tha t not more than 5 g/cm 2 are t raversed even in 109 years. Both are hard to realize.

However, they are also necessary only if since the (( big bang ~ the conditions in ~he Galaxy have remained unchanged. A halo ejected in an explosion and now shrink- ing under gravi ta t ional a t t ract ion ((~ falling back ~)) can lose part icles by escape, and still maintain a constant cosmic-ray densi ty in the disk. For in this model the disk has no sources of i ts own. I t is supplied b y the halo flux a t a ra te of p~. (c/4g)- ~a. (~/~) part icles per second, just as in the case of extragalact ic origin. Thus a constant q~ implies constant density ~a in the boundary region, bu t not a constant number of cosmic- r ay part icles in a contract ing halo.

An exact quant i ta t ive t r ea tment of the model, though feasible in principle, would serve l i t t le purpose because of the uncer ta in ty of v i r tua l ly all par t iculars concerning the (( big bang ~). But a few more general and semi-quant i ta t ive s ta tements can be made:

i) Le t the contract ion of the halo be described b y a characterist ic t ime T~, and the escape of cosmic-ray part icles from the halo by Th (which may still be a func- t ion of the t ime t). Near-constancy of the cosmic-ray density then requires T o ~ 3<Ta>.

ii) In all l ikelihood To ~ 109 y must hold if escape is permit ted. The t ime scale est imated by BU~BIDGE and HOYL]~ (x2) of is the order of a few 10Sy. Their value might have to be increased sl ightly if the effect of the magnetic fields is taken into account.

iii) W i t h regard to the t ime dependence of T h no safe predict ion can be made. I f we assume, merely for i l lustration, t ha t the diffusive motion in the halo is due to scat- tering by (( eentres ~ whose number remains fixed throughout the contraction, one has

(lo) Th(t) = rh (o) .R~( t ) /R~(O)

in obvious notat ion. Thus a present value of ~ l0 s y appears easily compatible with ii).

iv) The (( slab thickness ~ xh t raversed in the halo,

T

(II) xh = c" i'~h(t)dt = <~h>-cT

o

(T s tands again for the t ime elapsed since the (( big bang )), and ~h for the gas density in the halo) may well be less than x0= ~o'cT~ = 5 g/cm ~ if the contraction does not set in too rapidly. Hence a sizable fraction of the (~ slab thickness ~) Xo remains for the motion in the disk; T~ can still be of the order of 10 c y, and the normal models of disk propagation can be applied. The relat ive contributions of halo and disk to the fragmentat ion are essentially given by (~h/~a).(T~/T~), and again radioact ive clocking with lOBe could establish whether the (~ cosmic-ray big bang ,~ theory is tenable. A very short l ifetime would demand a small halo contribution, t ha t is, a small T~ possibly conflicting with our s ta tements i) to iii).

However, a t this stage our re-examinat ion indicates tha t nei ther the assumption of extragalact ic origin of the entire cosmic radiat ion, nor tha t of a (~ cosmic-ray big bang )), can be considered as definitely disqualified. This remark must not be taken as an uncondit ional defencc of those unorthodox theories. I t is merely a reminder that , unless disproved by new arguments, they should not rest forgotten.