O N M E T A G A L A C T I C C O S M I C RA Y S

V.L. G I N Z B U R G

P.N. Lebedev Physical Institute, U.S.S.R. Academy of Sciences Moscow, U.S.S.R.

(Received 10 October, 1967)

Abstract. The simple argument is presented to show that the average energy density of cosmic rays in the Metagalaxy must be much smaIler than in the Galaxy. This conclusion could, in principle, be not valid in the Lema~tre cosmological model. The gamma-ray astronomical data now available testify, however, against the possibility of the cosmic-ray storage during the 'stop' phase of the Lema~tre model. The measurements of the diffuse background gamma-ray intensity with energy exceeding 10 MeV could definitely solve this problem.

A simple argument has come to light to support the view that the mean-energy density of cosmic rays in the Metagalaxy should be considerably lower than that in the Galaxy. This conclusion could, in principle, be shown to be invalid in the fi'amework of the cosmological model of Lemaitre. However, the observational evidence from gamma- ray astronomy already now argues against the possibility of storage of cosmic rays in the 'stop' stage of Lemaitre's model. A study of the intensity of the diffuse back- ground of gamma-rays with in excess of 10 MeV could answer this question conclus- ively.

In metagalactic models of the origin of the main component of cosmic rays found in the vicinity of the earth, it is practically inescapable that the energy density Wug of cosmic rays in metagalactic space (at least in the vicinity of the Galaxy) should be of the same order as the energy density of cosmic rays in the Galaxy - i.e.,

~VMg ~ W G ~ 3 x 10 -12 erg/cm 3 . (l)

This assertion has been previously considered more than once (cf. GINZBURG and SYROVATSEn, 1965, 1967a, b) and its reiteration is not remarkable. Let us only note that, in the preceding references, the value of W~ was as usual taken to be about 10-12 erg/cm 3. As a matter of fact, near the earth, at a period of solar minimum and for cosmic rays with kinetic energies EK >~ 100 MeV/nucleon, the value of Wc = 0.6 eV/cm a. However, there are reasons to believe that even at the time of a minimum the intensity of cosmic rays at a distance from the solar system is several times greater than that in the earth's neighbourhood, leading to an estimate of W c ~3 x 10 -12 erg/cm 3.

One of the basic arguments against the validity of relation (1) as an average for the whole metagalaxy (with a transformation to our time) as is accepted in the homo- geneous (universal) metagalactic model, is concerned with energy considerations. In what follows we shall present these considerations in a rather general and simple form.

The mean density of matter concentrated in galaxies, is considered (at our time) to

Astrophysics and Space Science 1 (1968) 125-128 ; �9 D. Reidel Publishing Company, Dordrecht- Holland.

126 V.L. GINZBURG

be p~ ~ 3-5 x 10- 31 g/cm 3 and Ea = pcc 2 ~ 4 x 10- lo erg/cln- 3, Equation (1) ob-

viously indicates that W~g~ 10 .2 Ea. However, such a relation is, generally speaking, highly improbable.

As a matter of fact, cosmic rays could not be accelerated in the early stages of metagalactic evolution because the proton-nuclear component with which we are concerned is strongly absorbed in a layer having a thickness of only 100 g/cm 2. Fur- thermore, the observed chemical composition of cosmic rays in all probability cor- responds to their passage through a thickness of the order of 3 g/cm 2. In this manner the presently observed cosmic rays could only have been accelerated at the very begin- ning of the formation of galaxies or somewhat earlier. Acceleration at such a time could occur in the process of the formation of proto-stars and also in the galactic nuclei and quasars. However, in the case of star formation, the gravitational energy is transformed as the average to a quantity of the order of (GM2/r)~ 10-4 to 10-5 Mc 2, where M represents the mass of the star and r its radius.

Furthermore, it seems scarcely possible for a large amount of energy to be converted into cosmic rays during such an event. Yet, from all the data, the efficiency of trans- formation of gravitational energy into the energy of cosmic rays ~ ~ 1. Even in a collapse (for realistic models of quasars see GINZBURG and OZERNOi, 1967; OZ~RNOI, 1966) ~< 10 -3. Similarly, it is evident that during the formation of stars, not more than 10 -7 of the rest mass can be converted into cosmic rays.

In the formation of galactic nuclei and quasars this coefficient ~ reaches 10-3, but in the nuclei and quasars themselves, in the framework of the ordinary evolutionary cosmological model not more than ( ~ 10-2-10 .3 of all the mass is transformed. In this way we conclude that no more than ~(pcc2~<10 -5 p c c 2 ~ 4 x 10 - i s erg/cm 3,

where the transformation of the density Pc to our time has already been carried out. However, if cosmic rays originated in the period of the formation of the galaxies,

that is at z>~ 2, then it is to be remarked also that the energy of the individual cosmic particle decreases by a factor of 1 +z>~3. In this manner, in our time WMg~< 10 -15 erg/cm 3. It is possible to come to this conclusion even from an analysis of the energy release in radio galaxies (GINZBURG and SYROVATSKIL 1966, 1967a, b ; SCHMIDT, 1967) where the neglect of the region z < l leads to an estimate of WMg~10 -16 or 10 -17 erg/cm 3. Some of the estimates introduced here are certainly quite crude, but they all lead to values of WMg at least three or four orders smaller than 3 x 10-12 erg/sec. In this way, the result of importance, that WMg ~ Wc is proved with a wide margin to spare.

The question arises, however (and this in particular prompted the author to write this article), whether the situation could not change in the cosmological model of LemaRre. The data relating to the red shift of the emission and absorption lines of quasars making this model attractive and, in any case, deserving consideration (cf. PETROSIAN, SALPETER, and SZEKERES, 1967; KARDASHEV, 1967).

In the model by Lemaitre which has been used, at z = 2 the metagalaxy has for practical purposes almost not expanded over a period of T~ = 5 • 10 ~~ years at the time of the formation of the majority of galaxies and evidently quasars as well.

ON METAGALACTIC COSMIC RAYS 127

Over such a long time-span the transformation of matter in galactic nuclei, quasars

and stars could, in principle, take place many times, the density of cosmic rays could grow* and the relation (1) would cease to look so improbable. This suggestion regard- ing succesive transformations of matter is admittedly unorthodox and seems rather implausible. Yet it is impossible to exclude it completely. It would be desirable to have a method of testing similar possibilities and, specifically, the possibility of storage of cosmic rays in the 's top' stage of expansion at z = 2 .

As a matter of fact, such a method is known, and consists of measuring the flux of y-rays resulting from the disintegration of zc ~ mesons generated by cosmic rays. The intensity of the resultant rays originating during the period of 's top' , observed at

present, should be represented by

I. e = 2anclMgcTc -- 3 x 10-2 IMg photons/cm2/sec/ster, (2)

where cr = 1.3 x 10-26 c m - 2 represents the 7r ~ meson interaction cross-section averaged

over the spectrum of cosmic rays (G~NzBtJRG and SYROVATSKIb 1964, p. 28). The coefficient 2 takes into account the formation of two photons at the disintegra-

tion of a zc ~ meson, and n c is the concentration of the gas at the period of ' s top ' ; the intensity of metagalactic rays IMg in (2) refers, on the other hand, to our time and in this way the effect of evolution is subtracted both for the photon and for the cosmic

rays. The disintegration of arc ~ meson gives rise to y-rays of energies Ev, o = 67.5 MeV. I f they originate at z=1.95, then for the photons received at the earth, Ev=Ev ,o /

(1 + z ) = 2 3 MeV. I f we take into account the widening of the energy spectra brought about by the movement of 7r ~ mesons, we conclude that it is the intensity Iv(> Ev) of photons with energies exceeding about 10 MeV which should be of interest to us.

Unfortunately, the measurements (cf. KRAUSHAAR, CLARK, and GARMIRE, 1.967) refer to photons of E v/> 50 MeV, where Iv(> Ev) ~< 10- 4 photons/cmE/sec/ster. Accord- ing to a number of calculations (FELTON and MORRISON, 1966; DUTHIE, 1967) it is possible to take I.r 10 MeV)~< 10 -3. However, a considerable contribution to this intensity could be due to photons resulting from electron scattering on the optical thermal radiation. For this reason it seems probable that the full intensity of y-rays originating from the disintegration of rc ~ mesons at z = 2 does not exceed I v = 3 x 10-4.

From this, and in accordance with Equation (2), IMg ~< 10 .2 particles/cm2/sec/ster.

This value must be compared to the intensity Ic---0.3 used by GINZBURG and SYROVATSKn (1964) and in fact in (2). In this manner it seems now possible to advance a suggestion that the intensity of cosmic rays of primordial origin in the neighbourhood of the Galaxy is, even from the Lemaltre cosmological model, at least an order of magnitude smaller than the galactic intensity. This conclusion requires, however, some further examination and scrutiny.

A conclusive solution of this question clearly lies within the capabilities of y-ray astronomy, even in its present stage of development. To this end it is necessary to find

* In keeping with the period of 'stop', which is of the order of 5 • 101~ years (KARDASHEV, 1967), the mean density of matter pc -~ 5 • 10 -19 g/cmL For this reason, for the time Te, a relativistic cosmic ray passes through a thickness of only cp~T~ ~ 1 g/cmL

128 v.L. GINZBURG

the upper limit of the intensity of y-rays from the disintegration of n o mesons at z = 2.

The appropriate measurements would be quite useful - even if we take into account

the fact that, even in Lemaitre 's model, the t ransformat ion of cosmic rays of a quan-

tity of energy WMg at taining a percentage of the value of pG c2 seems to us - we wish

to stress again - to be quite unlikely.

Acknowledgment

The author is indebted to Dr. L. M. Ozernoi and Dr. S. I. Syrovatskii for discussions

of this question.

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References

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