Adv. Space Res. Vol.3, No.10-12, pp.477-480, 1984 0273-1177/84 $0.00 + .50 Printed in Great Britain. All rights reserved. Copyright ©COSPAR

ON A N O N - P R I M O R D I A L ORIGIN OF THE COSMIC B A C K G R O U N D R A D I A T I O N A N D P R E G A L A C T I C D E N S I T Y F L U C T U A T I O N S

H.-E. Fr6hlich, V. Miiller and H. Oleak

Zentralinstitut far Astrophysik, Potsdam-Babelsberg, G.D.R.

ABSTRACT

Dusty pregalactic Population III objects may provide a mechanism for an effective thermalization of the star radiation. They may generate the observed microwave background and so the high cosmic photon entropy. &ssuming a tepid universe a smaller primordial entropy con- tribution results in reasonable mass scales and amplification factors of pregalactic density fluctuations.

KEYWORD8

Cosmic background radiation; Population III objects; intergalactic dust; galaxy formation; cosmology.

I~[TERCALACTIC DUST DXTINCTION

It is well known that sometimes astronomers were made a fool of by dust grains in the interstellar space and had therefore to revise their ideas about the structure of the Galaxy. U~%y should not inter- galactic dust play the same "game" with us with respect to our ideas on the structure of ¢le universe as a whole? To get an insight we will first present an estimate about the optical depth provided possibly by intergalactic dust. If one assumes that tile mass fraction of dust has the same order of magnitude like the_ fraction Z of the heavy elements in metalspoor stars (i.e Z ~ 10 -5 ) and considers du~;t ~rain~ of size, ~ • 10- cm, than on the average such a dust will lead to an optical depth ~ I in the visual wavelength at a redshift z = 4 (This holds in the Einstein-de Sitter universe. For an universe with qo = 0.I, the optical depth 1 is reached for z = 7.) The mean mass density of the dust component will be still as low as 5.10 -~s gcm -3 . Chiao and Wickramasinghe (1972), Oleak and Scluuidt (!976) already ascribed the quasar cut-off to an intergalactic extinction by dust grains. ~he lacking of quasars in the redshift range 3.7 L z ~ 4~7 according to the search by Osmer (1982) points to the same interpretation. Also the fruitless search for primeval galaxies may be explained in this way.

EHERO'.': COITSI DERATIOI,IS

If the sky will become opaque at some redshift (say below z ~ 10) the radiation of more distant objects will be thermalized at least at optical and shorter wavelengths° Rowan-Robinson, Negroponte and Silk (1979) suggested that thermal radiation of dust may contribute partly to tile cosmic background radiation (CBR). Shortly after the detection of the CBR some authors discussed the possibility that the CBR might be fully explained by tn~rmalmzed star radiation (see Rees 1978 aid papers cited therein)° The reason is the following one: It seems convincing that the present ener~J density of the CBR rough- ly equals the ener~j delivered during the formation of the present

477

478 H.-E. Frohlich, V. Muller and H. Oleak

cosmic abundance of the heavy elements. By considering the different redshift dependences of the radiation energy density ~(1+z) * and matter density ~(1+z) ~ Carr (1981) estimated the epoch when the CBR could have been generated. Assuming an efficiency of 0.007 for conversion of matte] in energy he found z ~ 70 or t ~ 2.10 years for qo = 0.5. (This age corresponds to the lifetime of a 30 ~-star of pure hydrogen.) On the other hand, the production of metals provides the basis for the origin of the dust which can thereupon thermalize this radiation of the first generation stars.

MECHAN!SM FOR THE THERNALIZATION AT CM WAVELENGTHS

In all up to now proposed hypotheses where the CBR is assumed to originate from stellar radiation the problem of thermalization enters difficulties at longer wavelengths (see for instance Negroponte, Rowan-Robinson and Silk (1981) t Hayakawa (1983)) because dust is ineffective there. Also free-free scattering in a hot gas considered by Cart (1981) is too ineffective up to red- shifts z ~ 70. For this he discusses a possible generation of the CBR by more efficient energy sources (massive black holes) in earlier times. The mentioned difficulty could be weakened in the following way: If there was enough dust concentrated around the sources of the CBR themselves the stellar radiation could be already thermalized at the place of its origin. Suppose the universe was filled at some z with opaque dust clouds embedding the primary energy sources of the CBR. A complete covering of the sky already at non-cosmological distances requires

r2~o(~÷~)3 ~ 4/~M , where r and n o are the radius and the

(present) number density of thesuccessor objects, ~ stands for the then horizon distance (~ (1+z) -~ in the Einstein-de Sitter case). To fulfil the inequality under the additional condition of a sur- face temperature of the dust spheres of 2.7-(I+z) K the mass-to- light ratio M/L (in solar units) has to be smaller than

)- ~/2..0. , I,[/L < 14.2.(I+z • where A~ denotes the mass fraction in units

of the critical cosmological density of such objects. In case that primeval galaxies be the sources of the CBR the required mass-to- light ratios are far too low, despite the fact that the large infrared output of some active galaxies (i.e. Seyfert's) demonstrates how efficient the thermalization inside galaxies works. ~assive Population III stars in an opaque environment are more reasonable for their higher luminosities. For an example, taking M/L = 10 -~ we get z ~125 for X~= 0.01. Moreover dusty stars at such large distances offer the advantage that to observe a thermalized radiation at, say, 10 om wavelength only thermalization up to I mm is needed at the place of origin. The required optical depths are drastically reduced: from Zv~10 ~ in the case of uniformly distri- buted dust to merely 10 ° in the case of a clumpy distribution. (Such a high optical depth is not by far unreasonable as a compa- rison with compact HII regions shows, which are sometimes strong farinfrared emitters.) Free-free transitions could further raise the optical depth, especially in the long wavelength region. As scattering acts like a random walk process the path length of the photons in the dusty environment increases raising the dust extinction. The factor the dust extinction has to be multiplied is just the optical depth caused by free-free transitions.

A TEPID EARLY ~IIVERSE

Summarizing the preceding point it seems that at least a large part of the CBR can be due to thermalized star radiation. The resulting cold universe had some advantage for the theories of galaxy formation (see for instance Cart (1977) and references there). Bu0 a really cold big bang seems to be u:~natu~al because of many entropy generating processes in the very early universe° ~nerefore we believe th%t in the CBR ti~ere is still a primordial blackbody component leading to a tepid universe (Carr and Rees, 1977), One has strong restrictions from the primordi~.! nucleo-

Non-Primordial Origin of C.B.R. 479

synthesis for the value of its present temperature T O . To< 0.3 K has to be excluded to obtain not too much helium (Y ~ 0.3) (Olive and co-workers, 1981, Gautier and ~ven, 1983). The observed Deuterium and Lithium abundances could provide even stronger constraints. But even a temperature of the relict radiation lowered to, say,

0.3 K has interesting consequences for mass scales and ampli- fication factors of density perturbations. First, the recombination era (z~) is shifted to the past, 1+z~ = 3000/To, second, the transition from the radiation universe to the matter universe (z T ) lies far in the past before the re- combination:

2 ~ ' ~ c ~ % (1+z ) 1 + z T = ~ ~ = 400 - T~ ~ "

~SS SCALES AND AMPLIFICATION FACTORS OF DENSITY PERTURBATIONS

The Jeans mass as the critical mass for gravitational instabili- ties

~ c~" ~/2 M~ = 3

just before recombination depends only on the specific entropy s = 0.37. n¥/n B

M~ = 9.1.s2.(I + 2.8 • I0-4°s~3 l~o~ 9.s~ ~'~e

(the last equation holds for To~ 1K) and thus is lowered in a tepid universe to masses 10~*... 10~5~,~ o comparable with clusters of galaxies (see Fig.). These values are smaller by some order of magnitude than the mass within the horizon. The Jeans mass just after recombination is proportional to ~and therefore remains at I0S...I0 ~ M® kno~ from the standard model. Density perturbations below the Jeans mass behave as sound waves within the plasma. They are strongly damped at short wavelengths because of the finite free mean path of photons (Silk, 1968). This critical mass scale also depends slightly on s and is given by ~D = 3.103 s ~/* M®

~or lower s-values it comes into the range of normal galaxies. The smaller Jeans- and Silk-masses just before recombination give reasonable upper and lower limits of surviving sound modes being possibly produced within the plasma era. Additional entropy per- turbations would become ~ravitationally instable after recombina- tion with mass scales 10 ~ ... 10 W If® . They may trigger the generation of a pregalactic population II!.

~0 ~

fO s

"--........~# qo-o.s

I.

2.7 1 ro(~:)

qo .o.o s

0.3 0.1 2.7 ~ 0.3 Of to(KS

Mc/usters of Go/oxies

MOo/oxms

MG/obu/or s/or c/us/ers

Fi~j° Critical mass scales at de coupling : Horizon, Jeans and damping mass. In the shaded mass region adiabatic sound waves surive.

a~O H.-E. Frohlich, V. Muiler and H. Oleak

If one takes as a necessary condition that small fluctuations have to reach at present ~@/~ ~ I in order to describe the ob- served mass inhomogeneities, strong restrictions result for their values at the epoch when they originated. In the Einstein-de Sittez universe we have

~/~ ~ t2~(1+z) -~ ,

which demands initial values at recombination between I0-3... 10 -~ (for To = 2.7 ... 0.3 X). For smaller qo -values the pertur- bations c~ase to srow at z ~I/5 qo • ~hus higher initial ampli- tudes I0-~... 10 -° are required. But small scale fluctuations are not observable in the CBR for a tepid universe because it is mainly generated by physical processes considered above. For T o = 0.3 k and qo = 0.5 density fluctuationo of I~_ 10 are even larger than the Jeans mass before decoupling. The density contrast can grow up after entering the horizon when it had to be only 2.5 .10 -~. If on the other hand a cluster of 10~ would be build up from elements of the Silk mass just after decoupling (10 ~ I~), the corresponding statistical fluctuations would become large already for z ~ 10 (and even for all q~ 0.01). In the case of a lower primordial photon entropy smaller initial fluctuations are sufficient to explain the observed imhomogeneities on large scales th~ in the conventional picture of the universe.

REF~ ~JC.~o

Cart, B.J. (1977)o Astron. Astrophys,, 60, 13-26~ Cart, B. Jo, and ~!.J. Rees (1977)~ Astron. Astropl\ys.q 61, 7@5-709. Car r, B.J. (1981). !,~on. Not, R, astr~ Soc.~ 195, 669-684. Chiao, R.Y., and )ToC. Ufickramasinghe (1972). l lon. l~ot. Ro astr.

Soc., 159, 361-373o Gautier, D., and T. (~en (1983)~ iTature~ 302, 215-218. Hayakawa, S. (1983). These proceedings° i,Tegroponte 9 J., PJ. Rowan-Robinson, and J° Silk (1981). Ap.J.~ 248~

38-46° Oleak, H., and X.-H. Schmidt (1976)o Lstroi~o i~achro, 297, 71-76. Olive, i(.&0, D01T. .Schramm, G~ Steigman, I{.So ~armer, and Jo ~-~.n<~

(1981),, Ap.J., 246, 557-568° Osmer, P.S~ (1982)o {p. Jo, 25~, 28-37~ P~ees, i[.J~ (!978). ~Tature, 275, 35-]7~ Rowan-Robi~son, P~., J. ITegroponte, and J. Silk (1979).

ITature, 281 635-638. Silk, J. (196SI. '~p.J.,j521, 459-471o