T H E Z E L ' D O V I C H E F F E C T AND T H E I N T E R G A L A C T I C

D U S T IN G A L A X Y C L U S T E R S

S. AIELLO Cattedra di Fisica dello Spazio, University of Florence, Italy

F. MELCHIORRI and F. MENCARAGLIA* Infrared Group of lROE-CNR, Florence, ltaly

(Received 3 August, 1977)

Abstract. The observations of the Zel'dovich effect in galaxy clusters are reviewed. The failure to detect the effect at short wavelengths is interpreted as proof of the existence of intergalactic dust. Small and fast spinning grains can emit the power needed to compensate the decrease in tempera- ture expected from the Zel'dovich effect.

1. Introduction

In the framework of the standard hot Big Bang model the cosmic background radia- tion has maintained its Planckian character from the decoupling era up to now. However, many authors have discussed in the past the possibility of significant distortions in the cosmic background spectrum arising from various causes:

(a) emission of photons at the time of decoupling (Zel'dovich and Sunyaev, 1968; Peebles, 1968);

(b) slow recombination rate for primordial plasma (Aldovrandi and D'Olival, 1968); (c) injection of energy by perturbations during the plasma era (Sunyaev, 1974); (d) interaction with hot gases after recombination (Zel'dovich and Sunyaev, 1968); (e) emission of photons by unresolved extragalactic sources (Burbidge and Wolfe,

1969); (f) emission of photons by galactic sources (Fazio and Stecker, 1976); (g) variations in fundamental constants for old photons (Noerdlinger, 1973). Among these possible causes, point (d) - usually referred to as the 'Zel'dovich

effect' - has attracted the interest of experimentalists for the following reasons: (1) Satellite observations have proved the existence of strong X-ray fluxes in the

direction of clusters of galaxies, thereby supporting the idea that hot, dense inter- galactic gas is responsible for X-ray bremsstrahlung emission (Giacconi, 1974; Mitchell et aL, 1976).

(2) The Zel'dovich effect should produce a decrease in the temperature of the cosmic background radiation in the direction of the cluster. The values anticipated by Zel'dovich are easily detectable with the presently available radio telescopes and easily distinguishable from other effects (radio emission, far infrared emission, etc.) since the

Astrophysics and Space Science 53 (1978) 403-409. All Rights Reserved Copyright �9 1978 by D. Reidel Publishing Company, Dordrecht-Holland

404 s. AIELLO ET AL.

Zel'dovich effect is characterized by a negative signal in the well-known technique of differential sky modulation.

The interaction between cosmic background radiation and hot intergalactic gases can be described by 'Stage IV ' of Sunyaev's paper (Sunyaev, 1974). The inverse

Compton effect has not enough time to establish the B6se-Einstein equilibrium

distribution and, independent of the amount of energy release, a 'superimposition

spectrum' of various black-bodies is produced. The net result is an increase in the

photon's energy: the number of photons at low frequencies decreases and the cosmic background spectrum is apparently shifted towards higher frequencies. The change in

the photon number An due to Compton interaction is given by

An = No e~(e * - 1)-~(x tanh -* (x/2) - 4}xy,

in which x = hv/kT and y = - f (kT/mc2)ncrc dt, where a is the Compton cross-

section. In Figure 1 we report the behaviour of AI for a value of y = 10-2, about ten

times lower than the maximum value suggested by Zel'dovich. The decrease in flux in the radio region is evident from this figure.

Few attempts have been made to detect the Zel'dovich effect (Partridge, 1976; Gull

and Northover, 1976); the results are collected in Table I. In the Gull experiment at

3 cm wavelength a negative signal (as expected for the Zel'dovich effect) has been

detected in clusters 576, 1656 (Coma) and 2218. In the same clusters the observations

toO. AI ~o-{3 t t og.,r (k) {0 -14 / / / ';;at t/era z. mr./~m Watt/era 2. mr. Fm /f

IC14SJ /// L 1 ~;o ,o'oo ~o'oo so'oo

1~ 1

10,00 2o1oo , 50100

,d '6

~ff,

~c~Y

.._..--

Fig. 1. In the small box we have illustrated the distortion of cosmic background spectrum by the Compton effect. In the figure we have also reported the intensity difference (with respect to a 2.8 K black-body radiation) versus wavelength. A change in the sign of the effect around 1450 microns

is evident.

THE ZEL'DOVICH EFFECT AND THE INTERGALACTIC DUST IN GALAXY CLUSTERS

TABLE I

405

Abell No. AT in m K AT in m K measured AT in m K measured measured by by Gull at 3 cm by Gull at 3 cm Partridge at 9 mm (first experiment) (final result)

376 +0.54 -T- 0.80 1.22 -T- 1.24 -0.13 -T- 0.66 401 -0.39 -T- 0.61 426 (Perseus) + 1.91 -T- 0.82* 478 0.405 T 0.391 0.33 -T- 0.52 576 -0.34 T 0.51 -0.389 -T- 0.301 -0.71 T 0.57

1656 (Coma) +0.60 -T- 0.81 -2.003 T 0.989 -1.50 -T- 0.40** 2079 -0.035 T 1.24 2218 - - -0.356 T 0.369 --1.94 -T- 0.54 2319 0.27 -T- 0.77 -0.078 -T- 0.225 --0.13 -T- 0.41 2666 1.86 -T- 0.86 -0.561 -T- 0.270 --0.27 -T- 0.35

* Strong radio source ** Note Parijskij observation (1973)

of Par t r idge at 9 m m wavelength gave no appreciable devia t ion f rom zero, within

exper imenta l errors.

This s i tua t ion led us to examine the possible existence of a source of mil l imetr ic

rad ia t ion which emits enough power to compensate for the Ze l 'dov ich effect at 9 m m

and the efficiency of which is reduced at least by a factor 10 at 3 cm, where the

Ze l 'dov ich effect becomes dominant . The aim of the present paper is to discuss this

poss ib i l i ty in terms of in tergalact ic dust.

The existence of in tergalac t ic dust has been proved in the pas t on the basis of

var ious observa t iona l results : e.g., the decrease in the number o f galaxies or clusters o f

galaxies in the di rect ion of the core of near clusters; the dependence o f the colour

index on the redshif t for the quasis tel lar objects, etc. In the present paper we assume

a mass gra in densi ty of 5 • 10 -30 gr cm -3 in the cluster and 2 x 10 T M gr cm -3 in

the in tergalact ic space (outside the cluster) (Schmidt , 1975).

2. Thermal Emission from Intergalactic Dust

Firs t we discuss the wel l -known mechanism of thermal emission by grains. They

absorb the visible and ul t raviole t l ight emit ted by the galaxies and re-emit i t a t much

longer wavelengths. This emission, per uni t area, is described by the law

I(~t, Tg) = Q(a, ,~)BO t, To), (2.1)

where To is the gra in t empera tu re and Q is the emission efficiency, with B(~, Tg) the

P lanck ian law of emission.

Let us wri te Q(A, To) as

Q(a, ~) = Q(a, ho)(;~o/h)%

where )~o is a reference wavelength.

406 S. AIELLO ET AL.

Furthermore, since in the wavelength range of interest hc/kZTg << 1, we can ap- proximate the Planckian function by the Rayleigh-Jeans law. Equation (2.1) then

becomes

I(A, Tg) = Q(a, Ao)(ho/h)bcl/c2h-4Tg, (2.2)

where cl and c~ are the radiation constants. The shape of the emission spectrum

depends on the value of b, which in its turn depends on the grain material properties.

Before proceeding further we must investigate: (a) which b is required to fit the observational data; (b) which material, among those believed to be possible candidates

for interstellar dust grains, could satisfy this requirement. Let TRj be the temperature of a body obeying the RJ law and emitting, at wave-

length h and in the interval dh, the same amount of energy as that of a grey-body with

temperature Tg. Then

I(a, To) = (cl/c2)rBaA -4. (2.3)

Making use of (2.2) and (2.3) it is easy to show that if observations are made at two

wavelengths, t l and 12, then the folldwing relation exists between corresponding RJ

temperatures:

Tr~a.al = Ta~a,a2(12/11) b,

b = log (Z~,~I/Z~j,~:)/log a2/a~. (2.4)

We know that at h = 0.9 cm, TRj = 10 -a K. I f we assume that at h = 3 cm, Taa = 10 -4 K, then from (2.5) we obtain b = 1.91.

An upper limit of 2.83 for b is obtained assuming that at A = 1 mm TRj < 0.5 K

(in fact at h = 1 m m no observational data are available). Thus it seems not too

arbitrary to assume that, to explain the observations, dust grains must emit with the

efficiency

a(a, t ) = a(a, 1o)(1o/t) 2-3. (2.5)

Extrapolating to the centimetric region the data available in the literature about far

I R optical constants of various materials (silicates, graphite, ice, iron), we obtain: graphite Q ~ A -2.07

silicate Q ,-, A- 2.85

iron Q ~ t -2"~ ice Q ,-~ A -~

One can see that these materials, except ice, satisfy requirement (2.5). For the sake of simplicity we assume that the cluster (for instance, the Coma cluster)

is filled with particles having a radius a and a constant density of n particles cm-a.

The power flux received at the Earth from such a radiating sphere of radius R and

volume V is given by

q~(1) = (nVf)4rra2Q(a, h)c~/c21-~Tg, (2.6)

THE ZEL"DOVICH EFFECT AND THE INTERGALACTIC DUST IN GALAXY CLUSTERS 407

wheref i s a geometrical factor given by

f = (DO[R)2(4rrD2)-I ;

| being the half-angle subtended by the cluster and D the distance from Earth. This radiation must compensate for the decrease of the order of 10- a K in the cosmic

background radiation due to the Zel'dovich effect. Assuming that the core of the cluster completely fills the telescope beam, we have

n = 3{4a2Q(a, A)R} -1 x 10-8/T~. (2.7)

To calculate Tg we made use of the balance equation between the radiation absorbed and the radiation emitted by grains in the form shown by Kaplan and Pikel'ner (1970). The integral density of the intergalactic radiation field is of the order of 3 • 10- 5 erg cm-2 s-1 ster-1 (Felten and Morrison, 1966). If we add the cosmic background field we obtain the following values for the grain temperatures:

Graphite grains (a = 0.05/z), Tg = 25.2 K, Silicate grains (a = 0.16/~), T o = 6.7 K. Taking for D a value of 90 Mps (Abell, 1965) we obtain for the observed 0.9 cm

region in Coma a linear diameter of 130 Kps. Finally, under the assumption that the intergalactic dust in the Coma cluster is composed mainly of graphite particles for which Q (= 0.9 cm) _~ 10 -1~ from (2.2) we obtain n = 10 -8 cm -3, a value compar- able with the density of grains in the densest dusty regions of our Galaxy. For the silicate grains we obtain a similar value.

This result strongly excludes the possibility that the thermal emission from intra- cluster dust could explain the failure in detecting the Zel'dovich effect in the millimetre region.

3. Emission by Spinning Charged Grains

A grain immersed in a hot gas at temperature Tgas has a charge given by (Spitzer, 1968)

Z = ~bkT~,sa/e 2, (3.1)

where ~b is an appropriate parameter depending on the gas temperature (Burke and Silk, 1974) and e is the elementary charge. Hoyle and Wickramasinghe (1970) first suggested that the rotating charged grains can emit dipole radiation. The frequency of emission is related to the temperature of the gas Tg~, to the grain radius a, and to the grain material density Q by

v = (3/47r)(5/2~rQ- kTgas)l '2a- 5,2. (3.2)

The radiated power is given by

= (16~4/3c3)v4e2a2Z.

408 S. AIELLO ET AL.

We have to assume a size distribution for the grains in such a way as to compensate for the 0.9 cm Zel'dovich effect, while the emission must be negligible at 3 cm. I f

N(a) da is the normalizeddistribution, we have, for the emission

etot(h) dh = (noR/3)| 4/3ca)kTg~saar da, (3.3)

where no is the total number density of the grains, and R is the radius of the emitting

region. From (4.2) we obtain

a = { 4 , ~ / 3 ( 2 , ~ / 5 k T ~ S ~ } - 2 ~ 5 ~ - 2 %

da = 2/5{4rr/3(27rr 1/2}- 2/%- 7/5 dr,

for h = 0.9 cm (v -- 3.3 x 10 l~ Hz) and ~ = 3.5, which is an appropriate value for silicate grains, a = 7 x 10 -7 cm.

I f we insert these equations and the numerical values in (3.3) we have

etot(X ) dA = 1.8 x lO-59R| dr. (3.4)

The condition that, at 0.9 cm, the emission is that of a 10 -a K black-body gives us

the following expression for the density of the emitting grains - assuming a gas

temperature of 10 a K (Lea et aL, 1973; Kellogg et aL, 1975)

noNR = 1012r -1,

Taking r = 1 and R = 70 Kps (see w we obtain

non = 4.76 x 10 -12 cm -a ,

which corresponds to a mass density of 2 x 10 -29 gr cm -3 and to an extinction of

5 x 10 -3 mag Mps -1, a value much lower than that observed in the cluster of galaxies, Am ~ 1 mag Mps -1 (Karachentsev and Lipovetski, 1968). We can explain

this if we assume that very small grains (a _ 10- 6 cm) coexist in intracluster space with

grains of greater size (a ~_ 10-a cm), which are responsible for the observed extinction.

4. Conclusions

While thermal emission by grains of conventional size cannot compensate for the Zel 'dovich effect, the emission by rotating small grains appears to be adequate to produce this effect. The presence of a very hot and relatively dense intracluster gas (as suggested by X-ray observations) can justify the existence of such rapidly spinning

charged grains emitting dipole radiation. The crucial assumption in the present approach is the existence of very small grains

in order to produce the millimetre radiation. These small grains could be produced by destruction, due to gas-grains collision, of the conventional sized grains ejected from

the galaxies into intracluster space (Chiao and Wickramasinghe, 1972).

THE ZELrDOVICH EFFECT AND THE INTERGALACTIC DUST IN GALAXY CLUSTERS 409

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