Juan 14I. USON

THE MICROWAVE BACKGROUND RADIATION

National Radio Astronomy Observatory*, P. O . Box O, Socorro, NM 87801, USA

Nuclear Physics B (Pros. Suppl.) 28A (1992) 38-47North-Holland

The microwave background radiation is a remnant of the early Universe . It is blackbody radiation with a temper-ature TCBR = 2.735 i 0.060 (0.017) K and no measured spectral distortions . It is isotropic to (ATIT) < 5 x 10-`'over all angular scales, except for a dipole component which is attributed to our motion with respect to thepreferred reference frame of the radiation .A small-scale anisotropy has been detected towards a few dense clusters of galaxies that is attributed to inverse-Compton scattering of the photons of the backgroud radiation by the hot gas that is responsible for the X-rayemission from these clusters . This is the Sunyaev-Zel'dovich effect .

1 . INTRODUCTIONA background of blackbody radiation was predicted

in 1946 by Garnow 1 as a necessai °- component ofthe BigBang theory. Alpher and Herman estimated a temper-ature TCBR = 5 Ii from the observed abundance of 4He.Dicke and his collaborators3 set a limit T < 20 Ii inde-pendently and although his measurement and Gamow'sprediction appeared in the same issue of the Physicalreview neither group became aware of the other's work .The notion of a background of radiation was indepen-dently re-invented by Dicke4 in the context of a cyclicmodel of the Universe and lie urged Roll and Wilkinsonto set out to measure it . The microwave background ra-diation was serendipitously discovered by Penzias andWilson in 1964 through a careful measurement whichthey reported as an "excess antenna temperature at4080 11c/s .'"

In this review I will briefly discuss the physics rel-evant to the microwave background radiation as wellas review the present experimental "bottom-line" withsome emphasis on a few recent measurements. Thetheoretical facts have been reviewed by Sunyaev andZel'dovich. 6 A more detailed review of the experimentsup to 1986 can be found in the contribution that DaveWilkinson and I made to the second edition of "Galacticand Extragalactic Radio Astronomy.''? I will not discuss

5632/9ZSOS.00 0 1992- Elsevier Science Publishers B.V

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the upper limits on the polarization of the microwavebackground nor their cosmological implications as thisis not an active field and the situation remains as dis-cussed in ref. 7 .

2. THE SPECTRUM OF THE RADIATION2.1 Cosmological scenarioIn the Big-Bang scenario, the early Universe was

hot and in thermal equilibrium : matter was immersedin blackbody radiation . At redshifts Z > 104 , theUniverse was radiation dominated which means thatit was mainly p,. that decelerated the expansion . Aspr oc (1 + Z)4 and prn oc (1 + Z)3 , Pr decreased fasterwith time than p,n and at Z < 104 the Universe be-came matter-dominated. At Z - 103 , the tempera-ture dropped below 4000 K and the Universe becamemostly neutral.$ As the cross-section for interaction ofthe matter and the radiation dropped drastically, theUniverse became transparent to the radiation . At thisstage, the radiation liad a blackbody spectrum due toits prior state of thermal equilibrium . The subsequentexpansion only lowered the temperatur` as

TCBR(Z) oc (1 + Z)

(1)

The credibility of the hot Big Bang model is basedon two key predictions : (1) The thermal spectrum of

* The National i~ adio Astronomy Observatory is operated by Associated Universities, Inc ., under cooperative agree-ment v.-ith the U. S . National Science Foundation .

the background radiation, and (2) the universal abun-dances of light elements : 2H, 3He, 4He and 7Li (dis-cussed in this workshop by Gary Steigman) . For exam-ple, an abundance of 4He of 24% requires a temperaturefor the microwave background of 2.75 K to within 10% .

The early Universe departs from thermal equilib-rium in many ways but the effects on the radiationspectrum are small because in the early Universe theheat capacity is mostly in the radiation. The epochsprobed by measurements of the spectrum of the mi-crowave background lie in the range 109 > Z > 103,as before Z = 109 thermal equilibrium is establishedquickly by electron-positron pairs and after Z = 103the radiation has decoupled from neutral matter. De-partures from the blackbody spectrum would reflect theout-of-equilibrium conditions that must have predatedthe formation of today's structure in the Universe .

Distortions due to different cooling rates and to thedecoupling process are very small (OT/T < 10-5). Butthe electrons can be heated by dissipation of turbulenceor annihilation of antimatter. The hot electrons thenhave two effects : (1) Inverse-Compton scattering shiftsphotons to higher frequencies and (2) Low-frequencyphotons are emitted through Bremsstrahlung and theCompton effect . The predictions are uncertain and thelimits not yet very strong . The shape of a distortionwould reflect the epoch at which the dominant energyinjection occurred. An early time (Z > 4 x 104) would

result in a Bose-Einstein spectrum characterized by its

chemical potential y whereas a later injection wouldproduce a Compton spectrum characterized by the "y-parameter" (see ref. 6 for. details) . Inverse-Comptonscattering by hot electrons in clusters and protoclus-

ters of galaxies at recent epochs (Z < 10) should alsoproduce distortions in the spectrum of the radiation.9The predicted y-parameters are of the order y - 10-5 .

2.2 . Observational statusThe measurements are, at this time, consistent with

a blackbody spectrum with TCBR = 2.735 K . Measure-ments o£ the spectrum of the cosmic background radi-ation are generally not limited by statistical errors but

by systematic errors . As the radiation is omnipresent

l.M. Us6n /The microwave background radiation 39

the traditional "on-off" observing method is insensitiveto the radiation and an absolute measurement is nec-essary. In general, two different sets of measurementsmust be made: a measurement of the radiation fromthe sky and a measurement of the radiation from aknown reference, usually a blackbody immersed in abath of liquid helium. Care must be taken that the in-strumental contributions do not vary between both setsof measurements and, in addition, all contributions thatare not common to both sets of measurements must becarefully det-mined either through direct measi-:meat(for example the atmospheric contribut:jn) or accuratecalculation (for example ground pickup or losses fromhorns and waveguide) . For example, a ground-basedmeasurement would determine

TS -TR=TCBR+TA+TRS+TG+TH+TO (2a)

and

TL - TR = THe + TW + TOI +TH

(2b)

where the subscripts refer to the contributions of thesky (TS), a stable reference (TR) against which the skysignal is "Dicke-switched", the radiation (TCBR), theatmosphere (TA), the galactic (and extragalactic) back-ground (TRS), the ground (and other ambient contam-ination) (TG), the horn and other instrumental losses

(TH), some offset(s) due to the instrumental setup thatcould very well vary over the duration of the measure-ment (TO, T0), the absorber (THr) as well as the wall

of the dewar (TW) . Combinig both measurements pro-

vides an estimate of the difference

TS-TL = TCBR+TA+TRS+TG+TH+OTO-THe-TW

and zenith scans are customarily used to determine TA

through its secant-law behavior .Ground-based measurements have been limited by

atmospheric contamination at frequencies above 3 GHz-

At shorter wavelenghts, the contribution from the walls

of the dewar that contains the cold load becomes impor-tant and cannot be minimized unless a costly oversizeddewar is used. At still lower frequencies (below 1 GH-,),the contributionfrom the Galaxy dominates and is hsrdto evaluate. In addition, ground pickup also increasesas the antennas as well as the necessary ground screenshave to be prohibitively large . The most sensitive mea-surements from the ground come from a concerted effortperformed at five different frequencies from 2.5 G1 .z to90 GHz by a USA-Italian collaboration l® whose mea-surements are consistent with a blackbody with temper-ature TCBR = 2.73f 0.05 K. The quoted errors on theindividual measurements rmige from 0.08 K to 0.16 K.

In order to reduce the contributions and uncertain-ties due to the various terms on the right-hand sideof equation (3) Johnson and Wilkinson" flew in op-timized radiometer from a balloon at an altitude of26 km. This virtually eliminated TA. Variable offsetswere minimized by cooling the horn (most of the throatwas inside the dewar) and sliding a load in its place forthe cold-load measurement . Their measurement was

TCBR = 2.783 i 0.025 K. The main correction was thecontribution of the part of the horn that was outsidethe dewar, which led to a correction TH = 0.49 f 0.12 .

At higher frequencies, recent high-sensitivity mea-surements have superseeded previous hard efforts whichhad indicated the possibility of spectral distortions . 12No spectral distortions are seen by the latest generationofinstruments which have been taken outside the atmo-sphere with the CORE satellite 13 and with a rockctl4 .Both instruments are liquid-helium cooled polarizingMichelson interferometers with different schemes usedfor calibration and control of systematic errors . Thesmallest errors have been quoted by the group at theUniversity of British Columbia who made the rocket-borne measurement . They found an undistorted black-body spectrum with a temperature TCBR = 2.736 f0.017 K. Their limits on possible distortions yield"y < 0.001 and p < 0.008 . The COBE team haveonly publishedIO thus far the result of 9 minutes ofdata as TCBR = 2.735 f 0.060 K . They limit the de-viations from a blackbody spectrum to less than 1%

!.M! Use/Themicrowave background radiation

which yields the same limits on y and p as those fromthe UBC experiment . Their measurement has the po-tential for much better sensitivity (a - 0.01 K) butwill certainly be limited by systematic errors . Theirquoted error is larger than that of the UBC group dueto inconsistencies (at some unspecified lower level) intheir absolute calibration as given by several indepen-dent thermometry calibrators (the UBC group had asingle thermometry calibrator) . Thus, both measure-ments are essentially equivalent as published and theiragreement quite remarkable . It is worth noting that al-though the result of Johnson and Wilkinson describedabove" is a few standard deviations high, the differenceis of the order of their main correction (TH) . It is quitepossibly that some systematic corrections might havebeen underestimated so that no claim of a distortionhas been made at this time .

Future measurements might yet detect distortionsin the spectrum of the microwave background. At thispoint, the most room for such a signal would seem tobe at long wavelengths (a > 10 cm) where the experi-ments have not yet achieved the precision of the mea-surements described above . However, contaminationform our Galaxy and fiom extragalactic radio sources isa serious problem which might be addressable throughmultiwavelength measurements . Efforts are under wayby a number of groups to pursue this problem .

2.3 Cosmological ImplicationsThe blackbody spectrum leads to a number of im-

portant conclusions :The Universe was once in thermal equilibrium .

® The Universe has evolved from a hot initial state,a Big Bang .

® The isotropy of the microwave background radia-tion supports the Cosmological Principle and also limitsthe extent of possible anisotropies in the expansion rateof the Universe.

® The background radiation provides us with a snap-shot of the Universe in its infancy, at an age of about3 x 105 years, about 1.5 x 1010 years ago, which mightfix the initial conditions from which the structure of theUniverse has evolved . As discussed below, the problem

is perhaps that it might be too isotropic .

3 . ISOTROPY OF THE RADIATION3.1 . A ScenarioSoon after the discovery of the background radia-

tion, Peebles15 pointed out that it could show the initialconditions, power spectra and characteristic lenghts andmasses from which the matter in the Universe evolvedinto today's large-scale structure . Subsequent scatter-ing could modify or blur this picture if the Universewent through a phase in which an appreciable fractionof the mass was reionized, perhaps because of a largeinput of energy released at the epoch of galaxy forma-tion or associated with a phase of intense supernovaactivity l6 . Such a phase has been suggested to occurat a variety of redshifts from Z = 100 to fairly recentepochs .

The structure in the Universe has evolved from verysmooth initial conditions . The "gravitational instabil-ity" principle is that seed fluctuations grow because ofgravity which tends to increase the lumpiness of theUniverse with time . The dynamics is assumed to begeneral relativity (its newtonian approximation beingadequate) and the boundary conditions determine thatthe Universe must have evolved into what is seen today:galaxies and clusters of galaxies, from whatever the ini-tial conditions were . Those initial conditions can per-haps be determined by detecting small-scale anisotropyin the microwave background radiation .A plethora of models are considered . Their main

characteristics are :- Their dominant component which could be ordi-

nary matter, massive neutrinos ("hot dark matter") oraxions, photinos, gravitinos or some other heavy parti-cles ("cold dark matter") .

- How much of it which determines the density ofthe Universe, conveniently parametrized in terms of the"density parameter" (9) or ratio of the density of theUniverse to that of a "flat" Einstein-deSitter Universe .

- The power spectrum of the density fluctuations atdecoupling which fixes the relative abundance of differ-ent kinds of seed fluctuations .

1.M. Wn /Themicrowavebackground radiation 41

Let us assume a baryon-dominated Universe. Be-fore the decoupling era the Universe was optically thickto the radiation and matter was mostly ionized and inthermalequilibrium . Matter, the radiation and the neu-trino background can be treated as a single fluid withpressure mainly due to photons and neutrinos althoughthese decoupled early, when the temperature was about5 x 109 K. The photon pressure provided an opposingforce to gravity and the evolution of fluctuations wasdetermined by their superposition . The evolution of amass perturbation depends on its size when it becamecontained within the horizon. There is a characteris-tic mass scale, the so-called Jeans mass, such that forhigher mass perturbations gravity will dominate andthe perturbations will grow as t 2 /3 ; whereas lower massperturbations will oscillate instead . The Jeans mass de-pends on the density and temperature of the Universeand grows with time as the Universe expands and coolsuntil the decoupling time when it has reached about17

Mj = 3 x 1014Q-2h-4M0

(4)

(h is Hubble's constant in units of 100 km s-1 Mpc-1and M(D is the mass of the sun) .

Another important mass-scale is that below whichdamping results due to photon diffusion. 18 This mass-scale grows as the density of the Universe decreases andthe mean free-path for photons increases accordingly.Its value at decoupling is called the "Silk mass"

MS ^' 1012-5/2n-5/4MO

(5)

Adiabatic fluctuations of lower mass will be severelydamped and mostly erased before decoupling whereasi .,_ `hermal fluctuations will have evolved uninfluencedby this mechanism.

At decoupling, the Silk mechanism ceases to operateand the Jeans mass drops to about 106M(D . so that afterthis epoch, matter fluctuations are free to evolve undergravity and gas dynamics independently of the back-ground photons . Density fluctuations (Sp/p) will havegrown at most by a factor (1-f- Zdec)-1 since the decou-pling time given by Zdec . If the density parameter S2 isless than unity the growth of fluctuations will essentially

42

stop at a redshift Z - SZ-1 -1. The maximum growthis therefore a factor of about 103 , so fluctuations of or-der by/p - 1 as seen today, require seed fluctuations ofthe order by/p N 10-3 at decoupling . Detailed calcula-tions show that for the adiabatic scenario this requiresfluctuations in the background radiation of orders

T-SbP >10'4

in order to account for present-day structures ifthe fluc-tuations are adiabatic . In the isothermal case, matterfluctuations do not directly result in anisotropy in theradiation but fluctuations are induced by Doppler shiftsat the last scattering of each photon at the level of

~. V >5x10-s (7)

The relation between angular scales on the sky ob-served today and physical scales at the decoupling timeis strongly dependent on the value of the key cosmo-logical parameters Ho, qo and R but a mass of order1015K1p subtends at the decoupling time about 5~.

As discussed above, small-scale anisotropy in the ra-diation imprinted at the decoupling time could havebeen erased if a significant fraction of the matter be-came ionized once again at a much later epoch duringgalaxy formation . The initial burst of star formationthat is postulated in order to produce the "heavy" ele-ments that are seen even in the oldest stars could havereleased enough energy to achieve a significant degreeof ionization and sufficient optical thickness . This couldhave erased fluctuations in the radiation on angularscales corresponding to areas causally connected duringthis phase; although some degree of polarization couldresult due to protogalactic magnetic fields19 . Silk2o hasargued that such a phase cannot have affected the back-ground radiation in a relevant way due to insufficientoptical thickness and that we are indeed getting a clearpicture from the decoupling time.

Detailed predictions of anisotropy require a modelfor the initial fluctuations, i .e. their mass spectrum andstatistical properties . For simplicity a power-law spec-trum is normally assumed, i . e . bplp oc kn, and n = 1is the most popular exponent . Divergences at one car

JM. Usdn /The microwave background radiation

both ends of the spectrum have to be prevented by in-troducing suitable cutoffs . The model Universe is thenevolved after choosing the Hubble constant and den-sity parameter and the normalization is usually set bymatching the galaxy autocorrelation function to thatof the observed Universe. This leads to a predictedanisotropy in the background radiation for each modelUniverse . Assuming that the dominant component ofthe mass is non-baryonic allows for a smoother back-ground radiation as the seed fluctuations in the massare provided by the weakly-interacting particles andthe baryons and, therefore, the radiation can be moresmoothly distributed . After decoupling, the baryonsfall into the potential wells provided by the seed fluctu-ations and their evolution under gravity and structuredevelops rapidly.

The difference between cold and hot non-baryonicparticles is that the hot particles (massive neutrinos)smooth out small-scale seed fluctuations before decou-pling due to their high peculiar velocities and large-scalestructures (clusters and superclusters of galaxies) mustthen form first and later fragment into smaller, galacticsize, objects . In the "cold" case (axions, photinos, . . . )galaxies or even globular clusters form first and lateraggregate into clusters and superclusters .

Predictions of minimal anisotropy in OTIT rangebetween 10-3 and 10-5 depending on the model Uni-verse under consideration . The predictions are some-what lower for angular scales below about 30' due tothe finite "thickness" of the re%ombination epoch (seeref. 20 for a review) .

3.2. Other sources of anisotropyVery-small-scale anisotropy (0 < 1~) might result

from re-ionization due to explosive processes during theformation of individual galaxies. This would be a highlynonlinear process and no detailed predictions have beenmade.

Intermediate-scale anisotropy (0 - 2° - 6°) resultsfrom the Doppler effect due to peculiar motions at thedecoupling time . In addition, it could be the dominantanisotropy if reionization erases structure on smallerscales .

Anisotropy on even larger scales results from theSachs-Wolfe effect : photons from different directionshave "climbed out" of different gravitational potentialsand are therefore gravitationally redshifted by differentamounts . 21 The effect results from Poisson fluctuationsin the mass distribution . Indeed, a randomly placedsphere of radius r contains a mass proportional to itsvolume with uncertainty proportional to the square-root of this mass. This leads to fluctuations in the grav-itational potential which in turn lead to fluctuations inthe induced gravitational redshift and therefore in theradiation temperature which are roughly proportionalto

T oc ô¢(r) ocb1Ll oc

r1/2

(8)

This effect which grows larger with angular scale wasonce invoked to explain a quadrupole anisotropy in theradiation which has since been shown to be due to mea-surement errors . Today's estimates of the quadrupolecomponent induced by this effect yield an amplitude ofthe order of ATIT - few x 10-5 , once again dependenton the assumed dominant component to the mass of theUniverse. This effect will also induce a dipole compo-nent . The predicted amplitude for this component isin the range ATIT - 10-4 - 5 x 10-3 although theuncertainties are large. 20

Finally, an intrinsically isotropic radiation only ap-pears isotropic to an observer in the "preferred" refer-ence frame in which this happens . An obsever in motionwith respect to the former one will see the radiation hot-ter in the direction towards which (s)he is moving andcolder on the opposite side . Moreover, the anisotropywill take the form of a dipole component and its ampli-tude will be

AT vT c

for non-relativistic velocity v . Notice that the ampli-tude is independent of frequency. An estimate of thevelocity of the Sun in our Galaxy leads to a predicteddipole amplitude of about 10-3 due to this local effect .

J.M. UsGn /Themicrowavebackground radiation 43

3.3 . Anisotropy measurements.No anisotropy has been seen on any angular scale

to a level ATIT < 10-4 except for a dipole compo-nent which can be interpreted entirely as due to ourmotion through the radiation although some ofit couldindeed be intrinsic to it . The agreement between thevarious large-scale anisotropy experiments22-25 is quitespectacular. All data are consistent with a dipole com-ponent of amplitude OTmaa = 3.3 f 0.2 mK towardsRA = 11.2 f 0.1 h, Dec = -7.0 ° f 1.0". This is an im-portant consistency check as both the D6ppler as wellas an intrinsic dipole component should be independentof frequency if the cadiation has a blackbody spectrum .Indeed, any discrepancy in the amplitudes measuredby the various groups can be entirely ascribed to uncer-tainties in the absolute calibrations . The measured am-plitude translates in a solar speed of 365 f 18 kin s-1 .The earth's rotation around the sun was detected bythe Princeton group22 at the 7 - o, level on compar-ing two flights taken six months apart . The solar mo-tion implies a motion of the Local Group of galaxiesat 622 f 20 km s-1 towards25 RA = 10.2 f 0.4 h,Dec = -27" f 5" .

No other anisotropies are detected at any angularscales with upper limits ATIT < 5 x 10-5 (18" <

8 < 180*) . The report26 of a possible detection ofanisotropy at an angular scale of 8° has not been con-firmed by subsequent measurements . The upper lim-its constrain the makeup of the Universe as well asthe possible scenarios for its evolution. The most se-vere constraints come from measurements ofsmall-scaleisotropy (6 Z 1°) . Here the limits have been pushed toATIT < few x 10-5 at several angular scales .27-29

The most spectacular progress in this area has beenmade recently by Lubin and his collaborators who havebuilt several special-purpose instruments and successfully used them from balloon-borne platforms as wellas from a high and dry site near the South Pole. Theyuse a one meter off-axis Gregorian telescope with a half-power beamwidth which is adjustable from 20' to 50` .They have used an SIS receiver operating at 90 GHz.Beam switching is accomplished by rotating the sec-

44

ondary reflector which results in a sinusoidal patternon the sky, nearly equivalent to a square-wave modu-lation by ®8 - 1" . They use this uncommon schemein order to minimize sidelobe pickup.29 Their publishedlimit is ®T/T < 3.5 x 10-5 at an angular scale of 20' .More recent (yet-to-be-published) observations at theSouth Pole site have lowered their upper limits by a.factor of two, to OT/T < 1.7 x 10-5 at angular scalesof 20' < 0 < 1" . In addition, they have also used theirtelescope with HEMT receivers to provide four contigu-ous bands of width Ov = 2.5 GHz between 25 GHz and35 Ghz . Here the galactic contribution is expected tobe minimal . The half-power beamwidth for this experi-ment is about A9 - 1.5° . They detect fluctuations thatare correlated between the lower frequency channels andwould seem to be due to galactic foreground contami-nation. Spectral fitting might allow them to remove thecontamination . At this point, the data from the higherfrequency channel (32.5 - 35 GHz) allow them to set anupper limit OTIT < 2 x 10-5 at an angular scale of 1 .5 °at the 95% confidence level, based on nine (siightly cor-related) sky patches . The data are still being analyzedand this limit could be lowered . The potential sensi-tivity of the full experiment is OT/T - 4 x 10-6 (1-0)but is unlikely that the contaminating signals could beremoved to this level of precision .

3.4 Cosmological implicationsTaken at face value, the measurements rule out adia-

batic models of the Universe that contain only baryonicmatter for all interesting values of the density param-eter l . Universes dominated by non-baryonic (dark)matter are also excluded by the results discussed in theprevious section ; unless Ph > 0.7 for universes domi-nated by cold dark-matter particles . Should the mea-surement of Lubin's group result in an upper limit be-low the 10`5 "barrier" even these would be excluded .Of course, cold dark-matter models might be in evenmore serious trouble to explain the large-scale struc-ture of the galaxy distribution and streaming motions .

Baryon-dominated isothermal models have been outof favor for some time as their premise seems hard to ar-range. Aside from this, the predicted anisotropy in the

JM. Usön /Themicrowave background radiation

background radiation is still below the limits discussedabove for all values of Q if the index of the perturba-tions is n = 1, which is the favored value. Therefore,the isotropy measurments of the background radiationdo indeed allow for a baryonic Universe .

Nevertheless, the constraints are not too serious . Onone hand, a simple way to avoid the confrontation be-tween the predictions and the results is to invoke thehypothesis that perhaps light does not trace matter . Inthis case, the observations of large scale structure inthe distribution of the galaxies would not describe thedistribution of the dominant component to the mass ofthe Universe and the expected anisotropy in the back-ground radiation would be much smaller if the Uni-verse is dominated by a smooth distribution of unseenmatter . In addition, the measurements have sampled asmall number of independent fields, a very small sam-ple of the Universe. The confrontation rests heavilyon the assumption that the fluctuations have gaussianstatistic and the limits are actually making strong state-ments about the tail of a distribution that they do notmeasure. Finally, the theories are normalized to thepresent distribution of galaxies using the volume inte-gral of the galaxy autocorrelation function. There isprobably room for up to one order of magnitude in flex-ibility between the theoretical predictions and the ex-perimental limits so that none of the model Universesis definitely ruled-out except for baryon-dominated adi-abatic models.

4 . THE SUNYAEV-ZEL'DOVICH EFFECT4.1 . Theory and cosmological applicationsDense clusters of galaxies are copious sources of X-

rays emitted through thermal bremsstrahlung by thehot ionized intergalactic gas . The X-ray spectra showemission lines which axe attributed to highly ionizediron and yield gas temperatures as high as 108 K insome of the denser and hotter clusters . The mass ofthe hot gas is as large as that of the stellar component.This gas is heavily processed material (as it containsheavy elements with approximately solar abundances)which must has been probably stripped from the parent

galaxies by galaxy collisions and through ram pressuredue to the hot intergalactic gas.30

The Sunyaev-Zel'dovich effect3l is the result of thescattering of the photons in the microwave backgroundwith the hot gas in clusters of galaxies. Because thegas is so much hotter than the radiation, the interac-tion will be through inverse-Compton scattering whichconserves photon number . As a result, the gas willcool and the spectrum of the radiation will be distortedas the scattered photons will emerge with higher en-ergy (frequency) than the incoming ones . This will de-plete somewhat the Rayleigh-Jeans side and increasethe number of photons on the Wien side with no effectat a frequency of about 218 GHz, slightly higher thanthat where the undistorted spectrum peaks (162 GHz) .

Combining measurements of the Sunyaev-Zel'dovicheffect and of the X-ray emission from a cluster of galax-ies would allow, in principle, an independent determi-nation of Hubble's constant32 as the X-ray emissionand the Sunyaev-Zel'dovich effect provide two indepen-dent probes of the electron density. Indeeed, obser-vations of the X-ray emission provide the run of tem-perature (from X-ray spectra) as well as the integralof N,2T,0.5 as a function of the distance to the clusterwhich sets the scale for the X-ray images of the clus-ter . This can be written in terms of Hubble's constantas Ne T~ S(cZ/Ho)93 where 0 is the angle subtendedby the cluster . The Sunyaev-Zel'dovich effect gives theintegral of the electron pressure which is proportionalto NeTe(cZ/Ho)8. It should be possible in principle tosolve for Hubble's constant from both sets of measure-ments.

Sunyaev and Zel'dovich estimated the change in thespectral energy density of the radiation as

OF(v) = " v dv

v4civ [v-3F(v)] )

(10)

with E. = kTeT/mec2 ; N .,"here k is Boltzmann's constant,Te is the temperature ofthe electron gas, me is the massof the electron, c is sthe speed of light and r is the lineintegral of the electron pressure

J.M. Usdn/The microwave background radiation 45

T=INe cTdl (11)

taken along the line of sight through the cluster, withNe being the electron density and aT the cross-sectionfor Thomson scattering.

In the Rayleigh-Jeans side of the spectrum F(v) ocv2 and the fractional spectral distortion

AFRJ

FRJ

-2 y

(12)

is independent of the frequency.Let us derive some predictions for the well-studied

Coma cluster ofgalaxies which is a a redshift Z = 0.023 .X-ray observations33 yield a gas temperature Te = 7.9±0.3 keV and a surface brightness in the few keV bandwhich is well described by34

2 -1SX(e) = So

1 +

2

(13)X

with So = (1.2±0.1) x 10-8 watt m-2 and OX = 12.8'±0.5' . The velocity dispersion for the galaxies inside theX-ray core radius 8X is35 aV - 1200 kin s-1 . If theplasma scale height is of the same order as that of thegalaxies :

T -

2kay - 7.7 keV

(14)

This (likely fortuitous) agreement encourages usinga simple isothermal model for the cluster, with a centralelectron density Ne - 3 x 103 m3 which yields r0.015 and a predicted Sunyaev-Zel'dovich effect

2 -1/4ATRJ = AT, 1 +é2

(15)X

with AT. = -1 .2 mK. Notice that the half-width athalf maximum ofthe Sunyaev-Zel'dovich signal is aboutfour times the size of the X-ray core radius . The effectbecomes larger towards the peak of the blackbody sp,-c-trum and changes sign on the Wien side .

4.2 . MeasurementsMany observers have sought to detect the Sunyaev-

Zel'dovich signal since it was first predicted (see ref. 7

46

for a discussion of the observations) . Early efforts werelimited by systematic errors and observers obtained dis-crepant results . Reference positions were not taken farenough from the cluster center and, in addition, con-tamination from radio sources was a serious problem.Spectral observations of a cluster would be important,as the Sunyaev-Zel'dovich effect has a well-understoodfrequency signature . In addition, observations of theeffect on the Wien side would be desirable. Unfortu-nately, observ=ations at frequencies above 35 GHz areonce again limited by the atmosphere .

Measurements made since 1980 have shown consis-tent results . Although there are still some problemsand a tendency by some observers to underestimate themeasurement errors, the Sunyaev-Zel'dovich effect hasbeen detected by two different groups, with differenttelescopes and systematics . 36,37 The effect is seen in theclusters 0016+16, Abell 401, Abell 665 and Abell 2218at a frequency of about 20 GHz. The derived centraldecrements are about AT - -0.9 mK with signal-to-noise ratios about 4 to 6 (with ruy conservative estimateof systematic errors ; some of the quoted errors lead todiscrepancies at the few sigma level) .

4.3 Cosmological implicationsUnfortunately, it is not straightforward to derive

Hubble's constant from the presently available data .Although the principle is clear, in practice it is hardto solve for the electron density ar_d temperature of acluster for several reasons : (1) In order to de.provect theX-ray data an assumption of the shape of the gravita-tional potential has to be made. (2) In addition, if thetemperature is not constant, spatially-resolved X-rayspectra are also necessary. (3) No convincing (perhapsagain my own bias) spatial information is available forthe Sunyaev-Zel'dovich. This is important as one con-sequence of the different functional dependence of bothprobes into the cluster gas is that they might not be"seeing" the same gas . For example, a diffuse hottercluster gas halo could contribute significantly to theSunyaev-Zel'dovich signal without significantly affect-ing the X-ray emission .

Nevertheless, observations of the cluster Abell 665

J.M Wn /Themicrowave background radiation

combined with recent X-ray observations made with theROSAT satellite have produced a value for the Hubbleconstant

Ho = (40 to 50) f 12kms 1

(16)

which the authors38 would probably be first to admitshould be considered to within a factor of two in lightof the uncertainties just enumerated . Nevertheless, thefact that a determination that is totally independent ofthe usual stepwise method does agree so well with pre-vious results is quite encouraging and provides a strongconsistency proof to the standard Big-Bang model ofthe Universe .

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