Fig. 4.7. The y-parameter distortion of the CMBR spectrum is illustrated on the left and the ^-distortion on the right.

this parameter when the recoil effect may be neglected. These y-distortions allowed us to relate any energy release in the universe at 2 < 5 x 104 to the deviation of the CMBR spectrum from blackbody. The left-hand graph in Figure 4.7 shows that the deviation is especially strong in the shorter wavelength Wien part of the spectrum, where, at that time, observations showed a significant excess of the background spectrum over a blackbody radiation curve.

Zel'dovich realized the importance and the beauty of these solutions, but, as I have noted above, it took a long time to be published in Western journals. He decided to send the first edition of the article to the Soviet Physics Uspekhy review journal. There is a reference to our never-published paper in this journal in a wonderful article by Zel'dovich and Shakura (1969) on spherically symmetric accretion onto a neutron star, where our solution is used to obtain the radiation spectrum of a shock wave in the vicinity of a neutron star surface. After Zdenek Kopal's visit to Moscow, Zel'dovich changed his mind and recommended that I send the article to Astrophysics and Space Science for publication. The publication of the article was significantly delayed, to March 1969.

In a subsequent article (Sunyaev and Zel'dovich 1970a) we demonstrated that earlier energy release (at 2 > 105) led to another effect: Bose-Einstein distortion or ^-distortion of the relict radiation spectrum. This is shown in

Figure 4.7 (from Sunyaev and Zel'dovich 1970b). In scattering by free electrons that preserves the number of photons the radiation spectrum relaxes to the form characteristic of a boson gas with nonzero chemical potential ¡.

But bremsstrahlung (and double-Compton emission) can create photons at low frequencies, which Comptonization can raise to higher energies, lowering ¡ , and even relaxing back to a true blackbody spectrum. We demonstrated that any energy deposited at redshift z > 107 would leave no trace in the observed relict radiation spectrum. Later (105 < z < 107) energy release would lead to a Bose-Einstein spectrum distortion.

At the end of the 1960s, Hannes Alfven visited Moscow (I was present during his conversations with Zel'dovich) and argued for the possibility of annihilating matter and antimatter, which would inject energy that could affect the CMBR spectrum. Leonid Ozernoi and Artur Chernin (1968) were actively developing a turbulent model of the universe, which could also lead to significant energy release. Nowadays decay and annihilation of different elementary particles is widely discussed, including those which possibly are connected with dark matter.

Observations conducted at the end of the 1960s allowed, and sometimes indicated, large spectrum distortions. However, even then unexpected experimental facts emerged. I remember a seminar by I. S. Shklovsky and V. I. Slysh on McKellar, who, back in the 1940s, evaluated the excitation temperature of a CN molecule in the intergalactic medium by the observation of absorption in the ultraviolet doublet line of this molecule in the spectra of bright stars. This measurement of the relict radiation temperature at wavelength 2.54 mm, and similar data on CN+ and CH molecules obtained by Thaddeus, Field, and others were for quite a while the most important constraints on the CMBR spectrum in the Wien region. Only a really great instrument, COBE/FIRAS (let's also mention a Canadian rocket experiment, Gush, Halpern and Wishnow 1990) much later provided extremely rigid upper limits for both y and i (Mather et al. 1990) and, consequently, energy release in the early universe, thus considerably limiting the freedom of action for theoreticians.

The CMBR and clusters of galaxies

The history of the "SZ" effect in directions toward clusters of galaxies goes back to the discussions of the problem of the search for "missing" matter in clusters of galaxies. I do not remember now who told me first about the existence of a paradox of "missing" mass in clusters formulated by Fritz Zwicky in the 1930s. Most likely it was Samuil Kaplan, a professor from Gorkii University.

I began to read papers about clusters of galaxies and very soon strongly believed that there is a lot of hot intergalactic gas inside clusters because the limits to the amount of neutral hydrogen there were very strict. It was simple to show that Thomson scattering of isotropic CMBR photons on electrons in this gas leaves no trace in the angular distribution of CMBR. When I told this to Zel'dovich, he began to laugh and said only "Tindal effect: smoke from the chimney in a fog."

A beautiful and unexpected result came when the change of the photon frequency due to Comptonization on the hot electrons was taken into account. The CMBR brightness in the directions toward clusters had to decrease at centimeter and millimeter wavelengths. The corresponding increase of the brightness in the submillimeter band did not excite anybody at the time. This behavior of the CMBR brightness toward clusters was a direct consequence of the solution (Zel'dovich and Sunyaev 1969) of the Kompaneets equation with small y.

Obviously I told Zel'dovich. However, he at that time was not interested in individual objects and their properties: the universe as a whole was his main interest. Therefore, I had no reaction from him during or after this conversation. Nevertheless, he was not against it when I included this topic in one of my talks in the Sternberg Institute seminars, or I spoke about this prediction with radio astronomers. My thoughts about the CMBR brightness change toward the directions of clusters of galaxies are included in the paper Sunyaev and Zel'dovich (1970c). The case of Coma cluster of galaxies was considered. This was at the end of the paper, which YaB usually had no time to read. I had little doubt that he would object to the comments on the effect of clusters of galaxies on the CMBR. I was sure everything was correct. It was known that differential observations to detect this effect are much easier than absolute measurements. I learned this from conversations with Aleksandr Salomonovich, Yury Pariiskii and Kazimir Stankevich. It allowed me to dream that the effect would be observed earlier than the global spectral distortions due to energy release. That has proved to be the case.

In 1971 the UHURU spacecraft confirmed that the nearest rich clusters of galaxies are very bright X-ray sources. Scientists participating in the discussion in the Sternberg Institute All Moscow Astrophysics Seminar had very different opinions about the origin of this X-ray emission. The majority of them liked the model of inverse Compton scattering of CMBR photons on ultrarelativistic electrons accelerated in the bright radio sources or coming from shock waves in numerous supernova remnants in the galaxies belonging to the cluster. YaB and I were happier with the thought that this might be the result of free-free emission of the hot intergalactic gas. Such a model was proposed by George Field. It was necessary to look for independent methods that could prove the existence of intergalactic gas in clusters. This time, already at the end of 1971, Zel'dovich began to request that I write a separate paper on the thermal effect on the CMBR toward clusters of galaxies. Then he accused me as usual that I am not "a writer" and finally dictated to me himself the first page of the paper that was submitted to Comments on Astrophysics and Space Physics (Sunyaev and Zel'dovich 1972). YaB was right as usual; it was important to write a clear separate paper.

The peculiar motion of a cluster was also able to cause a significant decrease (or increase) of the CMBR brightness just due to the Doppler effect influencing photons scattered by electrons moving together with the whole cluster relative to the unique frame in which the CMBR was isotropic. We both knew about the "kinetic effect" at that time and this is distinctly mentioned in Sunyaev and Zel'dovich (1972). However, our detailed paper on the "kinetic effect" (Sunyaev and Zel'dovich 1980) was published much later.

I remember well my first talks when I tried to describe the thermal effect to physicists. For me the most interesting fact was that this effect if observed would permit a demonstration that the CMBR originates at redshifts greater than the redshift of the cluster itself. Some physicists and astronomers at that time still had doubts about the cosmological origin of the CMBR. I was excited that the spectral dependence of the effect and its amplitude were independent of redshift. This was really unusual; it opened a way to observe very distant clusters. Nevertheless, the audience was usually much more interested in the possibility of proving the existence of hot intergalac-tic gas in clusters and disproving the hypothesis of a nonthermal origin of the X-ray emission due to inverse Compton scattering on relativistic electrons. It is rather difficult to say that the reaction to my first talks was enthusiastic. The information about the physics of the effect was perceived silently and with obvious distrust. However, there were exceptions. Yury Pariiskii began attempts to observe the effect in the direction of the Coma cluster of galaxies after several conversations with me in 1970 and 1971. A rumor of detection of the effect (Pariiskii 1972) was one of the reasons why Zel'dovich started to press me to publish the "separate paper" about the effect.

Gas in clusters has a small Thomson optical depth. The rare single scatterings of a small fraction of the photons crossing the cluster defined the change of the CMBR brightness. I was very curious and wanted to find the kernel of the integral equation which could lead to the Kompaneets equation after a Fokker-Planck type expansion. It turned out to be not a simple task. Practically ten years went by before the kernel describing the profile of the line after single scattering was ready for publication (Sunyaev 1980; see also Sazonov and Sunyaev 2000, where the kernel taking both Doppler and recoil effects into account was obtained). This kernel allowed one to find the spectral dependence of the effect in single-scattering approximation. Naturally this spectrum fully coincided with the spectrum obtained by solving Kompaneets equation.

Here I am glad to write words of gratitude to the radio astronomers who spent a significant part of their lives to detect thermal effect and to make it possible to use these measurements for the purposes of cosmology. I should mention John Carlstrom, Mark Birkinshaw, and Francesco Melchiorri first.

Small-scale fluctuations of the CMBR

I remember being very impressed by Joe Silk's articles (1968b,c) where he, for the first time, wrote about small-scale damping5 of density perturbations due to radiative viscosity, and he indicated the simplest equation for adiabatic perturbations in the radiation temperature,

Pm T

Of course, everybody was familiar with this relation, but in Silk's article it was used to predict the level of expected angular fluctuations of the relict radiation. For me it was easy to agree that it had been exactly like this until the moment of recombination, when there would be mixing and blurring of radiation fluctuations on small scales. This simplest and beautiful equation was valid only under the approximation of instantaneous recombination.

Some time in the fall of 1968 I had come up with an approximate analytic solution describing hydrogen recombination. This allowed me find an analytic expression for what is now called the "visibility function" that describes the zone from which photons, freed by recombination, come to us without further scattering. Later this derivation was included in Sunyaev and Zel'dovich (1970c), which reached the journal in June 1969. According to the WMAP satellite, the redshift where the peak of the visibility function is located, and its effective width differ by just a few percent from the value obtained in those early years.

5 I should mention that I earlier heard about the importance of viscous damping from Andrei Doroshkevich, but Silk's papers reached us before Andrei finished his work.

Our interest in the amplitude of primary CMBR fluctuations was increased by the statements by radio astronomers (first of all, by Yury Pariiskii) that the measured fluctuations were substantially weaker than what Silk had predicted. We needed a more realistic method of estimating the amplitude of the angular fluctuations. That was easy to do. Baryons together with electrons were moving due to the growth of density perturbations at the last stages of recombination. Scattering of photons on moving electrons was changing their frequencies (and temperature), due to the Doppler effect. The resulting change of the radiation temperature was defined by the simple equation:

where ui is the projection of the velocity along the direction of the ray. Taking into account the analytic expression for the "visibility function," we obtained the expected value for the amplitude of angular fluctuations on the angular scale of tens of minutes of arc at the level of 2 x 10_5. This is close to the value measured later by Boomerang, Maxima-2, WMAP, and many ground-based experiments.

Baryonic oscillations and acoustic peaks

I very much liked a "duck's beak" diagram Zel'dovich once drew on a blackboard in my presence. It described the evolution of density perturbations at different length scales; a version is shown in Figure 4.8. I had read in different articles and reviews that in the expanding universe (as in any object affected by Jeans' instability) density perturbations on scales smaller than a Jeans wavelength had to behave like acoustic waves. I remember a very interesting conversation on this topic with Lev Gurevich, almost blind at ig t

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