Rashid Sunyaev is Director of the Max-Planck Institute for Astrophysics, Garching, Germany, and Chief Scientist, Space Research Institute, Russian Academy of Sciences, Moscow, Russia.
Meeting and working with Zel'dovich
I became Yakov Zel'dovich's student in March 1965, half a year short of the news of the discovery of the CMBR by Penzias and Wilson (1965a) reached us in Moscow. At that time Zel'dovich (Figure 4.6) was putting together his group at the Institute of Applied Mathematics that he had joined a year before. There were already several people in the group, including Igor Novikov and Andrei Doroshkevich.
For over a year I was the junior member of the team. Before my first meeting with Zel'dovich I had never heard about him. I was proud that in 1963,
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Fig. 4.6. Yakov Zel'dovich on the left, Aleksandr Solomonovch Kompaneets on the right. The inscription was written by Zel'dovich on a copy of the book Rel-ativistic Astrophysics (Zel'dovich and Novikov 1967). The inscription reads: "To dear Rashid, with wishes that the period of Sturm and Drang (see Addition VIII) continues without weakening for the nearest 90 years. Ya. Zel'dovich."
despite intense competition, I, a student of the fourth year, was admitted to the Elementary Particle Physics Chair of my university - PhysTech (the Moscow Institute of Physics and Technology). This Chair was based at the Institute for Theoretical and Experimental Physics - at that time a research center with a proton accelerator, nuclear reactor, more than two thousand employees, and an excellent theoretical department.
The majority of students in our group were looking forward to getting involved with elementary particle theory. We took numerous courses and passed a lot of exams, but instead of the welcome moment of being admitted to the ranks of theoreticians we were offered more and more courses and exams. It was only later that I found out that the Theory Department did not have vacancies for PhD students. We were considered a reserve of knowledgeable physicists for the Institute's experimental groups that had no shortage of PhD student positions.
I remember my first conversation with Zel'dovich. He told me that he was involved in astrophysics, and that would be the topic of my dissertation. I responded that I had over a year left to finish my diploma, and only then could I take a PhD course. Unexpectedly to me, Zel'dovich said that it had been many years since he stopped advising graduate students, and that he was just selecting the best university graduates to work for him. I did not expect such a reaction, but for whatever reason, Zel'dovich, having a change of heart, all of a sudden winked with his right eye and said: "Let us try, but don't get offended. If you fail, then you will need to finish your diploma somewhere else." After hearing this I threw off reserve and repeated what my department chair had said, that astrophysics was a useless science, and I said that I would prefer to work on elementary particle theory. Zel'dovich smiled and promised me that after I helped him solve one or two of the problems in astrophysics that he was most excited about we would both go back to studying elementary particles. I would like to note right away that after I had published, together with Yakov Borisovich (YaB), the very first two articles in the Astronomical Circular (a timely publication of Sternberg Astronomical Institute in the Russian language only) I never went back to my desire to study field theory. Thanks to Zel'dovich! He never reminded me of those words said during our first conversation. At the conclusion of the meeting, he told me that my excellent grades and oral answers to his questions were not sufficient and he would ask me to solve a couple of simple problems and present solutions in a few days. After I had passed this test as well, he said that he would try to transfer me to his group.
For some reason Zel'dovich liked the fact that I had learned a lot about elementary processes not only in the interaction of relativistic particles, but also in the radiation processes in a rarefied plasma and collision of electrons with atoms and ions, recombination, level excitation, and ionization. He also liked that on PhysTech written exams in mathematics I usually scored almost a hundred percent and that I had an offer to transfer to mathematics.
The majority of the people he had hired by that time for his group at the Institute of Applied Mathematics were interested mostly in general relativity and hydrodynamics. He put me on physical cosmology, suggesting that I focus on methods of helium detection in intergalactic gas. This task was very interesting and I soon realized the importance of the two peaks in the temperature-dependence of the emissivity of a hydrogen-helium plasma. Unfortunately these first results were initially published only in the Astronomical Circular. Nowadays hardly anybody knows the publication existed. Later Andrei Doroshkevich joined me in this research. Together, we published a preprint version of our paper and, almost two years later, our paper (Doroshkevich and Sunyaev 1969) was published in Soviet Astronomy Journal. We showed a two-peak curve, at sixteen thousand and a hundred thousand degrees, and we discussed the role of Compton cooling of intergalactic gas. By that time Ray Weymann's article on the same topic was well known in the West. I remember Zel'dovich telling me, after an issue of The Astro-physical Journal with Weymann's article started circulating in our department, that we had to insert a reference to it into our article's proof sheets.
I write about these first works, virtually unknown to anybody, only because they later led me to understand the role of Comptonization in the formation of distortions in the relict radiation (CMBR) spectrum and the effect of Lyman-a resonance line photons, which happened to be so important in the problem of cosmological hydrogen recombination. It was at that time (back in 1965) when Zel'dovich advised me to read an article written by Kompaneets in 1956.
Yu. N. Smirnov describes in his essay in this book how YaB taught himself and his theoretical group in the Sarov (Arzamas-16) nuclear center, how they became proficient in general relativity, and learned astrophysics and cosmology.
Zel'dovich liked to write reviews. This was his way to learn. It permitted him to add his own opinion when describing results of other scientists, to describe his own (often significantly simpler) way to derive important results and to add original details. In 1965 I read practically all the reviews in cosmology and astrophysics he had written at the beginning of 1962 and published in the journals Soviet Atomic Energy, Soviet Physics Uspekhy, Advances in Astronomy and Astrophysics, and in the collected articles and reviews, The Issues of Cosmogony (which was not translated into English). Outstanding reviews (Zel'dovich 1965) written before the CMBR discovery, and immediately after (Zel'dovich 1966), became the basis of cosmology chapters of the excellent books published together with I. D. Novikov. The first, Relativistic Astrophysics, appeared in Russian in 1967 and became the manual for many young (and not so young) scientists. Its 5500 copies sold out immediately. It is a pity that the English translation of these books was greatly delayed despite efforts by Kip Thorne, David Arnett, and Gary Steigman. One reason was the rapid development of astrophysics and cosmology: the authors were too busy adding descriptions of fresh results to the book.
The review of the hot model of the universe (Zel'dovich 1966) is written in beautiful Russian. It is really a pity that the translation into English was of low quality. Now it is possible to read a significantly improved English version of this review in the book of selected works (Zel'dovich 1993). It is very impressive to see how much YaB knew about the hot model at the moment CMBR was discovered. It is a great surprise to see how different in subject and style are the three reviews (Zel'dovich 1966 on the hot model, Zel'dovich 1965 on global properties and instabilities in the universe, and Zel'dovich 1968 on the A term) and how much was known at that time. However, our knowledge now is much deeper and more detailed, and practically all theoretical models and assumptions are confirmed or checked by the observations and detailed simulations that later became possible.
Meeting Yakov Borisovich completely changed my life. From the time I met him up to 1970 my life was full of festivity. Nearly every day he would call me in the morning (or I would call him, when I spent the night in
Dolgoprudnyi, at PhysTech) and ask what was new with me, tell me his own news, and make an appointment to meet. After his death in December 1987 it became emotionally difficult for me to come, at the invitation of his daughters, to the building on the former Vorobiev Road, to the room where he worked and to which he invited everybody - where I was at least two thousand times during two decades of working with him.
I arrived in Zel'dovich's group at a time that was happy for him, and indeed for all astronomy. In Russia many remember the All Moscow Astrophysics Seminars at the Shternberg Astronomical Institute in 1965 to 1968, when they were supervised jointly by Zel'dovich, Vitaliy Ginzburg, and Iosif Shklovsky, exceptional people in their behavior, scientific level, activity, and scope of interests; with Solomon Pikelner prepared at any minute to step up and explain the incomprehensible to physicists; with the young L. M. Ozernoi, A. G. Doroshkevich, I. D. Novikov, N. S. Kardashev, V. S. Imschennik, V. G. Kurt, Y. N. Efremov, V. F. Shvartsman, L. P. Grishchuk, G. S. Bisnovatyi-Kogan, and A. M. Cherepashchuk actively participating; with Evgeny Lifshitz, Isaak Khalatnikov, or Andrei Sakharov showing up occasionally. I remember the conference hall at the Shternberg Institute, usually packed to the limit, with doors open on both sides, behind which clustered the latecomers for whom there weren't enough seats. Many of the young people there later became the cream of Soviet astrophysics.
When The Astrophysical Journal issue with the article on the discovery of the CMBR by Penzias and Wilson (1965a), and a Princeton Group article on the importance of this discovery, reached Moscow, and was received, as far as I remember, by Shklovsky, it naturally caused a sensation and a heated discussion at a seminar in the Shternberg Institute. Iosif Shklovsky immediately termed it "relict radiation." This term has become firmly rooted in Russian science and popular science literature.
I also remember that YaB expressed regret at the seminar that he had held to the cold model of the universe until the discovery of the relict radiation. It was striking how he immediately acknowledged the correctness of Gamow's point of view and delightedly praised it, which was not so simple at that time (as Gamow had fled the USSR in the 1930s, which was unforgivable). In general, YaB has done a lot to ensure that the names of Friedmann and Gamow and their great contributions to cosmology are appropriately reflected in the USSR scientific literature.
He loudly bemoaned his own mistake, when he made an attempt to explain (including in a published paper) the newly discovered phenomenon of radio pulsars as the effect of processes on white dwarfs. At that time, he told me that his mistake was the result of his many years of work in weapons research: it was sometimes necessary during the course of a single night to make a decision about what to do the next day. There had to be only one final option, and it had to be realistic, simple, reliable, and the most economical. Mistakes were not permitted. Nature, he convinced himself time and time again, could allow itself things that seemed at that time absolutely unexpected or improbable, although, from the point of view of physics, those also were entirely natural solutions. In his later years, he, who was absolutely certain that the neutrino has zero mass, radically changed his point of view and used to repeat: everything is allowed that is not forbidden. Not everybody can survive such a radical change in perceptions and start working based on a new philosophy.
YaB was ready to acknowledge the hot model. He was used to accepting the results of straightforward and beautiful experiments and, long before the discovery of Penzias and Wilson, while realizing the importance of Gamow's predictions4 on the existence of the 5- to 6-K relict radiation, supported and recommended for publication in Soviet Physics Doklady the work of Doroshkevich and Novikov (1964) on the compilation of radio observations of background radiation.
To him, the appearance of a new point in the background radiation spectrum was a long-awaited, however unfavorable, experimental fact. He could not but acknowledge this experimental fact and therefore had to agree right away that our universe was hot. During the previous four years, when getting ready to be transferred from Arzamas-16 to Moscow, and during the first two years in Moscow, Zel'dovich, intensely and with great interest, worked on the theory of physical processes in the expanding universe within the frameworks of both cold and hot models. The latter was important in order to find predictions, which were supposed to contradict current and future experimental data and observations.
I remember the first improvised seminars after the discovery of the relict radiation, when YaB talked, as if it were obvious, about the dipole anisotropy as a means of measuring Earth's velocity, and about the presence of a unique reference system that could be defined by this radiation.
4 Zel'dovich knew about every paper by Gamov and his colleagues. At his request librarians at Arzamas-16 had searched everywhere for all of Gamow's old papers. Gamow also knew about Zel'dovich's papers and was following them. I remember how proud I was when a thick package of reprints of his hot model papers reached me. This was in 1968, and this was his reaction to my first papers and preprints I had mailed him. Not too many great scientists knew my name at that time. Every reprint had a stamp with an image of "Gamov's dacha" and several handwritten words.
I remember how I first heard from him at these seminars about the quadrupole anisotropy component in an anisotropic universe, and the unavoidable existence of angular fluctuations of the radiation. Only a year later, reading fresh issues of Nature, Physical Review Letters, and Astro-physical Journal Letters, did I understand that there is a level of knowledge starting from which such things became evident, and cosmologists of this level in Cambridge, Princeton, and Moscow could seize this simultaneously. And then I realized for the first time that to be alongside YaB meant, as a minimum, to be at a world-class level.
As a person who had been denied travel abroad, YaB was long certain that if he were ever allowed to go to some major conference in the West something important would come of it. For almost 20 years, he put it that he had "only sub-orbital velocity:" he was allowed to travel only to Eastern Europe.
In 1967, he was able to get me - his postgraduate student - approved to join a group of young scientists going to the General Assembly of the International Astronomical Union (IAU) in Prague. That was my first and next-to-last trip abroad for more than 12 years of being banned to travel out of the country. Naturally, I remember this meeting well. The mood of the people, carried in the air, was unusual to us, and clearly heralded the imminent arrival of the "Prague Spring." But I also remember YaB, fully busy, escorted by his students and fellows to meet various celebrities (and these meetings were scheduled one after the other). At them I first saw Ed Salpeter, Margaret and Geoffrey Burbidge, Herbert Friedman, the young and active Riccardo Giacconi, George Field, and Dennis Sciama. Professor Sciama was memorable also for being accompanied by a student who later became well known - Martin Rees. I also met Joe Silk for the first time. During these short meetings, YaB managed to say something about his latest work, ask several specific questions, primarily on experimental data, and also let his young students talk, though some spoke English with difficulty. He led us to a swimming pool, where he, as always, swam pleasurably and talked about a movie he had seen the day before. At intervals, he could be seen sitting on a sofa and rapidly writing several lines in his large, expressive handwriting, usually forwarding his notes to I. D. Novikov to be included in the next book.
In Moscow Zel'dovich behaved essentially in the same way: he was usually not late for appointments, of which he had many each day, he regularly went skiing or walking, and he was writing something in thin school notebooks nearly every free minute. Everything he wrote he tried to give away immediately for inclusion in a book or a paper, or simply to be used as food for thought. Sometimes this was a prepared text, sometimes only equations or estimates with questions between them. I have kept many such sheets. However, he quickly understood that I was "not a writer" and very disorganized. As a result, I was left primarily with questions and sometimes equations.
It was striking how he could instantly concentrate, settle himself comfortably, fall silent, and rapidly write. Then, completely unexpectedly, he would come out of this state and begin a conversation on a new topic. If the papers were not given to someone on the spot, they were intended for somebody else, most likely for books. He also valued experimental data, and he was pleased with his pupils' works that predicted straightforward experimental tests.
YaB carried a colossal burden. While we were working in close collaboration with him during 1966 to 1973, he at the same time wrote reviews, worked on a book on low-energy nuclear physics, reissued Higher Mathematics for Beginners, Elements of Applied Mathematics (jointly with Myshkis), very popular books then, and, together with Yury Raizer, worked on a wonderful, serious book, on the physics of shock waves and high temperature hydrodynamic phenomena (Zel'dovich and Raizer 1966), all the while continuing research on the theory of combustion. Two or three times a week he would come to the Institute of Applied Mathematics for several hours, quickly report something on a blackboard, or set up a small improvised seminar, and then have a short conversation with some of his young colleagues.
If initially (in 1965 to 1966) I failed to show him something new, then for the next few days he practically ignored me until I could tell him that I had original and, from my point of view, interesting news. Quite often on the next day he would call me or ask a secretary to find me in a dormitory and invite me to come to his home or to meet with him at one of the institutes where he had other business to attend. He himself worked almost without breaks, and he wanted at least the same from me. At the same time he knew how to, and liked to, rest: he liked to drive a car, travel all over the Soviet Union, and did not forget every year to spend a month on the Black Sea in his beloved Crimea. But even there he worked a lot and sent me letters or sometimes summoned me to Crimea to talk and to find out what I had come up with.
We worked at a mathematical institute where such well-known mathematicians as Mstislav Keldysh, who soon became President of the Academy of Sciences of the Soviet Union, Israel Gelfand, and many others worked at that time. There I began working with outstanding people - Timur Eneev, Ilya Sobol, Vladimir Gol'din, Nikolay Kozlov, Boris Chetvertushkin, and
Lev Pozdnyakov, who remained my friends for life and taught me a lot. YaB approved of this collaboration. Thanks to his recommendations I got acquainted also with the leading specialists in atomic processes - Leonid Vainshtein and Israel Beigman of the Lebedev Institute of Physics, with whom I continue to discuss problems of common interest.
In 1968 Malcolm Longair, a young Scottish (as he made clear to us right away) scientist from Cambridge came to Moscow for an internship in an exchange between the Academy of Science of the Soviet Union and the Royal Society. Prior to that, he had graduated from a Russian language course in England. For us it was a huge event - Malcolm happened to be a kindly and a pleasant person to socialize with. He was a good conversationalist and managed to have a great relationship with all the scientists he happened to meet at the Lebedev Institute of Physics and the Shternberg Institute. He kept company with such giants as Vitaly Ginsburg, who had invited him to the USSR, Yakov Zel'dovich, and even Victor Ambarzumian, who invited him to visit his Byurakan Observatory in Armenia. It was interesting for all of us to observe how he behaved and thought, to listen to him talking about experimental results of Martin Ryle's group and Tony Hewish's radio telescope that detected pulsars. It was most interesting when he talked about the cosmological evolution of radio sources.
I was banned from travel abroad; however, somehow Zel'dovich managed to arrange for me to be present during his meetings with foreign scientists visiting Moscow and to participate in international conferences in Soviet territory. (I need to note that I never worked on defense issues and never had access to any special secrets.) Malcolm and I used to meet and talk after seminars at the Shternberg Institute, then I dared to walk him to the Lebedev Institute, and by the end of his stay we would often go for walks in Moscow. I even used to invite him to my tiny room in a shared small Krushchev-time apartment that Zel'dovich "pushed through" for me. I was very proud of this room of my own, and Malcolm never allowed himself to explain that this pride was groundless.
In those days young scientists of my rank "were not recommended" to see foreigners without supervision of somebody who was more "experienced and tested." I knew that people responsible for security at the Institute of Applied Mathematics and the Academy of Sciences were perfectly aware of my meetings with Malcolm and his regular phone calls to my home (he never called at work). But nobody demanded that I immediately stop these meetings. Sometimes they jokingly asked why we were walking around as a couple, but they treated with respect the articles written jointly with Malcolm when I would bring them for finalizing and sending out to "GLAVLIT" (Main Administration for Literary and Publishing Affairs). Apparently there was some sort of an arrangement behind my back, or maybe it was done to demonstrate to the Royal Society that exchange scientists visiting the Academy of Science had a real opportunity for collaboration.
In a year, Malcolm and I coauthored several articles. We thought about CMBR angular fluctuations due to the presence of the foreground of extra-galactic radio sources (Longair and Sunyaev 1969). I learned a lot from him. That was not only in acquiring skills to write articles in a completely different style than was customary in Soviet journals, but also in presenting papers and formulating my ideas with precision. I will not even mention how he helped me improve my quite mediocre (wretched, to be honest) English. It was much later that I learned that Malcolm did a huge favor for us. After coming back to Cambridge, he visited several leading universities around the world and at seminars there reported what was going on in Moscow in the field of cosmology along with explanations of the major results obtained by Zel'dovich and his group. I am grateful to Malcolm for suggesting to students, immediately upon his return to Cambridge, that they should seek to detect a decrease in the brightness of the relict radiation in the direction of clusters of galaxies, what was later called the "SZ effect". He heard with interest and told others about our work with YaB on angular fluctuations of the relict radiation and the baryon oscillations and on cosmological hydrogen recombination. It was a learning experience for me to work with him on a review of cosmic background radiation (CBR), from radio to 7-rays, and an attempt, never finished, to write a two-volume book on physical cosmology and extragalactic astronomy under the comprehensive name The Matter and Radiation of the Universe. I have to admit that I am to be blamed for this failure. However, I shall always remember how Malcolm piously followed the well-known motto of the Soviet postrevolutionary poets - "not a day without a line." Unfortunately I was not capable of such deeds. I would rather stay up at night fiddling with my equations, thinking over better solutions and clearer graphs. If not for insistence, and, sometimes, strictness, on the part of Zel'dovich, many of the results of these nightly vigils would have never been published.
Why did we publish in these particular journals?
In those far-away years it was not possible to publish a paper, even in a Soviet journal, before it was reviewed by a special expert commission at the Institute. Naturally, this practice caused delays in publication. Later this would become an issue between the journals themselves and GLAVLIT -a special agency responsible for ensuring that no state secrets and no suspicious information, from the government point of view, got into the open press. At the beginning of the 1990s a lot was written about GLAVLIT, so my words are targeted only at Western readers who did not follow the internal Soviet Union problems disclosed during the years of Glasnost and Boris Yeltsyn's rule.
It took even more time to obtain a permit to publish a preprint or send an article to a foreign journal. An article that had passed an expert commission at the Institute had to be turned over to GLAVLIT and then sit and wait for permission for the article to be sent abroad. Normally that took from one to three months. Translation into English was a big problem for us. Very often, our translations done with help of professionals received negative feedback due to unreadable English. It was next to impossible to publish an article in a journal of such a level as The Astrophysical Journal. People who were responsible for mailing articles abroad (and they were the ones who handled all our foreign correspondence) knew that one needs to pay to be published in such journals, and just didn't let these envelopes go through.
That is why Zel'dovich advised me to send a series of articles on the relict radiation to the journal Astrophysics and Space Science, as Zdenek Kopal, a publisher from Manchester, offered not only to publish our articles in two languages - English and Russian - which was politically correct, but also took it upon himself to translate them. Similarly, Martin Gordon's visit to Moscow resulted in the publication in Comments on Astrophysics and Space Physics of a number of articles, which, as we both thought, were quite important. In 1969, I mentioned our problems with publishing our results in a conversation with Stuart Pottash, who at that time was one of the editors of Astronomy and Astrophysics. Sometime later, Stuart sent letters on official letterheads to YaB and myself with an offer to send him articles that he was ready to publish for free, if the referee reports were satisfactory. We then started publishing our work in this journal as well.
It is natural that the bulk of our articles were printed in Soviet scientific publications. Unfortunately, for the majority of the Soviet journals, it took over a year or a year and a half for an article to be published. Sometimes, Solomon Pikelner of Soviet Astronomy managed to publish our group's original articles significantly faster, but sometimes even he failed to do it. The best (but not all) Soviet journals were translated into English. However, translation caused another delay of at least eight to nine months, and the translations were available only at the libraries of the big science centers.
That is why Zel'dovich told me a few times that I had to identify a problem and solve it at least a year prior to my Western colleagues, as they were writing in their mother tongue and they didn't have our problems with translation, slow mail, and GLAVLIT.
He considered preprints as one of the possible solutions to this problem and he went to a lot of effort to get them published regularly at the Institute of Applied Mathematics. While time still was wasted on procedures at the Institute, as well as on waiting for GLAVLIT's approval and mailing, at least there was no need to wait for a year while an article was put on hold by a journal's editorial staff. Also, it was possible to work on translation while procedures at the Institute and GLAVLIT were taking place. Most of the results that I mention below were first published as preprints and sent out to the leading world groups and libraries long before they were published in the journals.
Zel'dovich was very well aware that in his country in the field of cosmology he was equal to none, and that only in the West could the beauty of his theoretical work be appreciated. He used to tell me: "You compete with the whole world, as you practically don't know personally anybody you compete with, and you don't know their intellectual potential and abilities." For a person of his class it was obvious that in the Soviet Union the sciences of mathematics and theoretical physics were outstanding. At the same time, the gap between the United States and the Soviet Union in the area of experimental astrophysics was rapidly increasing despite the country's huge investments in a 6-m optical telescope, the radio telescope Ratan-600, and space research. Not a single great astrophysical discovery of the 1960s - the relict radiation, quasars, radio pulsars, compact X-ray sources, the cosmo-logical evolution of radio sources and quasars - was done in the USSR. And this increased YaB's desire to tell the best observers in the world, as early as possible, about the new ideas generated by his group.
In the spring of 1966 I got interested in CBR in different spectral bands. It was at this time that I became friends with Dima (Vladimir) Kurt, who, with the interplanetary probe "Venera," was observing the solar Lyman-a line scattered by interplanetary hydrogen. Dima used very simple detectors with filters, which made it possible to measure the very intense Lyman-a line brightness using a broad filter (1050-1340 Á) simultaneously with a broadband of wavelengths longer than Lyman-a (in the range 1225-1340 Á). We hoped to detect this line produced by intergalactic plasma and displaced by redshift (Kurt and Sunyaev 1970). It was this that later led me to the idea of external zones of ionized hydrogen in galaxies. It is natural that hydrogen in these zones could have been ionized only if there were a cosmic ionizing radiation background. And, the other way round, the lack of a cutoff in the distribution of neutral hydrogen and the emission measure in these zones allowed an estimate of the extragalactic ionizing radiation background (Sunyaev 1969), something impossible to measure in any other way. It was very important to me that at that time Ed Salpeter valued this work.
In September 1966 I gave a talk at the All Moscow Astrophysics Seminar in the Sternberg Institute where I mentioned hydrogen recombination in the universe, and I noted that, according to the Saha equation, it occurred at redshift z ~ 1300. Dima Kurt came up to me after the seminar and asked: "And where are the Lyman-a line photons emitted by the recombining atoms and displaced by the redshift?" I immediately explained that because of the high-specific entropy of the universe there would be a relatively small amount of these photons, and that they come to us in a range of wavelengths that was observationally inaccessible at that time. But Dima's question sunk into my mind. The optical depth in the Lyman-a line is huge. The cos-mological redshift caused these photons to very slowly escape through the long wavelength wing of the line. With Dmitry Varshalovich of the Ioffe Institute in Leningrad we solved an integral radiative transfer equation for the spectrum of Ly-a radiation from intergalactic gas (Varshalovich and Sunyaev 1968). At that time I was interested in the spectrum of this line, although Kurt's detectors were unable to resolve it. I told YaB about our solution and about Kurt's question. YaB advised me to try to compute the line profile by the method of characteristics, and also to look up an article by Kipper (1950) on the rate of two-photon decay of the 2s level of hydrogen.
To my surprise, the very slow two-photon decay rate (8.1 s_1) was (with the cosmological parameters accepted at that time) more likely to happen than escape of Lyman-a photons through the wing of the Lyman-a line. Knowing the lifetime of the 2s level it was not hard to calculate the strongly delayed hydrogen recombination process, and to find the effect of emission by the two-photon decay on the relict radiation spectrum in the Wien region. Another implication was that the residual ionization could not be lower than 10"4. A result that astonished me was that Compton heating kept the electron temperature close to the CMBR temperature, and before redshift z ~ 150 electron collisions transferred enough heat to the hydrogen to keep it at the radiation temperature. Only at lower redshifts did the hydrogen cool more rapidly, in accordance with the difference in adiabatic indexes of matter and radiation. These results were obtained fairly fast, but I, as always, was slow in perfecting the article. I was naive to suppose that it would occur to nobody else to check how recombination differed from the classical Saha thermal equilibrium solution.
When all results of the Zel'dovich, Kurt and Sunyaev (1968) paper had been obtained, Zel'dovich told me that Iosif Shklovsky from the Shternberg Institute and Igor Novikov from our group were going to the United States to attend the Texas Symposium in 1967 and that I had to immediately formulate all our recombination research results concisely and clearly on a couple of pages and submit them to Shklovsky and Novikov. The world had to know about our results! Almost two years after I learned about the results of this action, when I saw Jim Peebles' (1968) article in The Astrophysical Journal, in which he, referring to Shklovsky's remarks at the Texas Symposium, obtained the same results that we were so proud of.
At that time publications were appearing saying that thermalization of starlight by intergalactic dust might imitate the observed spectrum and high isotropy of the relict radiation. (The accuracy of the spectrum measurements was not very high, and many astronomers didn't doubt that there could be large deviations from a blackbody spectrum.) It was clear that it was necessary to study in detail the physical processes that could affect the CMBR spectrum: is it at all possible to create the blackbody radiation during the evolution of the universe?
I was very surprised, when making the simplest estimates, how incredibly small the Rosseland optical depth of the universe was due to bremsstrahlung. It became large only at z > 108, due to the appearance of electron-positron pairs.
I looked for traces of bremsstrahlung emission of intergalactic gas. In 1967 I managed to demonstrate that in the history of the universe a period of neutral hydrogen was unavoidable, judging by the absence of measurable low-frequency bremsstrahlung in the decimeter range as well as by the upper limit of possible nuclear energy release due to all the existing baryons. The mathematical task was reduced to finding the extremum for a simple functional. YaB liked the result although he thought the answer to be evident. He recommended this article for publication in the Reports of the Academy of Sciences of the USSR (Sunyaev 1968). This journal was considered very prestigious, as only Academy members could publish there or recommend articles for publication. Unfortunately it is little known in astronomical circles, even the part of it translated as Soviet Physics Doklady.
The outstanding paper by Gunn and Peterson (1965) made it clear that intergalactic hydrogen must be highly ionized at z < 2. With Gennady Sholomitsky we thought about the role of Thomson (that is, nonrelativistic) scattering of the CMBR by free electrons and the resulting polarization. At large z (before recombination) the optical depth for this process was very high, but it does not change the spectrum. But after listening to lectures at ITEPh I remembered that Compton scattering by near-relativistic electrons changes the photon frequency and creates photons (double Compton). I had already in my hands an article on the subject by Aleksandr Kompaneets (1956), and a book, Quantum Electrodynamics by Akhiezer and Berestetsky, still one of my favorites, on the bookshelf in my dormitory room.
I learned a lot from Kompaneets' article. (It made even more interesting my occasional meetings with Professor Kompaneets.) At different times YaB would tell me by bits and pieces how they managed to guess at this equation that describes the evolution of the spectrum of radiation exposed to the frequency shifts of Compton scattering by electrons in a hot plasma.
Only the exact form of a diffusion operator in a standard Fokker-Planck equation was calculated. The terms responsible for the recoil effect and induced Compton scattering were found using an elegant trick, based on the condition that the equation predict no distortion of a blackbody spectrum at full thermodynamic equilibrium. Now I know that this is a fairly standard method.
It was amazing to know that even Lev Landau and the famous mathematician Israel Gelfand were engaged in the work of solving the Kompaneets equation at the request of Zel'dovich's group in Arzamas-16. Several times Zel'dovich told me, with sadness, about the role of Sergey Dyakov in the work on the equation. He drowned in the Moscow river in a suburb of Moscow. (Kompaneets referred to Sergey Dyakov and to all the scientists mentioned above in the last lines of his article. It is written there that the "problem was formulated by Zel'dovich.")
Zel'dovich told me that attention was drawn to this beautiful equation during the analysis of the highest plasma temperature that could be reached in a hydrogen bomb explosion. In the early 1950s, it was found that radiative and other mechanisms did not allow the temperature to significantly exceed a million degrees, so the Compton cooling could be neglected. It became clear that the Kompaneets equation was useless for weapons research, and in 1955 these results were declassified.
I wanted to take a look at the original description of the derivation of the equation, obtained at the end of the 1940s. In his article, Kompaneets refers to a report of the Institute of Chemical Physics of the Academy of Sciences published in 1950, which had been declassified for a long time and was located in the Library of the Russian Academy of Sciences. Unfortunately, the report, which I was shown, didn't have a single word on the derivation of the equation and contained only an attempt to find energy losses of plasma due to Comptonization in a cylindrical geometry.
It is natural that the giants who worked on the Kompaneets equation solutions in those far away years were not interested in a time-dependent problem, which is critical for the uniform expanding ionized gas of the early universe. Reading Kompaneets' paper again one sees that the author and his colleagues were not interested in the effect of Comptonization on the radiation spectrum. Their main goal was to find the cooling rate of hot plasma due to this effect, and to bremsstrahlung that provides low-frequency photons for Comptonization. In astrophysics, the complete solution of the Kompaneets equation has not been found, but we managed to find beautiful and simple solutions in particular cases, when it was only a diffusion operator related to Doppler broadening that matters, or only recoil or induced scattering effects dominated (see a review by Pozdnyakov, Sobol and Sunyaev 1983).
Physics of Fluids published an article by Ray Weymann (1965) with an equation identical to the Kompaneets equation, referencing a Livermore Lab report. In 1966 Weymann published numerical calculations for the distortion of the relict radiation spectrum when extremely large energy is released in the plasma. The journal with this article reached us in the spring of 1967, but by that time we, together with YaB, were fully engaged in the work on analytical solutions describing spectrum distortions in useful limiting cases. I was really lucky that nobody before was interested in analytic solutions of the type we found.
The energy exchange between electrons and radiation due to Comptoniza-tion (that is, redistribution of the photon energies in the process of multiple Compton scatterings on hot electrons) is characterized by the parameter
In our article (Zel'dovich and Sunyaev 1969) we found analytic solutions describing spectrum distortions both at small y values and at any value of
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