Dark Matter and Cosmic Web Story

by Jaan Einasto

  Rüütel did not tell anybody about the threats from Moscow and continued preparations for the Supreme Soviet meeting. He asked Vaino Väljas to preside the meeting — this helped to create a favorable atmosphere among russian-speaking delegates of the Supreme Soviet. Also a number of Estonian intellectual leaders were invited as speakers, in addition to members of the Soviet. They could not participate in voting but in their speeches gave support to the declaration. The declaration was very carefully worded to avoid attacks as we planned to separate from the USSR. The declaration asserted Estonia’s sovereignty and the supremacy of Estonian laws over the laws of the Soviet Union. It also laid claim to the republic’s natural resources: land, inland waters, forests, mineral deposits and to the means of industrial production, agriculture etc. in the territory of Estonias borders. The declaration was accepted by a large majority of voters on the meeting of the Supreme Soviet on November 16, 1988.

  I remember this evening very well. I listened to the broadcast of the Supreme Soviet by radio. When the Estonian foreign minister Arnold Green recited the declaration with a solemn voice, I broke out into tears — the first time in my adult life. I understood that I had dreamed of a free Estonia all the time, but had suppressed this dream in everyday life. When the declaration was accepted, all astronomers living in the Observatory rushed out to congratulate each other.

  But the story was not over. A problem was to publish the declaration immediately in the open press, since all declarations and laws come into force only after they are published. The declaration was published in a special issue of the newspaper “Rahva hääl” (Voice of the People).

  Rüütel was immediately ordered to go to Moscow for questioning. He was again threatened and commanded to cancel the declaration. He refused to do so. Some time later the All-Union Congress of People’s Deputies held its Meeting, and Rüütel was strongly advised to declare the abolishment of the Estonian Supreme Soviet declaration. In the Meeting of the Congress over 2500 delegates all over the USSR gathered. The Meeting was also attended by several hundred foreign journalists. But instead of nullifying the Estonian declaration, Rüütel justified it on the basis of economic as well as political arguments. When he finished, the large congress hall was dead silent. Finally Gorbachev clapped his hands a few times. Thereafter, a storm of applause emerged. Within a year or two almost all Soviet republics accepted their own declarations of sovereignty, most importantly the Russian Soviet Federative Republic. The dissolution of the Soviet Union had started.

  This happened in 1988, a year before the velvet revolution in Prague and the fall of the Berlin wall.

  At the same time (first days of November 1988) Remo Ruffini organised in Tallinn a small meeting to discuss the collaboration between Italian and Soviet cosmologists. With him was the director of the Vatican Observatory, George Coyne, and his friend Sergio Romano, the Italian Ambassador to the USSR. For diplomats visiting Soviet republics was a problem, but in this case Remo used his right to take with him some scientists, and Romano is a historian. After the meeting we walked in the beautiful nightly atmosphere of old Tallinn and noticed that in all churches there were people praying for the freedom of Estonia. In one church a folk-ensemble was singing songs of freedom. A year later I was visiting Italy, and Sergio Romano invited me to his home. We discussed the situation in Estonia, and Romano finally asked: “What do you actually want?” My response was: “Our own money and passports, and economic independence.” Romano replied: “But this means secession!” I answered: “Of course.” Romano is also a publicist, a bit later he wrote in an Italian newspaper a detailed review on the development in Soviet Union, citing our conversation.

  On August 23,1989 there was the 50th anniversary of the Nazi–Soviet Nonaggression or the Molotov–Ribbentrop Pact, which divided East Europe into spheres of influence between Nazi-Germany and the Soviet Union. This Pact allowed Germany to attack Poland, and Soviet Union to occupy of Estonia, Latvia and Lithuania. The Popular Front of Estonia jointly with similar Latvian and Lithuanian organisations prepared a peaceful mass demonstration to mark this event. From Tallinn over Riga to Vilnius a continuous chain of up to three million people was formed. The preparations to form the chain were very well made, the route was fixed and sections divided between various organisations who helped to transport people to the right place.

  In 1989 academician Isaak Khalatnikov with his wife Valentina Glebovskaya had their summer vacation in our Observatory guesthouse. Valentina’s roots come from a famous Polish family: one of her great-grandfathers is Hetman Khodkevich, the commander of the Polish–Lithuanian army during the Polish–Russian war in the early 17th century. Also we had a postgraduate student of Ruffini, Daniela Calzetti, visiting Tartu Observatory (now she is an astronomy professor at the University of Massachusetts, USA). So when I drove to our assigned place Valentina and Daniela were also with us. During the trip we stopped at the Helme cemetery and put flowers on the graves of my grandfather Jaan Lammas and grandmother Anna Lammas. One small section near the Latvian border was given to Tartu Observatory. We arrived a bit earlier. At the right moment all people linked hands and started to chant “freedom, freedom”. This protest action against Soviet rule brought the national liberation movements into the spotlight of the world community. During the 13th Marcel Grossmann Meeting in summer 2012 in Stockholm I met Isaak and his wife Valentina. Isaak told me that his wife remembers with pride that she participated in this protest action.

  In spring 1989 the new All-Union Congress of People’s Deputies was elected. This time elections were almost free (at least in Baltic republics), and a number of intellectuals were elected to the Congress. Estonian Popular Front won the majority of seats reserved for Estonia. Among the elected delegates there were several academics from Tartu University: economist Mihhail Bronshtein, social scientist Marju Lauristin, chemist Viktor Palm and some others. Bronshtein in his speech justified the transition to a market economy. Palm was an initiator of the Interregional Group of Deputies (IRGD) and one of the co-leaders of the Group. The five co-leaders included human rights activist Andrei Sakharov and Boris Yeltsin. As its only non-Russian co-leader, Palm became an essential link between the Baltics group of deputies and the Russian reformers of the IRGD.

  Delegates from the Baltic countries had a basic goal — to prepare our countries for separation from the rest of the Soviet Union. The first tactical goal was to make the agreement between the Soviet Union and Germany in 1939 public, and to void this agreement by the Congress. Under pressure from the Baltic countries a committee was formed to investigate the case of the Molotov–Ribbentrop Pact.

  One member in the committee to investigate the Molotov–Ribbentrop Pact case was Endel Lippmaa, a prominent Estonian physicist. He got an invitation to a physics conference in USA, and used this chance to search in US archives for documents related to Soviet foreign policy in 1939. He found not only copies of the Molotov–Ribbentrop Pact and its secret Annex, but a number of other documents, showing preparations of the Soviet Union to get back territories the czarist Russian Empire had lost after WWI. He was clever enough to get for all important documents affirmation from the archives that the copies are correct. One argument of the Russian delegation was that the documents are falsifications by Germans. Lippmaa had foreseen this possibility. He organised an independent analysis of documents which showed that the secret Annex and open documents, written during the Molotov-Ribbentrop Pact signing ceremony, were typed with the same typewriter. In this way for every argument of the Russian delegation he had a well documented counterargument. So, on December 24,1989 the All-Union Congress of People’s Deputies recognised the presence of the secret Annex to the Molotov-Ribbentrop Pact. Also the Congress acknowledged the Pact and its Annex as null and void. This was a great shock for the Russian public since Soviet propaganda had always accused Nazi-Germany of unleashing World War II.

  Chapter 7

  The structure of the cosmic web

  In the 1970’s our main atte
ntion was devoted to the qualitative study of the distribution of galaxies and clusters of galaxies in space. This led us to the discovery of the cosmic web, and to an understanding of the meaning of the structure — the present structure is the remnant of the structure at the time of galaxy formation, and this structure itself depends on properties of dark matter, the dominant population of the Universe. As Zeldovich insisted during the Tallinn symposium, now we need more quantitative descriptions of the structure. This was our main goal in the 1980’s.

  7.1 Quantitative characteristics

  7.1.1 The search for quantitative characteristics

  We summarised our basic observational results on the presence of the cosmic web in a paper to “Nature” (Einasto et al., 1980b). Zeldovich suggested that we should write a similar paper on structure formation theories. The paper was ready in summer 1982, and was sent as a Letter to “Nature”; also we made a preprint of it. Here we showed the distribution of nearby Zwicky clusters and galaxies in the Coma and Hercules supercluster regions, and compared the distribution with basic structure formation scenarios.

  Soon we got an answer from the “Nature” editor with a suggestion to write instead of a letter a review paper on voids, and to compare theoretical models with observations in more detail. So we started to think about how to improve the paper. The presentation of the distribution of galaxies and clusters in our previous papers was basically graphical. But in order to make comparisons with various models of structure formation quantitative tests were needed. This was emphasised already by Zeldovich (1978) in his Tallinn Symposium talk. Thus we started the search for quantitative methods to analyse the structure, which were sensitive to the features we had seen in the observed as well as in the model distributions.

  To make room for quantitative analysis we excluded from the observational part of the paper the distribution of Zwicky clusters. This was used in our later paper on the Coma supercluster analysis (Tago et al., 1984). Only the distribution of galaxies in two thin sheets of thickness 10 Mpc, crossing the Virgo and Coma superclusters, remained. The new analysis confirmed our earlier finding (see Figs. 5.5, 5.4) that galaxy chains, joining the Virgo and Coma superclusters, are very thin.

  In the search for methods to analyse the galaxy distribution Zeldovich suggested using the percolation method. This method makes use of the Friends-of-Friends algorithm to collect particles to a system. Let us draw a sphere of radius r around each sample particle (in our case a galaxy or a simulation particle). If within this sphere there are other particles they are considered as belonging to the same system, i.e. they are considered as “friends”. Now draw spheres around all new neighbours and continue the procedure using the rule “any friend of my friend is my friend”. The procedure stops when for a given neighbourhood radius no more new members can be added — a system is identified.

  This procedure is repeated using increasing neighbourhood radii. If the radius r is small enough, all particles are isolated, i.e. there are no systems of particles, and the length of the longest system is zero. With increasing radius more particles join to form systems. First high-density cores of clusters are formed, thereafter regions of lower spatial density join to systems found with smaller radius, see Fig. 7.1. At each radius the longest system is found. At a certain radius, called the percolation radius, the longest system spans the whole volume of the sample studied.

  Next we tried the correlation function. We already knew that the correlation analysis, used by Peebles and many other investigators for the apparent twodimensional distribution of galaxies, was not very sensitive to the presence of filaments, which we had seen in the spatial distribution, because the correlation function contains no phase information, see below. Now we applied it again, but using three-dimensional data we had for galaxies as well as for models. The left panel of Fig. 7.2 shows the spatial correlation functions for three samples. The absolute magnitude limited observed sample around the Virgo supercluster (using CfA redshift survey, complete up to m = 14.5) is designated as O. The sample A was calculated using the simulation of the adiabatic model by Klypin & Shandarin (1983). H is for the sample generated using the method to find a sample of particles in the hierarchical clustering scenario (it is not an actual dynamical simulation).

  To our surprise we found that the correlation function can also be used to find differences in the spatial structure of our samples. The most important feature of the O and A samples is the presence of a knee in the correlation function, absent in the H model. At small distances the correlation function is sensitive to the distribution of galaxies/particles at small mutual distances. At such small distances the majority of galaxies belong to clusters and groups, which have an almost spherical shape. At larger distances the correlation function feels the presence of strings/filaments of galaxies, which are essentially one-dimensional. Thus the geometry of the structure changes when we move from small to large mutual distances of galaxies/particles. The hierarchical model has no strings/filaments, thus the correlation function is featureless. As we see later, this behaviour is one of the characteristics of the structure’s topology.

  Fig. 7.1 Three views of a connected system of galaxies around the Virgo cluster. Upper panels are found with a neighbourhood radius r = 4 Mpc, lower panels with radius r = 5 Mpc. Using the smaller radius the central dense part of the Virgo supercluster is collected to the system, it consists of two sheets of galaxies on both sides of the Virgo cluster. The larger neighbourhood radius collects to the supercluster also the network of galaxy strings or filaments, which form a spider-like configuration with several “legs”. All distances are expressed using the Hubble constant h = 0.5 (Zeldovich et al., 1982).

  The FoF method allows us to use the length of the largest system as a test. The right panel of Fig. 7.2 shows the maximal lengths of systems of galaxies/particles as a function of the neighbourhood radius r (in this Figure distances are expressed using the Hubble constant h = 0.5). Here we compare the behaviour of four samples: the observed sample O, the models A and H, and the Poisson sample P.

  Galaxies as well as particles in simulations are clustered, this means that at small radii r the length of the longest system grows with increasing r faster than in the Poisson sample. But at larger radii the behaviour of samples is different. In the observed sample O as well as in the model sample A there are filaments joining clusters to a network. These filaments make the formation of longer systems easy, and the length of the longest system grows more rapidly than in the Poisson case. Fig. 7.2 shows that samples O and A have almost identical growth. In contrast, in the sample H at larger r the growth of the length L with radius r is slower than in the Poisson sample. The reason is simple: the density of the field particles of the sample H is lower than in the Poisson sample, since a large fraction of particles are used in clusters. Thus we see that this test is sensitive to the presence of filaments which join clusters to a connected network.

  Fig. 7.2 Left panel: the correlation function of the observed sample O around the Virgo cluster (cube of side 80 Mpc), of the sample generated by the hierarchical clustering model H, and of the adiabatic model A. Right panel: the maximal length LM of connected regions as a function of neighbourhood radius r for four catalogues: O, A, H, and P (Poisson model). All distances are expressed for Hubble constant h = 0.5 (Zeldovich et al., 1982).

  As a further test I suggested using the multiplicity function of systems of galaxies/particles, found for various neighbourhood radii r. At each radius r we counted the number of systems of certain multiplicity (number of galaxies/particles). The frequency of systems of various multiplicity for the neighbourhood radius r = 5 Mpc (for Hubble constant h = 0.5) is shown in Fig. 7.3. The multiplicity is expressed in a logarithmic scale, in powers of 2: 0 corresponds to 20 = 1, i.e. isolated galaxies, 5 to 25 = 32, i.e. medium rich systems, etc. Actually a histogram of multiplicities is shown; between indices i and i + 1 all systems with multiplicities between 2i and 2i +1 are counted.

  Fig. 7.3 Distribution of
galaxies according to the multiplicity of the system. Neighbourhood radius r = 5 Mpc (for Hubble constant h = 0.5). Multiplicity is expressed in powers of 2 (5 corresponds to 25 = 32). Samples are designated as in Fig. 7.2: O — observed, A—adiabatic model, H — hierarchical clustering model, P — Poisson model (Zeldovich et al., 1982).

  This Figure shows that all samples studied have different distributions of multiplicities. The observed sample has approximately an equal fraction of systems of various richness, i.e. there exists a fine structure of systems of galaxies of different richness. The largest fraction of galaxies belongs to one single large system — the Virgo supercluster. The A sample has also one large system, but the distribution of smaller systems is more similar to the Poisson sample distribution, i.e. there are almost no systems of intermediate richness — small-scale filaments.

  One more important difference: in the A sample there exists a large fraction of isolated particles — these are void particles, forming a smooth low-density population in voids, absent in the O sample. The H model has no superclusters and no population of smoothly distributed isolated void particles; multiplicities have a peak at medium multiplicity level.

  Our results were summarised in the revised version of the article by Zeldovich et al. (1982); a more detailed discussion of the analysis was published by Einasto et al. (1984). My original suggestion was to title the paper “Giant voids in the Universe: an eyewitness story of galaxy formation”; this title was actually used in the preprint. The last part of the title emphasised the similarity of the present structure to the structure at its formation. However Zeldovich wanted to have a simpler title, so the last part was omitted. The theoretical part of the paper was written by Zeldovich, while the numerical simulations were made by Shandarin and Klypin. My contribution was the observational part, the quantitative comparison of observations and models, and the final polishing of the paper.