by Jaan Einasto
At the last stage I had a problem: initially Zeldovich did not realise that our results show that his pancake model in its original form also has serious difficulties — the absence of fine structure in superclusters, seen both in pictures and in the multiplicity test. To avoid a conflict we formulated this result as follows: “Astronomers usually question whichformation scenario is correct. But both basic scenarios have weak points—perhaps it would be more correct to ask, which physical processes have led to the formation of structure in the Universe ”. In the original adiabatic pancake scenario small-scale waves are cut. In this aspect the Zeldovich scenario is practically identical to the neutrino-dominated dark matter scenario. This possibility was discussed in the paper.
In late 1981 I was visiting ESO to analyse the large scale structure. In collaboration with Dick Miller we prepared several movies where the third dimension was visualised by rotation of the galaxy sample (Einasto & Miller, 1983). I used the Huchra ZCAT data to compile several absolute magnitude (volume) limited catalogues of galaxies around the Virgo cluster, in the region between the Virgo and the Coma superclusters, and in the large void between these superclusters, the Northern Local Void. The program to rotate the galaxy sample was written by Dick Miller; he also prepared the original film by photographing individual plots of each time step after rotating the file on a computer monitor. The final copy of the film was made a few months later in the Tartu University photo-labor.
The first demonstration of the original movie was in the ESO conference room on December 22, 1981. All participants of the project looked with excitement and curiosity at how the galaxies are actually distributed in space — the title of the movie was “The Universe as it is”.
The first parts of the movie showed the structure of the Virgo supercluster; some views of this supercluster are shown in Fig. 7.1. The most important impression from the movie was: there exists no isolated field galaxies. All galaxies seen in the movie belong either to clusters/groups forming the cores of superclusters, or to filaments/chains of galaxies. The general impression of the structure of the Virgo supercluster showed its spider-like distribution of galaxy strings, which started from the Virgo cluster in various directions. A similar movie was made by Brent Tully using his HII radio observations of distances of galaxies in the Virgo supercluster; he showed the movie in the Tallinn symposium on 1977. Our movie contained more galaxies, but the general appearence was very similar.
Other parts of the movie showed large regions behind the Virgo cluster in the direction of the Coma and the Hercules superclusters, and the very large void between these superclusters. Here a thin network of galaxy filaments joining the Virgo supercluster with the Coma and Hercules superclusters was clearly visible. No sheets of galaxies which could separate voids were found. Our movie was screened at the IAU Symposium on Large-scale Structure in Greece in summer 1982, see below. The movie is included in the website accompanying this book. Using a bit more complete sample of nearby galaxies in ZCAT I prepared jointly with Dick Miller and his students a new version of the movie. The new version is called “The real Universe”. The final version was prepared at the NASA Ames Research Center, and both versions were digitised at the Tartu University Media Center.
To check the possible presence of galaxy walls which could isolate neighbouring voids I developed a simple algorithm to study the connectedness of empty or filled regions in the density field. My results showed that there exists no isolating surfaces between large voids defined by superclusters. More on this in the next section.
At this time Jan Henrik Oort was preparing a review paper on superclusters (Oort, 1983). To discuss the structure of superclusters, Oort invited me to the Netherlands. However, under Soviet rules I had no permission to visit the Netherlands during this visit, so we agreed with Oort to meet in Bonn, the German observatory closest to the Netherlands. I gave a seminar talk at Bonn University Observatory on December 28, 1981, and screened our recent movie.
Later we continued the discussion with Jan Oort privately. We agreed that there exists strong evidence for the formation of galaxies in chains: the velocity dispersion of groups and galaxies perpendicular to the chain axis is practically zero; main galaxies of clusters are elongated along the axis of the chain, as seen in the Perseus chain by Jõeveer et al. (1978) and Einasto et al. (1980a). Further, there are practically no galaxies in voids, but low-density primordial matter should exist there according to numerical simulations.
These results were important in several aspects. First, this was the earliest demonstration that no galaxies form in voids, i.e. galaxy formation is a threshold phenomenon: in real samples voids are empty; in simulations voids contain a rarefied sample of smoothly distributed isolated particles. This is the basic property of biased galaxy formation, see below. Secondly, galaxy formation occurs in situ in chains and clusters. Third, all previous structure formation scenarios had weak points, and a new better scenario had to be suggested. When I read the published version of the Oort (1983) review, I was happy to notice that Jan used in the review our pictures on the distribution of galaxies and clusters, and also Figures (7.2, 7.3) to show quantitative differences between observations and main theoretical scenarios. Also the general style of the review was in the same spirit as our discussion in Bonn.
We had our discussion in a cafe near the Bonn railway station. It was a beautiful winter day, and when scientific discussions were finished, Jan noted that in cold winters there is a skating tour in Holland. The tour is called Eleven Cities Tour, and it is almost 200 kilometres long on frozen canals, rivers and lakes between the eleven historic cities in the North of the Netherlands. The tour starts very early in the morning, and Jan said that it is very nice to skate through the winter landscape. To my question of whether Jan covered the full distance, he modestly answered: “in the last time only two thirds ”. The length of our Tartu ski marathon is 63 km, so he skated a distance twice the Tartu marathon!!! And Jan Oort was 82 years old when we discussed the structure of superclusters in Bonn.
I presented our results at the IAU Symposium on the Early Evolution of the Universe and its Present Structure, which took place in Crete after the IAU General Assembly in 1982 (Einasto et al., 1983b). Our main conclusions were:
(1) the basic structural elements in the Universe, larger than clusters of galaxies, are strings/filaments of galaxies, groups and clusters;
(2) no large sheets (flat pancakes) of galaxies have been found, small sheets surround some rich clusters near centres of superclusters;
(3) galaxy strings/filaments connect superclusters to a single intertwined lattice;
(4) no theoretical scenario proposed so far explains all observed clustering properties.
For further discussion of our results reported in 1982 at the IAU General Assembly and Crete Symposium see the sections on biasing and walls.
7.1.2 Topology of the cosmic web
According to Zeldovich’s ideas the evolution of density perturbations starts from pancaking to form flat sheets (walls) (Zeldovich, 1970, 1978). Filaments form by the flow of pre-galactic matter towards the crossing of sheets, and clusters by the flow of matter towards the corners of the cellular network. The first numerical simulations were two-dimensional (Zeldovich, 1978). If extrapolated to three dimensions, the structure resembles cells, with clusters of galaxies forming cell corners, galaxy filaments the cell edges, sheets the cell walls, and voids the cell interiors.
There are two possibilities to interpret the 3-dimensional distribution of particles in simulations and real galaxies. One possibility is to understand the cellular structure as a honeycomb, where cell walls isolate neighbouring voids. This corresponds to the classical pancake scenario, as described above. A different structure is realised if cell walls are so thin that galaxies do not form there. In this case cell walls do not form continuous and isolating surfaces: both galaxy systems and voids form connected intertwined regions.
When we started our study of the distribution o
f galaxies we did not have any prejudice to any theoretical scenario. We wanted to understand how the structure actually looks like. Already our first results indicated that the dominant structural elements are chains or filaments of galaxies, groups and clusters, arranged in superclusters, and that the space between filaments and superclusters is almost void of galaxies (Jõeveer et al., 1977; Jõeveer & Einasto, 1978; Jõeveer et al., 1978). Filaments form a more or less continuous network. The similarity of the observed structure to the simulated structure was obvious, thus we used the term “cellular” for the observed structure. We interpreted the cellular structure as a 3-dimensional lattice or supercluster–void network, filaments forming rods of the lattice, clusters and superclusters as knots, and voids as the interiors of cells.
In the early 1980’s new redshift data available—the first releases of the Harvard Center of Astrophysics Redshift Survey, complete up to 14.5 magnitude, and additional data from the redshift compilation ZCAT, prepared in Harvard by John Huchra and his students. New data allowed us to investigate in more detail three superclusters and their vicinity — the Virgo, the Coma, and the Perseus–Pisces superclusters, and galaxy chains/filaments joining these superclusters to a connected network (Einasto et al., 1980a, 1984; Tago et al., 1984).
We focused our attention on the question: Are principal structural elements filaments or rarefied sheets, forming surfaces of cell walls? As described above, I made in collaboration with Dick Miller and John Huchra for this purpose movies of the distribution of galaxies in the Virgo supercluster, and in the large void behind the Virgo supercluster in the direction of the Coma and Hercules superclusters (Einasto & Miller, 1983). Also I developed a program to find connected regions in the density field of galaxies, used in the study of the Coma supercluster by Tago etal. (1984).
We did not find evidence for the presence of wall-like sheets of galaxies between voids — the dominating structural elements were chains (filaments) of galaxies and clusters. Sheets of galaxies exist inside superclusters, an example is the Virgo supercluster, see Fig 7.1. However, sheets do not separate neighbouring voids. These results were discussed by Zeldovich et al. (1982), Tago et al. (1984), Einasto & Miller (1983), and by Einasto et al. (1983b) at the IAU Symposium in Crete in summer 1982. Our main conclusions were: the topology of the cosmic web differs from a simple honeycomb-like topology with a connected network of filaments, and disconnected voids. The connectivity test also indicated that voids form one large connected region.
In the early 1980’s several groups elaborated programs to simulate the evolution of structure using the fast Fourier transform to solve the Poisson equation. First three-dimensional numerical simulations of the evolution of the cosmic web by Klypin & Shandarin (1983), Centrella & Melott (1983), and White et al. (1983) show the formation of a cellular structure, as expected from earlier simpler twodimensional models by Doroshkevich et al. (1980). These simulations were made with the power spectrum cut on small scales. This spectrum corresponds to the neutrino-dominated dark matter scenario, as explicitly stated by all three teams. An essential feature of the evolution in this scenario is the formation of flat objects in the non-linear stage of the evolution, called pancakes by Zeldovich. The subsequent evolution leads to the intersection of the pancakes along filaments, and to the formation of a cellular structure, as predicted by the Zeldovich (1970) analytical arguments.
As discussed above, the models calculated for a neutrino-dominated dark matter Universe had serious difficulties. Adrian Melott simulated the formation of the cosmic web using both the neutrino-dominated (or Hot Dark Matter — HDM) and the axion-dominated (or Cold Dark Matter — CDM) types of dark matter. In 1983 he visited Moscow and Tallinn to discuss his models. A comparison of both simulations with observations showed that the axion-dominated CDM model agrees with observations quantitatively, and thus must be taken seriously (Melott etal., 1983).
Now we had a good model for comparison, and continued the study of the connectivity of both observational and model samples. But here we had a difficulty — so far we had a program by Enn to find the connected systems of particles, but we were also interested in the connectivity of empty regions. So, after some thinking Enn invented another program, which determined the connectivity of regions of the density field. It was much faster than my own similar code used in my preliminary determination of the connectivity. Connected systems could be defined either as over- or under-density regions, using a fixed threshold level. The Enn program is extremely fast and has been in use until now.
Equipped with these new possibilities we continued the connectivity study of observed and model samples. We used various density thresholds to define over- and under-dense regions. New calculations confirmed our previous visual impression and preliminary connectivity calculations, that there are no walls isolating voids, and that superclusters are joined by galaxy filaments to a connected network — the cosmic web. Both in the observed and the model samples voids form just one connected region. Similarly, at a certain threshold density the largest over-density region spans the whole sample volume under study.
Similar results were obtained by Shandarin & Zeldovich (1983) using computer simulations of adiabatic structure-formation models and their percolating properties.
We described our new results at the Crete Symposium (Einasto & Miller, 1983; Einasto et al., 1983b,a) and elsewhere (Einasto et al., 1984; Tago et al., 1984), but did not make any attempt to write a special paper to describe the topology of the cosmic web. But this was an error. During a visit to ESO in 1985 I discovered on the preprint shelf the preprint of the paper by Gott et al. (1986). In this study the same observational database was used, as well as the same simulation by Melott. The connectivity of high- and low-density regions was defined as the topology of the large-scale structure. So far “topology” meant the general character of the universe, an open or closed one etc. Now this term was used to describe properties of the cosmic web, not the universe as a whole.
Gott et al. compared our first results of the cellular model (Jõeveer & Einasto, 1978) with the hierarchical clustering model by Soneira & Peebles (1978). They described our model as a “Swiss cheese” model, in which isolated voids are surrounded by high-density medium. Next authors described in detail our movie shown at the IAU symposium in Crete (Einasto & Miller, 1983) which shows that real data support neither the honeycomb-like cellular model nor the hierarchical clustering model. The authors used the name “sponge” topology to describe the actual structure, where both the high- and low-density regions are multiply connected. To describe quantitatively this property the authors used the genus of the density field.
Reading this preprint I understood that it was high time to describe our own results studying this problem. I discussed the issue with Enn Saar and my other colleagues, and we decided to make the analysis a bit differently. Soon our paper was ready and was submitted to “Monthly Notices”. Also we prepared a preprint (Einasto et al., 1986a) which was sent to all observatories (in the published version Gott et al. (1986) refers to this preprint).
Fig. 7.4 Left panel shows the length of the largest system (in units of the box size) versus the density threshold (in units of the mean density of the sample). E (empty) denotes low density regions, F (filled) high density regions; MEL, GR-1, GR-5, and VIRGO denote Melott simulation, Gramann simulation at expansion factors 1 and 5.2, and the observed sample around the Virgo supercluster, respectively. In models solid lines indicate unbiased samples with all test particles included, dashed lines biased samples, where particles in low-density regions have been removed; for the meaning of lines of observed sample see text. Right panel shows the filling factor (in units of the total volume of the sample) versus the density threshold. Designations as in the left panel (Einasto et al., 1986a).
Our basic observational samples were centered on the Virgo cluster, had a length 20 h −1 Mpc, and were volume limited. The sample A had the apparent magnitude limit m = 14.5 of the CfA survey; the sample B co
ntained galaxies in magnitude interval 14.5… 15.0 and was composed on the basis of a dwarf galaxy radio survey; the sample C was the sum of samples A and B. The number of galaxies in these samples were 524, 486, and 1010, respectively. In Fig. 7.4 these samples are plotted by dashed, dotted, and solid lines.
The Melott simulation sample was calculated for the standard CDM model with density parameter Ωm= 1, it had cube length 32 h −1 Mpc, and had 643 particles in a 643 mesh. The other model was calculated by Mirt Gramann (1987), it was a ΛCDM model with density parameters = 0.2, ΩΛ = 0.8, had a cube length 40 h −1 Mpc, and contained 643 particles in a 643 mesh. For this model two epochs were used, the early epoch at the end of the linear regime of structure growth (expansion parameter a = 1), and the present epoch at the expansion parameter a = 5.2, designated as GR-1 and GR-5 respectively. In models we used all test particles, which corresponds to unbiased samples, and biased samples, where particles in low-density regions were removed.
Observed density fields were calculated with a top hat smoothing using a kernel of size 1.25 h−1 Mpc; for model samples the kernel size was 1 h−1 Mpc. These smoothing lengths applied correspond to the effective size of galaxy groups and clusters; they are approximately equal to the sizes of dark matter halos, the dominant population in the Universe. The biasing threshold level was chosen ≈ 1.5 in mean density units, in this case the biased samples contain about 1/8 of all test particles. By definition these particles are located in high-density regions. The shape of biased model high-density regions is very similar to the shape of observed galaxy samples in the smoothed density field. It should be mentioned that this topology study was the first application of the Mirt Gramann (1987) model with the cosmological constant.