Dark Matter and Cosmic Web Story

by Jaan Einasto

  Next we found that it was not sufficient to consider only the nearby environment of galaxies. To understand the formation and evolution of galaxies their large-scale environment is also important. This led us to the discovery of the presence of a cosmic web with galaxy filaments, filamentary superclusters, and voids between them. This was our third step in the development of a new paradigm.

  The nature of galactic coronas was a mystery; no known population fit all data and theoretical considerations. Finally the solution was that coronas must be made of non-baryonic matter, not yet detected experimentally by physicists. In the solution of this problem the whole community of cosmologists played an important role; the understanding came slowly and was made by many scientists.

  The next step in the development of the new paradigm was the understanding of the need to accept a rapid expansion of the early Universe, called inflation. Our young collaborator Lev Kofman participated in the development of the inflation scenario together with Alexei Starobinsky and Andrei Linde.

  Based on various observational and theoretical arguments we assumed in mid 1980’s the presence of the cosmological constant or dark energy, and included this in numerical simulations of the evolution of the structure of the Universe. Direct observational evidence for the existence of dark energy came in late 1990’s.

  Astronomers are real people who do their work in a certain social environment. Most studies which shall be discussed below were done when our home country Estonia was occupied and annexed by the Soviet Union. This has influenced our work and life. Thus I shall describe shortly our social life and environment. We were surrounded by the “Iron Curtain”, and it was not easy to have contacts with the rest of the world.

  Chapter 2

  Classical cosmological paradigm

  In this Chapter I shall describe what we knew of the structure of stars, galaxies and the Universe in the middle of the 20th Century, when I began my astronomical studies. Actually during this period the modern classical cosmological paradigm or world view emerged. It is interesting to note that in the formation of the classical cosmological paradigm one Estonian astronomer, Ernst Öpik, played an important role. This influenced also our view on astronomy.

  2.1 Astronomy in the first half of the 20th century

  Until the 20th Century cosmology was mostly a philosophical and metaphysical discipline, because very little was known about the actual global structure of the Universe, and the nature of the various astronomical objects within it. In the beginning of the 20th Century most astronomers believed that our Milky Way system is the principal constituent of the Universe. Sir Arthur Eddington (1914) wrote his famous book “Stellar Movements and the Structure of the Universe”, where he identified the Milky Way with the whole Universe. The presence of other stellar systems similar to the Milky Way was discussed but there existed no proof for this. Also the birth of the Universe and its age were only objects of speculations.

  The modern classical cosmological paradigm was elaborated step by step during the first part of the 20th Century. In the following I shall use the term “Universe” to denote the real physical world around us, and the term “universe” for its mathematical model.

  2.1.1 The nature of spiral nebulae

  In the early years of the 20th Century a hot topic was the nature of spiral nebulae — Are they gaseous objects within the Milky Way system or distant worlds similar in structure to our Galaxy? On 26 April 1920 the Great Debate between astronomers Harlow Shapley and Heber Curtis was held in the Smithsonian Museum of Natural History on the nature of spiral nebulae and the size of the Universe. Arguments in favour of both concepts were serious and it was difficult to decide who was right. The debaters did not know that the correct answer was already available.

  This problem interested also Ernst Öpik. In 1918 he delivered a talk at the Meeting of the Moscow Society of Amateur Astronomers, devoted to the study of the structure of the Andromeda Nebula, M31. The paper was published a few years later. Just recently the first relative velocity measurements near the centre of M31 had been published, and Öpik quickly developed a method to estimate distances to spiral nebulae from relative velocities within them. He used Newton’s law of gravity, which relates the speed of motion of a test particle around a massive body with the mass of the body and the distance of the test particle from the body. Öpik noticed that it is possible to substitute the mass with the product of luminosity and mass-to-luminosity (M/L) ratio. Apparent luminosity of the central region of M31 can be determined by photometric observations. He accepted for mass-to-luminosity (M/L) ratio a value of 1.54 in solar units, based on measurements of the stellar luminosity function in the solar neighbourhood. From the estimate for M/L, the observed luminosity and the internal rotation speed of M31 he measured the size of M31 and then obtained the distance of 785 kiloparsecs (kpc). This means that M31 is not within the Milky Way and must be an external independent system. A few years later he made a new estimate (Öpik, 1922a) using new determinations of the luminosity function by Kapteyn & van Rhijn (1920), and data by Jeans (1922) on the mass density in the solar neighbourhood. His new value for the mass-to-luminosity ratio is 2.63 in solar units which gives for the distance of theAndromeda nebula 440 kpc.

  Hubble (1925, 1926, 1929b) found cepheids in spiral nebulae NGC 6822, M33 and M31, using the 100-inch telescope of the Mount Wilson Observatory. This confirmed the large distance and the extragalactic nature of spiral nebulae. The existence of the world of galaxies was accepted by the astronomical community.

  2.1.2 The expansion and age of the Universe

  The modern era of understanding the global structure of the universe began with the publication of the Einstein (1916) theory of general relativity. In 1917 Einstein considered a static universe with cosmological term Λ. Based on this theory de Sitter (1917) suggested a model with Λ but with zero or negligible matter density. The zero matter density universe is called Milne’s universe. A few years later Friedmann (1922,1924) and Lemaître (1927) discovered solutions to Einstein’s equations that contained realistic amount of matter. Einstein & de Sitter (1932) proposed a model with the critical cosmological density. This model contains two parameters — the mean expansion rate of the universe, and its mean density. The expansion rate and density also determine the age of the universe.

  Actually Friedmann found three solutions for the cosmic evolution, one with ever-accelerating expansion, one periodic scenario with evolution from and back to zero radius (the oscillating universe), and the third, where initially the universe is decelerating due to gravity, but after some time the expansion accelerates due to the influence of the cosmological constant. Recent observations indicate that just the third scenario corresponds to the real Universe.

  In the 1920’s radial velocities of some tens of galaxies were measured, and almost all of them showed a shift of spectral lines to the red part of the spectrum — i.e. lines were redshifted. The larger the shift is, the fainter galaxies are, and soon the hypothesis was made that the whole Universe is expanding, the expansion velocity being proportional to the distance to the galaxy. The discovery of the expansion of the Universe is often ascribed to Hubble (1929a). Actually the story of the discovery of the expansion of the Universe is more complex.

  The first steps in this discovery were made by Wirtz (1922,1924) who found that redshifts and distances of galaxies are related. Wirtz (1924) suggests a clear relationship of this phenomenon with the de Sitter (1917) cosmological model. Lund-mark (1924) discussed the curvature of the space-time in the de Sitter universe, and the relationship between distances and redshifts. Lundmark (1925) compares various methods to determine distance to spiral nebulae, and found that distances estimated using novae, cepheids and the dynamical method by Öpik are the most reliable and give comparable results.

  Lemaître (1927) presented his new idea of an expanding Universe, derived the velocity–distance relation, and provided the first observational estimate of the constant of proportionality in this law. In
1931 he proposed that the Universe expanded from an initial point, which he called the “Primeval Atom”. Presently the theory is known as the Big Bang theory. This term was used first by Sir Fred Hoyle in one of his popular radio broadcasts in 1949. Hoyle (1948) and Bondi & Gold (1948) preferred a different theory of the origin of the Universe, called the Steady State theory, where matter is continuously created and the mean density of matter remains constant. According to this theory the Universe has no beginning and will have no end.

  The constant of proportionality of the velocity-distance relation is now called the Hubble constant; it is one of the principal constants not only in astronomy but in physics in general. The reciprocal value of this constant has a dimension of time, and measures the time from the beginning of the expansion if the expansion speed is constant.

  In the first decades of the 20th century most astronomers accepted the view that the whole stellar Universe is very old, of the order of 1014 years. This age estimate was based on the observation that stellar orbits in our Milky Way system are well mixed and relaxed. The relaxation time of this process by star-star encounters is very long, of the order mentioned above, and this estimate was taken as the possible age of the Universe.

  Öpik (1933) realised that the expansion time (called the Hubble time in modern cosmology) is approximately equal to several other completely independent fundamental age estimates. He finds an age ≈ 2 × 109 years, and writes: “if we regard the observed motion of the spirals as real, and trace the changes observed at present backwards, we find that a few thousand million years ago the universe was in a peculiar, more concentrated state, from which it started expanding, possibly as a result of some cataclysm ”. The second independent age estimate is the age of the Earth as derived from the decay of heavy radioactive elements, which is up to 5 billion years. Meteorites also have an age of the same order. The third age estimate comes from Öpik’s studies of double stars and related questions of stellar structure.

  Summarising the results of these completely independent age estimates Öpik (1933) writes: “we may say that the combined evidence presented by meteorites, by statistical data relating to wide double stars, by the distribution of stellar luminosities in globular clusters, and by the observed recession of spiral nebulae, all this evidence points to an age of the stellar universe of the same order of magnitude as the currently accepted age of the solar system: not much more than 3000 million years”.

  Modern data yield for all three ages larger values, from 5 to 14 billion years. But the method is the same as suggested by Öpik in the early 1930’s.

  The expanding Universe can be described by two fundamental constants: the mean expansion rate of space, measured by the Hubble constant, and the mean density of the Universe, expressed in units of the critical cosmological density. The critical density is the amount of matter/energy required to make the Universe spatially flat. A flat Universe has no curvature. If the density is less than the critical density, then the Universe will expand forever according to the classical picture. In the opposite case the density is greater than the critical one, and gravity is strong enough to make the Universe collapse back, the so-called “Big Crunch”.

  Very large efforts have been made to measure the value of the Hubble constant. First measurements by Lundmark and Hubble yielded a value about 500 km/s per megaparsec. The first major correction to this value came in the 1950’s when Walter Baade discovered that there are two types of cepheids. Some of them belong to Population II, which dominate in galactic halos and have a different luminosity–period relation. Also it was found that stars in the most distant galaxies, observed by Hubble, were actually star clusters. A detailed description of efforts to determine the Hubble constant is given by Huchra1. A special role in these efforts was played by the 200-inch Hale telescope in the Mount-Palomar observatory (Sandage, 1961; Sandage & Tammann, 1976).

  By the end of the 1970’s there were two schools debating on the correct value of the Hubble constant. Allan Sandage and his longtime collaborator Gustav Andreas Tammann favoured a value about 50 km/s/Mpc, whereas Gerard de Vau-couleurs (1978) and Sidney van den Bergh (1972, 1973) obtained values around 100 km/s/Mpc. This debate was settled when new methods were used, in particular the Hubble Space Telescope Key Program, a number of high-resolution observations of fluctuations of the cosmic microwave background (CMB) radiation, and observations of the spatial distribution of galaxies in the Sloan Digital Sky Survey.

  An important property of the expansion of the Universe is its smoothness. Sandage & Tammann (1975) write: “The local velocity field is as regular, linear, isotropic, and quiet as it can be mapped with the present material. The lack of measurable velocity perturbations, in spite of the observed density inhomogeneities, suggests that the gravitational potential energy is small compared with the kinetic energy of the expansion (provided that there is no high-density, uniform intergalactic medium), and hence that q0 < 1/2”. The expansion parameter q0 = 1/2 × Ω, where Ω is the mean matter/energy density of the Universe in units of the critical density.

  For an “empty” Milne’s model universe with density parameter Ω ≪ 1, the age of the universe is 1/H0, or 9.7 gigayears (Gyr) for h = 1, and 19.4 Gyr for h = 0.5. Here and in the following text we use the Hubble constant in dimensionless unit h, defined as follows: H0 = 100 h km s−1 Mpc−1. For a universe with critical density (Einstein–de Sitter model) the age is 2/3 of that for the empty universe. For the Hubble constant h = 0.7, and an empty universe, as assumed in 1960’s, the age of the universe is 13.5 Gyr. This age is considerably less than the age of oldest globular clusters, as estimated from the theory of stellar evolution in 1960’s. Thus there was an inconsistency between various cosmological parameters.

  2.1.3 The mean density of matter in the Universe

  Known objects in the Universe which contribute to the matter/energy density are galaxies, intergalactic gas and radiation. This was the common understanding in the middle of the 20th century. The contribution of radiation to the matter/energy density is in the CMB which makes up about 5 × 10−5 of the total density. Thus the basic constituents are galaxies and intergalactic matter.

  The mean density due to galaxies can be determined using the mean luminosity density calculated from the luminosity function of galaxies, and the mean mass-to-luminosity ratio of galaxies. Estimates available in the 1950’s indicated a low-density Universe, Ω ≈ 0.05.

  2.1.4 The distribution of galaxies

  Already in the New General Catalogue (NGC) of nebulae, composed from observations by William and John Herschel, a rich collection of nearby galaxies in the Virgo constellation was known. de Vaucouleurs (1953) called this system the Local Super-galaxy; presently it is known as the Virgo or the Local Supercluster. Detailed investigation of the distribution of galaxies became possible when Harlow Shapley started in the Harvard Observatory a systematic photographic survey of galaxies in selected areas, up to 18th magnitude (Shapley, 1935, 1937, 1940). Shapley discovered several other rich superclusters, one of them is presently named the Shapley Supercluster. These studies showed also that the mean spatial density of galaxies is approximately independent of the distance and of the direction on the sky. In other words, the Harvard survey indicated that galaxies are distributed in space more-or-less homogeneously, as expected from the general cosmological principle.

  A photographic survey was made using the 48-inch Palomar Schmidt tele-scope.Abell (1958) used the Palomar survey to compile a catalogue of rich clusters of galaxies for the Northern sky; later the catalogue was continued to the Southern sky (Abell et al., 1989). Using apparent magnitudes of galaxies approximate distances (distance classes) were estimated for clusters in both catalogues. Zwicky et al. (1968) used this survey to compile for the Northern hemisphere a catalogue of galaxies and clusters of galaxies. The galaxy catalogue is complete up to 15.5 photographic magnitude. Both authors noticed that clusters of galaxies also show a tendency of clustering, similar to galaxies which cluster to form groups an
d clusters. Abell called these objects superclusters; Zwicky called them clouds of galaxies.

  A deeper complete photographic survey of galaxies was made in the Lick Observatory with the 20-inch Carnegie astrograph by Shane & Wirtanen (1967). Galaxy counts were made in cells of size 10′ × 10′, and the distribution of the number density of galaxies was studied.

  The Lick counts as well as galaxy and cluster catalogues by Zwicky and Abell were analysed by Jim Peebles and collaborators to exclude count limit irregularities (Peebles, 1973; Hauser & Peebles, 1973; Peebles & Hauser, 1974; Peebles, 1974a). To describe the distribution of galaxies Peebles introduced the two-point correlation (or covariance) function of galaxies (Peebles & Groth, 1975; Groth & Peebles, 1977; Fry & Peebles, 1978). This function describes the probability of finding a neighbour at a given angular separation on the sky from a galaxy. On scales ≥ 25 h−1 Mpc the correlation function is very close to zero, i.e. the distribution of galaxies is essentially random.

  The conclusion from these studies, based on the apparent (2-dimensional) distribution of galaxies and clusters on the sky, confirmed the picture suggested by Kiang (1967) and de Vaucouleurs (1970), among others, that galaxies are hierarchically clustered. However, this hierarchy does not continue to very large scales as this contradicts observations, which show that on very large scales the distribution is homogeneous. A theoretical explanation of this picture was given by Peebles in his hierarchical clustering scenario of structure formation (Peebles & Yu, 1970; Peebles, 1971a).

  2.1.5 Structure of the system of stellar populations