Fig. 2.6 Participants of the Meeting of the Astronomical Council 1953. This Meeting was crucial for the future development of the Tartu Observatory (author’s archive).
After the plenum Kipper invited all the Tartu astronomers to a dinner at his home. After the first glass Kipper glanced at the astronomers gathered around the table (there were not many of us at the time so we fit around it well) and said, “Boys, now it’s time to work”. A special board was formed, which started preparations for the construction of the new observatory. One of the first ventures was to find the location. For that I made bicycle trips North and South of Tartu with my spouse Liia and a student, Ene Humal, looking for uplands the observatory could be built on. An interesting coincidence: our first rest stop was on Tõravere hill, where the observatory was later actually built. Ene soon married Valdur Tiit, the son of my wife’s uncle, and became Professor of Mathematical Statistics at Tartu University.
Fig. 2.7 Grigori Kuzmin delivering his talk at the Meeting of the Astronomical Council 1953 (author’s photo).
In the following years meteorological observations were done in chosen places both North and South of Tartu. We did not expect to find differences in the quality of the images of the stars, but we tried to ascertain possible differences in the number of clear nights, the frequency of autumn mists, et cetera. There were no significant differences between the North and South, so the decision was made in favour of South, where the connection with Tartu was better. To make the final decision for the location, the entire board of the observatory made additional bus rides to compare places. The chosen construction site was the upland of Tõravere, about a kilometre away from the Tartu–Riga road and the Tõravere railway stop. Kipper thought that important considerations were a suitable distance from major highways, so that traffic would not affect our work, especially the astronomical observations, but that on the other hand, bus stops and train stations should still be within a reasonable walking distance. As life in the new observatory has indeed shown, these standpoints by Kipper were very foresightful.
Fig. 2.8 With my wife Liia searching for the location of the new observatory, summer 1953 (author’s photo).
For the new observatory young astronomers were needed, so I started to think about how to prepare students in Tartu University as future astronomers. There were no textbooks on astronomy at University level, so it was evident that there is a need for such a monograph. At this time I had no experience in teaching, so I thought that to write a completely new textbook would be too difficult. Then I looked for existing textbooks in Russian, and found one which was more-or-less suited for our University. With several other young astronomers we translated the book into Estonian, I acting as the Editor. During the editing I discovered that in many places the Russian book is outdated. Thus about a half of the original text of the book was replaced with a new text written from scratch.
In 1957 a Satellite (Sputnik) Observing Station in Tartu University was organized. The first head of the station was Valdur Tiit; a year later I was appointed to this post. At this time orbits of satellites were known only approximately, thus a large team of students was needed for observations. Students were invited basically from the physics department of the University. Then I realized that it is possible to make use of the presence of the Station to give physics students a bit more education in astronomy. I gave regular courses on general astronomy and astrophysics to physics students. Both the practical observing experience and lectures gave good results — more than half of our present staff in Tartu Observatory came to us through the Satellite Station.
Fig. 2.9 With Ene Humal (Tiit) climbing to a geodetic tower during the search for the location of the new observatory, summer 1953 (author’s photo).
The actual construction building work began in spring 1957, and in May 1961 the first astronomers moved to Tõravere, including our family. The main building was not yet finished and for several years our temporary work space was in two apartments.
When I think back to my young years then two aspects in my education were especially important. First, my summers spent in Türgi farm. My grandmother was an exceptionally good organiser of housework. She never gave commands, just some hints on what needed to be done. Also I learned that work must be done whatever your mood is: in farming if some work is not done in a proper way and time, you do not get any harvest. The habit to work systematically came from this experience.
Fig. 2.10 A. Kipper, H. Keres and V. Riives overlooking possible locations for the new observatory, autumn 1953 (author’s photo).
The second important lesson came from my first supervisors at the Observatory, Prof. Rootsmäe and Grigori Kuzmin. They always gave you freedom to think yourself and independently. Their role was to help you to find errors in your work and to give hints on how to do things better. This freedom of thinking is extremely important in science. Tartu Observatory has always been a place where people had the freedom to think without any pressure.
1https://www.cfa.harvard.edu/~dfabricant/huchra/hubble/
Chapter 3
Galactic models and dark matter in the solar vicinity
In the 1960’s I was rather heavily involved in administrative work related to the preparations to build our big 1.5 m telescope and its dome. But parallel to these duties I started to think about how to improve models of galaxies, so that all available observational data on galaxies and their populations could be used in model construction. The general background of these efforts was a dream to learn more about the formation and evolution of galaxies. The first object for a more detailed analysis was our own Galaxy. Soon I understood that the overall structure of galaxies is better seen in external galaxies, so my next object for detailed study was the Andromeda galaxy M31.
3.1 Early Galactic models
3.1.1 Early Galactic models and first hints of the presence of dark matter
In the beginning of the 20th century little was known about the overall structure of the Milky Way system. Star counts suggested that it has a flattened shape, and that it consists of stellar populations of different type. Many astronomers tried to describe the structure of the Galaxy in a more quantitative way.
One unsolved problem was the possible existence of absorbing material near the plane of the Galaxy, which distorts distance estimates of stars. This problem interested Öpik (1915), who tried to estimate the possible density of the absorbing material by calculating the dynamical density of matter near the Galactic plane. For this purpose he calculated a simple dynamical model of the Galaxy. The Galaxy is a flattened system, thus the density in the Solar vicinity can be determined using vertical oscillations of stars around the Galactic plane. (Öpik determined the vertical distribution and velocity dispersion of flat stellar populations, assuming a normal distribution of velocities and spatial coordinates. From these data he estimated the total dynamical density. He found that the density is approximately equal to the density calculated from star counts. In other words: the amount of invisible matter near the Galactic plane is so small that it does not influence the dynamics. This paper seems to be the first determination of the possible presence of dark matter in the Solar vicinity. However, it was published in Russian in a not well-known journal, and remained unnoticed by the astronomical community.
Soon the same problem was studied by Kapteyn (1922). He used the latest observational data to compute a dynamical model of the Galaxy. To calculate the gravitational potential, the Galaxy was represented by 10 concentric ellipsoids of constant density and axial ratio 1/5.1. These ellipsoids were not related to any stellar population, and used only to express the changes of the mean density of the Galaxy. The Sun was placed near the centre of the Galaxy. Using kinematical data and star count Kapteyn was able to estimate the total spatial density of visible stars, as well as the total dynamical density. He noticed that these two quantities can differ due to the possible presence of some dark matter or faint stars. He writes “We therefore have the means of estimating the mass of dark matte
r in the universe. As matters stand at present it appears at once that this mass cannot be excessive “. The total density of matter near the Sun is 0.099 solar mass per cubic parsec. This is probably the first use of the term “Dark Matter” in its present meaning.
The analysis by Kapteyn was repeated by Jeans (1922) using the same data, but a different method of analysis. He comes to a conclusion that indicates the presence of two dark stars to each bright star. Both authors use the overall mean velocity dispersion of stars, not the dispersion in the vertical direction.
In the 1920’s new data on the structure of our Galaxy as well as on the Universe as a whole accumulated rapidly. The rotation of the Galaxy was discovered, as well as the position of the Sun far from the Galactic centre. Also it was found that the Galaxy consists of many stellar populations with different kinematical, spatial and physical properties (spectral class).
All these data were used by Oort (1932) in his study of the force exerted by the Galaxy in the vertical direction. Oort discussed in detail Kapteyn’s study and found that the dynamical density can be determined essentially by the vertical gravitational acceleration. Oort accepted the Sun’s distance from the Galactic centre as 10kpc, and the circular velocity as 300km/s. He calculated several dynamical models. In all models a centrally located massive population was assumed with a mass value, which corresponds to the observed rotational velocity near the Sun. The second population was a flat disk-like population. All models provided fairly consistent results for the dynamical density. Oort accepted as the most probable value 0.092 Solar masses per cubic parsec, very close to the value found by Kapteyn. He also calculated the density due to visible stars, and found a value 0.038 Solar masses per cubic parsec. This difference is often considered as an indication for the presence of dark matter. However, Oort estimated the total expected mass of faint stars, extrapolating the luminosity function. The extrapolated total mass gets very near to the value found from vertical motions of stars.
3.1.2 Density of matter in the Solar vicinity
Problems of the structure and evolution of stars and stellar systems were a central issue at Tartu Observatory. (Öpik (1938) developed the modern theory of stellar evolution based on the burning of hydrogen in stellar cores, which leads to the formation of red giant stars after the main sequence stage. Rootsmäe (1961) applied these ideas to kinematics of stars to find the sequence of formation of different stellar populations; similar ideas were developed independently by Eggen et al. (1962).
Grigori Kuzmin was a student of Ernst (Öpik. He graduated from Tartu University just before World War II, and got a position as an assistant in Tartu Observatory. Just before the war the first rotation curve of the Andromeda galaxy M31 was published by Babcock (1939), and Kuzmin started to think about how to use this information to calculate a dynamical model of M31. Andromeda is rather similar to our Galaxy, and Kuzmin hoped to use data from M31 to find a better model of our Galaxy too. The local structure is better known for our Galaxy, but the general structure of the system can be easier studied in the Andromeda galaxy. A similar approach was used by (Öpik in his determination to the distance of the Andromeda galaxy.
Next Kuzmin turned his attention to our Galaxy. He studied in detail the Oort (1932) paper, and thought about how to get a better solution. Here the central problem was the determination of the dynamical density near the Sun. Kuzmin soon realised that it is not needed to calculate the whole gravitational potential for the cylinder, perpendicular to the plane of the Galaxy at the Sun’s location, as Oort did. The dynamical density is determined by the Poisson equation, which connects the local density and the local values of the second derivatives of the gravitational potential (accelerations). Assuming rotational symmetry of the density distribution, and applying cylindrical coordinates, Kuzmin found that the radial and tangential accelerations can be expressed through the Oort constants of Galactic rotation A and B. The constant A describes the shearing motion in the Galactic disk near the Sun, while B describes the angular momentum gradient in the solar neighborhood, i.e. the vorticity.
The vertical acceleration can be expressed through a similar constant C, which has the same dimension as Oort’s constants. Subsequently this constant was called the Kuzmin constant. Simple estimates showed that C ≫ A, B, thus the local density is determined essentially by the constant C (a similar conclusion was obtained already by Öpik (1915)).
Fig. 3.1 Grigori Kuzmin explaining his formula to calculate the dynamical density of matter in the Galaxy, late 1970’s (author’s archive).
Kuzmin (1952b) found that the constant C is equal to the ratio of the vertical component of the velocity dispersion of stars to the vertical dispersion of star positions. This equality is more accurate the flatter the respective population. There were further problems related to random and possible systematic errors in the determination of both dispersions. Oort calculated the vertical velocity dispersion using radial velocities of stars near Galactic poles, and the thickness of the population using stars near the Galactic plane, i.e. different stars. Instead, Kuzmin used identical stars to calculate the ratio of both dispersions. For velocities he used vertical components of proper motions, and for spatial positions galactic latitudes; both quantities were calibrated using identical parallaxes of stars. In this way errors in distance influence both dispersions in the same way, and cancel each other out. The card catalogue of galactic-equatorial A and gK stars perpendicular to the Galactic plane was collected during the war time. This means that the method to calculate and find the dynamical density was elaborated already in the early 1940’s. However, there was a long way ahead to finish the study (Kuzmin, 1952b). His result was C = 56 ± 5 km/s per kpc, which corresponds to a density 0.05 ± 0.01 Solar masses per cubic parsec.
A few years later Kuzmin (1955) turned to the problem again, and made a reanalysis of his own data, as well as data by Oort (1932) and Parenago (1952). In the new analysis he found a value for the parameter C = 68 ± 3 km/s per kpc, which corresponds to the dynamical density 0.077 ± 0.008 Solar masses per cubic parsec. His student Eelsalu (1959) applied a slightly modified method, and found a value C = 67 ± 3 km/s per kpc for the dynamical parameter.
Approximately at the same time Leiden astronomers worked hard to calculate a new model of the Galaxy, and to find the dynamical density of matter near the Sun. The model by Schmidt (1956) shall be described in more detail below. He accepted the mass density 0.093 Solar masses per cubic parsec.
A very detailed analysis of the vertical acceleration was performed by Hill (1960). He used the same method as Oort (1932), i.e calculated the vertical acceleration for a wide range of distances from the Galactic plane, using radial velocities and density dispersion of K-stars. His result was 0.13 Solar masses per cubic parsec. In the same issue of the Bulletin of the Astronomical Institutes of the Netherlands Oort (1960) analysed recent determinations of the vertical acceleration, comparing Kuzmin (1955), Hill (1960), and Eelsalu (1959) analyses. Again the whole range of vertical accelerations was used as in previous Leiden determinations. His conclusion was that the Hill analysis is the most accurate one, and arrived at an even higher mean density of matter in the Solar vicinity — 0.15 Solar masses per cubic parsec.
So there was a large discrepancy between Tartu and Leiden results. The Leiden studies hint at the presence of a large amount of dark matter near the Galactic plane. The Tartu results showed that, if there is dark matter in the Solar vicinity, the amount should be small. Our collaborator Mihkel Jõeveer studied the problem again. First he reanalysed the motions of K and B stars (Jõeveer, 1968b,a), and confirmed the earlier results by Kuzmin (1955) and Eelsalu (1959). Thereafter Jõeveer (1972, 1974) applied a completely new method to find the vertical acceleration. I gave a detailed overview of this work in my talk at the IAU symposium on dark matter (Einasto et al., 1987).
Jõeveer (1972,1974) noticed that very young populations are not in a stationary state, but oscillate in the z-direction; the oscillation period is invers
ely proportional to the dynamical parameter C. Such oscillations are expected if stars form in gas clouds slightly away from the Galactic plane. After their birth stars are not bound to the gas cloud and start to fall toward the minimum of the gravitational potential in the plane of the Galaxy. The period of oscillations can be determined using ages, velocities and z-positions of young stars. He used data on early B8–B9 stars and cepheids, and found for the dynamical parameter a value C =70 km/s per kpc, and for the density 0.09 Solar masses per cubic parsec.
Bahcall & Soneira (1980) calculated a very detailed model of the Galaxy. A central problem in the mass model was the total amount of matter near the Sun, which was investigated separately (Bahcall et al., 1983; Bahcall, 1984b,c,a; Bahcall & Soneira, 1984; Bahcall et al., 1985; Bahcall & Casertano, 1986). Bahcall (1987) give an overview of earlier determinations of the density determinations, and finds that the total dynamical density exceeds the density due to known stars by a factor of 0.5… 1.5. At the same IAU symposium I gave my review of our work on dark matter. In the discussion after my talk Bahcall raised the question of why the Soviet (i.e. Tartu) studies of the local “missing mass” have given a different answer to those made in the West. My first thought was to explain that based on my experience at Tartu Observatory, Kuzmin had the same ability as (Öpik to find in a complicated situation the proper path to a correct answer. However, I did not want to discuss the matter in the context of the East–West controversy, thus I simply expressed my view that in such a complicated situation further detailed work is needed to find a better value of the local density.
Dark Matter and Cosmic Web Story Page 7