{ J. Einasto Geodeet 6(30) 1994 17-19 }

Öpik as a Pioneer in the Theory of Stellar Evolution

J. Einasto

Tartu Astrophysical Observatory, Tõravere, Tartumaa, EE2444 Estonia

Ernst Öpik on teinud olulisi avastusi pea kõikides astronoomia valdkondades. Ettekandes käsitatakse tema töid tähe-evolutsiooni teooria alal. Olulised tähe arengut ja ehitust määravad tegurid tegi Öpik kindlaks juba 20-ndate aastate alguses. Sel ajal oli valitsevaks arvamus, et tähed alustavad oma arengut punase hiiuna, kuumenevad kokkutõmbudes ja muutuvad valgeteks hiidudeks, ning seejärel jahtuvad ning lõpetavad oma arengu punase kääbusena.

Ta juhtis tähelepanu asjaolule, et sellise arengu korral peaksid tähed oma massi kaotama, sest punaste kääbuste mass on palju väiksem hiidtähtede omast. Kui massi kaotab kaksiktäht, siis peab komponentidevaheline kaugus kasvama. Uurides kaksiktähtede kaugusi jõudis Öpik veendumusele, et tegelikult on kääbustähtedes komponentide omavaheline kaugus hoopis väiksem kui hiidudel. Seega ei saa varasem ettekujutus tähtede arengust paika pidada.

Edasi näitas Öpik, et tähtede kiirgusvõime massi kohta kasvab väga kiiresti massi kasvades. Massiivsete tähtede temperatuurid on kõrgemad, seega peab tähtede energia allikas olema väga sõltuv temperatuurist. Kuna temperatuur kasvab tähe tsentri suunas, peab energia allikas asuma tähe keskmes. Ükski senituntud energiaallikas ei vasta nendele nõuetele, ning Öpik oletas, et tähtede energia allikaks on mingid senitundmatud subaatomilised protsessid. Vastavad protsessid avastatigi peatselt - selleks on nimelt vesiniku "põlemine" heeliumiks. Vesiniku põlemisel tekkiv energiahulk on teada, mis võimaldab arvutada ka tähtede eluea. Päikesesarnastel tähtedel on see mõni miljard aastat. See iga on lähedane Maa eaga, mis leitud radioaktiivsete isotoopide lagunemiskiiruse põhjal, samuti Universumi paisumiskiiruse põhjal. Öpiku arvates pole need kokkulangemised juhuslikud, vaid osutavad Universumi suhteliselt noorele eale kõigest mõni miljard aastat. Seni valitses arvamus, et see iga on vähemalt tuhat korda suurem.

Ernst Öpik has made pioneering contributions in almost all fields of astronomy. The most striking feature in his contributions is freshness of ideas, and the skill to make correct deductions at a time when observational evidence was still rather controversial. In the following we consider his approach to understanding new phenomena in the study of the evolution of stars.

One of the very first published papers by Öpik is devoted to the study of the structure and evolution of stars (Öpik 1915, 1916). Öpik returned to this problem many times later, his record on the problems of stellar astrophysics contains over 60 contributions until 1969.

He first develops a method to calculate stellar densities from apparent brightness, temperature and mass. This is possible for double stars with known orbits and parallaxes. Apparent magnitude and distance yield absolute magnitude, which in combination with temperature determine the surface brightness and radius of stars. Combining these data with masses gives directly stellar densities. Applying his method to 40 binary stars Öpik (1915, 1916) finds for one star, 40 Eri B, a density 25,000 times the density of the Sun. This was the first detection of a white dwarf. Unfortunately Öpik did not believe in this result, and thought that some other explanation is to be found. Both papers were written during his study in the Moscow University.

The next series of papers on stellar astrophysics was published when Öpik was already in Tartu (Öpik 1922, 1923, 1924). In this series Öpik discusses fundamental problems of stellar structure and evolution using observational data on the distribution of stellar luminosities, and statistical data on double stars. In the introduction of the 1922 paper he explains his approach to the problem: "The frequency-distribution of the luminosities of the fixed stars may be considered from two different standpoints. We may regard it as a mere chance distribution, in other words, as the result of a combination of unknown factors; or we may attempt to build up the distribution on the basis of certain hypotheses concerning the nature of the stars and the laws of their evolution". He adopts the second approach and tries to check some fundamental hypotheses concerning the stellar structure and evolution.

At this time astronomers adopted the Russel hypothesis on stellar evolution: stars born as red giants, they first contract to form blue giants, and then cool and move along the dwarf branch (main sequence) towards red dwarfs. The dominating source of energy according to Russel was gravitation or radioactive decay.

It is well known that the mean mass of stars in the main sequence is not constant - O and A type stars have masses 10-30 Solar masses, whereas masses of red dwarfs are only a fraction of the Solar mass. Öpik concludes that, if the Russel hypothesis is correct, the star evolution should be accompanied with mass loss. If mass loss occurs in double stars, the distance between components must increase from blue to red stars of the main sequence, while the expected increase is approximately 20 times. To check this result Öpik (1923) studies double stars, and finds, that contrary to the expectation, the mean distance between components of double stars decreases about 2 times.

Another fact contra Russel hypothesis comes from geological data which indicate that the mean temperature on the Earth surface has been almost constant during the whole geological history. If the Sun evolves according to Russel hypothesis his luminosity must decrease along the main sequence by a factor of thousand, and it is impossible to avoid similar changes of the temperature on Earth.

The first conclusion from these calculations was: Hertzsprung-Russel diagram is not an evolutionary diagram but a diagram of various initial conditions -mass and chemical composition. The energy production per unit mass of blue giants is much higher than that of red dwarfs, thus the energy production must depend on physical conditions in the star. In faint companions of double stars (i.e. on main sequence stars) the luminosity per unit mass is proportional to the mass to the 9th power (Öpik 1923, p. 18). The basic physical parameter which changes among main sequence stars of different mass is the temperature, thus a similar dependence must be valid also for the temperature. Since the temperature rises inwards, the energy source of stars must be located near the centre (Öpik 1922, p. 35).

Öpik discusses possible sources of stellar energy and comes to the conclusion that "the gravitational contraction as the only source of energy would lead to an improbably rapid decrease of the number of faint stars with decreasing luminosity, which contradicts observations", and only a "certain intra-atomic activity of matter can be the main source of stellar energy" (Öpik 1922, p. 45). At this time it was believed that in stellar interiors there was no convection, thus the active matter will be rapidly exhausted near the centre. To replace the active matter there must occur "explosions of intra-atomic character, ... through which large amounts of some active matter ... are transported towards the hot central parts of the stars" (Öpik 1922, p. 45).

With this series of papers Öpik discovered most important factors of stellar evolution - the nature of the Hertzspnmg-Russel diagram, the fact that the energy source is located near the centre of stars and intra-atomic character of the energy. At this time the structure of atoms was known only in very general terms. In order to find more accurately the energy source and stellar evolution Öpik waited until more data on the structure of atoms became available. He continued to think on these problems, and immediately after basic facts of atomic transmutations were available suggested a new much more accurate theory of stellar evolution.

In the Introduction to his major paper on the stellar structure and evolution (Öpik 1938) he again explains his approach to the problem - "stellar structure is a physical, not a mathematical problem. What matters are the premises, not the exact mathematical deductions from given premises; we want to know the actual physical conditions determining stellar structure and evolution; a correct mathematical theory may then easily follow. We believe that a mere qualitative picture, taking into account all the complexity of the conditions in stellar interiors, is still a better approximation to the truth than an exact mathematical theory based on simplifications which do not take into account certain most important factors of stellar structure and evolution".

The first important factor to be taken into account is convection. Since the energy source is located in the centre of the star, this leads to the convection, similar to the formation of convection in boiling water in a kettle heated from below. Due to convection the active matter is continuously replaced and there is no need to assume explosions in stellar interiors as he did in earlier papers. At this time the physical source of energy was found - atomic synthesis, mainly the transmutation of the hydrogen into helium. The energy supplying power of this process was also known, and Öpik was able to calculate models of stellar interiors taking into account energy production and transport.

Öpik considered two cases: (i) the star is fully convective (adiabatic), or (ii) it is convective only in the central parts, in this case its structure is a composite one - the convective core is surrounded by a radiative envelope. In the second case there exist no mixing of stellar matter between the core and envelope, and the chemical composition is also not constant. "In the composite, but originally homogeneous model exhaustion of hydrogen leads to an increase of molecular weight in the core" (Öpik 1938, p. 55). This process continues until the whole hydrogen is used. "A core devoid of hydrogen, thus presumably devoid of subatomic sources of energy, is doomed to collapse on a "Kelvin" time scale, i.e. with gravitation as the source of energy; high densities can be attained, and a super-dense core may be formed. The contraction of the core is a gradual one; instead of blowing up, the envelope gradually expands and adjusts itself to such low values of the effective density and temperature that the release of subatomic energy remains more or less normal. ... A typical giant structure results, consisting of a vast extended envelope of low density in radiative equilibrium, an intermediate zone in adiabatic (convective) equilibrium, ... and a contracting superdense core of zero hydrogen content and no subatomic energy" (id. p. 57-60).

The chemical inhomogeneity and composite structure were omitted by previous investigators, just they are "important factors" determining the structure of giants. Öpik's theory of the evolution of main sequence stars toward giants is now fully accepted, the only basic difference between his theory and modern data concerns the energy source of the giants. According to modern data giants also burn chemical elements to produce energy, first helium to carbon, and thereafter other heavier element until iron. Only after using all atomic “fuel” the core of a giant star collapses under gravity to form white dwarfs or neutron stars depending on the mass.

The amount of energy which is produced during the burning of hydrogen to helium is well-known, thus Öpik was able to calculate the maximal age of stars of different mass. For highly luminous early type main sequence stars this age is very short - about 10 million years (Öpik 1938, p. 98). "Thus, the presence of massive and luminous main sequence stars in the Galactic System we ascribe to stars being continually formed in the place of those which become giants ..." (Öpik 1938, p. 105). The idea of recent origin of blue main sequence stars was commonly accepted only after Ambartsumian's discovery of stellar associations in 50's. His theory of the formation giant stars was generally accepted also only in 50's when Hoyle and Schwarzschild repeated his calculations of the stellar structure. As we see, Öpik was ahead of time over 15 years.

Öpik was able to estimate approximate ages of stars even before the 1938 year paper. He used this knowledge in combination with other time estimates to calculate the age of the whole universe.

At this time the overwhelming view was that the Universe is very old, at least 1013 years. This conclusion was based on the estimate of the age of our Galaxy. In Galaxy we observe a well relaxed system with Gaussian distribution of stellar velocities. The relaxation time by star-star encounters is of the order 1013- 1014 years, evidently the age of the whole universe cannot be smaller.

Öpik (1933) analyses the ages of stars in the Galaxy, and finds: "proceeding to intra-atomic energy, the formation of heavier elements out of hydrogen, we find the maximum ages 5·1010 for the sun and 5·108 for the supergiant".

A completely independent time estimate is given by meteorites and the Earth crust. Öpik finds a maximal age 3·109 years for meteorites by the method of radioactive decay of heavy elements. The same method gives for oldest rocks of the Earth crust 3-6·109 years.

The third independent age is the expansion age of the universe, as determined from the expansion speed (derived by Hubble (1929)). Öpik cites an age ca 2·109 years, and continues: "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".

Summarising the results of these completely independent age estimates Öpik 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 10 to 20 billion years. But the method is the same as suggested by Öpik to early 1930ies.

These examples of the study of the structure and evolution of stars demonstrate Öpik's method to investigate unknown phenomena - the use of different data and various approaches. Experience has shown that to most cases he was able to find the correct answer many years before others, in spite of controversial data and the fact that his results disagreed with the opinion of authorities.

References

1. Öpik, E. 1915, Publ. Russian Astr. Soc, 3, 49.

2. Öpik, E. 1916, Astrophys. J., 44, 292.

3. Öpik, E. 1922, Publ. Tartu Astr. Obs., 25, No. 2.

4. Öpik, E. 1923, Publ. Tartu Astr. Obs., 25, No. 5.

5. Öpik, E. 1924, Publ. Tartu Astr. Obs., 25, No. 6.

6. Öpik, E. 1933, Popular Astronomy, 42, 71.

7. Öpik, E. 1938, Publ. Tartu Astr. Obs., 33, No. 3.