Modern Development of Space Physics1

J. H. Jeans, London.

Until recently, astronomy dealt almost exclusively with the sun, the moon, and the planets; the stars were only unimaginably distant luminous points, of little interest. Now Urania has gone beyond the speck of dust that we call the solar system, and lays claim to the entire universe; the astronomer’s interest is concentrated almost exclusively on the stars. The dynamical astronomer, for example, has lost interest in the motions of the planets and their satellites and studies the distribution and motions of the stars in the hope, at least, of discovering the general plan of the structure and mechanism of the universe; for him the universe is a single dynamical system, formed of innumerable particle-stars, each of which attracts another according to the law of universal gravitation.

The astronomical physicist is interested in the stars from another point of view. For him each individual star is an entire physical system. It is a crucible in which matter is subjected to the action of temperatures and pressures that are utterly inaccessible to the terrestrial physicist. By studying the radiation of the stars, the astrophysicist tries to understand their physical structure, to discover the source of their energy, and to understand the mechanism by which energy is transferred to the surfaces of the stars, subsequently being discharged into space in the form of radiation. In this way there is hope of learning about properties of matter that are inaccessible to the terrestrial physicist because of the limited range of physical conditions at his disposal. I will permit myself to make a comparison, accurate, at least, with regard to scale: bacteria in a raindrop can learn something about the properties of water by manipulating the particles of the drop by means of their negligible forces; but they can also learn something by observing Niagara Falls, which lies beyond their power.

The object of astrophysics is very much like Niagara; the ultimate goal of astrophysics is to merge cosmic physics with terrestrial physics in such a way that an all-embracing science results. Only after this has been accomplished will it be possible to understand the basic tendencies and facts of the physical universe.

Interpretation of Stellar Spectra

Only one method is suitable for this purpose—the study of the radiation of different stars. If we set aside unscientific conjectures, it may be said that astrophysics was born in 1863, when Huggins combined a spectroscope with a telescope and found that certain lines of stellar spectra coincide with lines that, in terrestrial laboratories, are emitted by known chemical elements. Earlier astrospectroscopists were convinced that they were studying the “chemistry of the stars,” but now we know that in fact they were beginning the investigation of a fundamental problem in stellar physics. For example, it was found that the spectrum of Sirius gives very strong hydrogen lines and very weak calcium lines. In the solar spectrum the relative intensity of these lines is in the opposite relation: the calcium lines are strong, the hydrogen lines weak. It was formerly concluded that hydrogen predominates on Sirius, and calcium on the Sun. Assuming that Sirius must someday turn into a star like our Sun, astrophysicists concluded that matter must gradually be transformed from hydrogen into calcium and other more complex elements. Thus, the old hypothesis seemed to be confirmed: that more complex elements were formed by gradual evolution from the simplest ones.

The true interpretation of these old observations, as was convincingly shown by the investigations of Saha, R. Fowler, and Milne, consists simply in the fact that on the surface of Sirius there is a temperature at which hydrogen especially actively emits and absorbs radiation; on the surface of the Sun the temperature is lower, hydrogen there is relatively inert, while calcium, iron, and so forth are active. Just as a physicist in the laboratory can obtain different spectra in one and the same vacuum tube by changing the method and conditions of excitation, so nature produces different spectra from one and the same stellar material at different temperatures.

It is clear that this circumstance deprives stellar spectra of any direct significance for understanding evolution. The spectra of stars tell us only about the temperature that presently prevails on their surfaces. If we arranged stars in the order of their ages, comparison of their spectra would show us only that their surfaces become hotter or colder; we would obtain no data whatever about chemical changes in the matter of stars.

Sizes of Stars.

However, knowledge of the temperature of the surfaces of stars opens the door to further valuable information. The hotter the surface, the more vigorously it radiates heat; knowing the temperature of a star’s surface, it is easy to calculate its radiation from \(1\ \mathrm{cm}^2\) of surface. For example, the Sun radiates approximately 90,000 calories per minute from \(1\ \mathrm{cm}^2\), which corresponds approximately to the power of an 8-horsepower machine. The hottest stars, in all probability, radiate from \(1\ \mathrm{cm}^2\) an energy at the very least 1000 times greater than the Sun.

In this way one can estimate the radiation of a star from \(1\ \mathrm{cm}^2\) of its surface. We can also estimate the radiation from the entire surface. This is at once calculated from the distance and the apparent brightness of the star. Simple division gives the magnitude of the star’s surface and, consequently, its radius and volume. The calculated radii of stars range from radii 300 times greater than the solar radius (Betelgeuse) down to 0.03 of the solar radius (the companion of Sirius).

It is well known that the diameters of certain stars have recently been directly determined with Michelson’s interferometer1, and the measured values coincide almost completely with the radii calculated by the simple method indicated. The interference method is applicable only to the very largest stars, but at the other extreme of the scale the theory of relativity came to the rescue. In the radiation of the companion of Sirius there was observed a displacement of spectral lines toward the red, predicted by Einstein as a necessary consequence of the theory of relativity2. The magnitude of the displacement found agrees exactly with the value of the radius calculated for the star by the method indicated. Much that was sensational has been written about these measurements of the sizes of Betelgeuse and of the companion of Sirius; however, it should be remembered that although the methods are new and represent enormous interest and importance, the results proved to be precisely those which everyone expected; they are practically inevitable, as a simple arithmetical calculation shows. There is only one shortcoming in this calculation. It is based on the assumption that the surfaces of stars emit their full thermal radiation like the surface of the Sun. If stars were transparent bodies, like planetary nebulae, or, conversely, solid bodies like the Moon, then the assumption made would be erroneous, as would have been revealed by observations.

The observations set forth have shown us the substantially new and positive fact that Betelgeuse and the companion of Sirius are not

neither transparent nor solid bodies, but perfect radiators like the Sun. Moreover, the three stars in question—Betelgeuse, the Sun, and Sirius’s companion—differ among themselves to the greatest degree possible for stars: they approximately represent the two extremes and the middle of the stellar scale, whatever its arrangement. Hence it is natural to suppose that all stars are perfect radiators, both with respect to the mechanism of radiation and in the similarity of their structure.

PHYSICAL STATE INSIDE STARS.

What, then, is the mechanism of radiation? And what can be said in advance about the physical state of stellar matter? Formerly spectroscopists, proceeding from an erroneous analogy with laboratory experiments, assumed that a heated gas always gives a line spectrum, while a continuous spectrum, like that of the stars, can be emitted only by solid and liquid bodies. Now everyone understands that this view is mistaken: the continuous spectrum of a star indicates only that it is opaque, and the question of the structure of the star remains open.

It is now the generally accepted view that stars consist of matter which, owing to the high temperature of the star, has to a considerable extent decomposed into its constituent electrons and nuclei, which move almost independently, like the molecules of a gas. Under more peaceful conditions, electrostatic attractions would quickly unite the wandering nuclei and electrons into complete atoms and molecules; but they are powerless in the general whirl of flying corpuscles and under the shattering blows of radiation quanta of high frequency, corresponding to the high temperature inside the star. When in 1917 I first expressed this view (Phil. Trans. 218, p. 209), I thought it entirely new, but subsequently learned that as early as 1644 Descartes had guessed that the Sun and the fixed stars were created from matter “which possesses such turbulent motion that, colliding with other bodies, it is broken into infinitely small particles.” My supposition is not a conjecture; it has incontrovertible scientific grounds. In 1907 Emdén published calculations1 concerning the internal state of the Sun and the stars. He supposed that the stars are masses of gas in equilibrium, like the lower clouds of the terrestrial atmosphere. This is a case of so-called “adiabatic” equilibrium, in which the presence of currents sufficient for the constant mixing of the constituent gases is assumed. On the basis of this assumption, Emdén wrote that if the Sun consisted of air, or of other diatomic gases of equal molecular weight, then the tempe-

ature in the center would have to reach 455 million degrees. If the Sun consisted of hydrogen, or of another diatomic gas with molecular weight 2, then the central temperature would be 31.5 million degrees. These temperatures are so high that no atom or molecule can withstand them. At 31.5 million degrees a quantum of thermal radiation possesses an energy of \(2.1\cdot 10^{-8}\) erg, sufficient for moving an electron in a field with an opposing potential difference of 13,500 volts. Yet even with such quanta flying about, atomic nuclei will remain whole; for the decomposition of nuclei into their constituent electric charges, temperatures far exceeding the temperatures at the centers of stars are needed. But the electrons must inevitably be torn from atoms of average atomic weight, and the nuclei will remain completely or almost completely bare.

As a first rough approximation, we may regard stellar matter, at any rate in the hot central regions, as a mixture of pure nuclei and electrons. From the center to the periphery of a star the temperature falls, and we encounter more and more fully formed atoms; finally, near the surface, the atoms are completely finished, with the exception, perhaps, of one or two outer electrons. On the surface of the coldest stars we even find molecules, for example titanium oxide and magnesium hydride, which are detected in the spectra of certain classes of stars.

The mechanism of the interior of a star.

A mixture of free electrons and nuclei, or of not quite fully formed atoms, must behave like a mixture of monatomic gases. In completely decomposed hydrogen, each hydrogen molecule gives rise to four moving units—two protons and two free electrons; the effective molecular weight of the mixture will be 0.5. The corresponding figure for helium is 1.33, for calcium 1.90, for iron 2.07, for lead 2.50; but lead atoms cannot be completely decomposed at stellar temperatures, and therefore the value of the effective molecular weight of lead in stars will be somewhat higher. Taking, for the time being, 2 as the mean molecular weight of stellar matter, then, according to Eddington’s calculations (for hydrogen molecules), we find for the central temperature of the Sun 31.5 million degrees. Various corrections must be introduced into this figure; they have, however, a comparatively small significance, and Eddington’s original value of 31.5 million degrees is probably not very far from the true temperature at the center of the Sun. Russell has recently pointed out that the considerable majority of stars have a temperature at the center very close to 32 million degrees (Nature, August 8, 1925).

One of the necessary corrections omitted by Emden in his calculation is the correction for light pressure inside stars1. At 31.5 million degrees the light pressure reaches approximately 2,500 million atmospheres. Colossal in comparison with terrestrial pressures, this light pressure nevertheless amounts to only about 5% of the gas pressure of the dissociated atoms and electrons at the center of the Sun. To take this light pressure into account would mean the same thing as lowering the mean molecular weight we have adopted by 5%, but in no case do we know this molecular weight with such precision. In exceptionally large stars the pressure of light assumes a somewhat greater significance. For example, at the center of a star with a mass roughly 10 times that of the Sun, the light pressure is approximately half the gas pressure. To allow for its effect in this case, we would have to lower the adopted mean molecular weight approximately from 2 to 1. In any event, we shall obtain a correct picture of the structure of stars if we imagine layers of stellar matter whose gravitation toward the center is restrained by the incessant pressure of a certain number of atomic nuclei, or partially stripped atoms with a “molecular weight” practically coinciding with the corresponding weight of complete atoms; together with the nuclei and atoms, gravity is opposed by an enormous number of free electrons with a constant “molecular weight” of 0.00055, and by a considerably smaller number of “radiation molecules,” whose molecular weight is exceedingly small. The combined pressure of these three types of corpuscles is what preserves the star from contraction under the action of its own gravity.

I believe that this is the most accurate rough picture of the structure of a star. A corresponding image of the mechanism of this structure will be obtained if, instead of nuclei, we imagine $\alpha$-particles; instead of free electrons, $\beta$-particles; and instead of radiation, $\gamma$-rays (although in most stars the principal part of the radiation has the wavelengths of X-rays), just as in the laboratory $\beta$-rays are more penetrating than $\alpha$-rays, while $\gamma$-rays penetrate more than either of them.

Transfer of Energy Inside a Star.

In the ordinary kinetic theory of gases, thermal conductivity is regarded as the result of the action of molecules—the carriers of energy. Ka-

each molecule possesses a transporting capacity exactly proportional to its thermal energy, its velocity, and the length of its free path. Inside a star, as we have seen, there are three different types of carriers: nuclei (or atoms), free electrons, and radiation. The relative transporting capacity of these three types of carriers can be compared by multiplying the energy, velocity, and free-path length of each carrier.

Nuclei and free electrons have, of course, quite definite free-path lengths. The same may be said with respect to radiation, if it is regarded as consisting of discrete quanta; at the moment of emission of a quantum the free path begins, and at the moment of absorption it ends. Whether we adopt the wave or the quantum point of view, we may suppose that a beam of radiation decreases in its intensity according to the factor \(e^{-k\rho x}\), passing through a thickness \(x\) of matter of density \(\rho\); here \(k\) is the absorption coefficient of the matter. Comparing this expression with the formula of kinetic theory,

\[ e^{-\frac{x}{l}}, \]

which determines the decrease in the strength of the flux of moving molecules, we see that the free path of radiation must be equal to

\[ \frac{1}{k\rho}. \]

If we use this value of the free path of radiation and calculate the transporting capacities in the manner indicated above, it turns out that the transporting capacity of both nuclei and electrons is negligible in comparison with radiation. The energy carried by nuclei and electrons may be much greater; however, the distance over which energy is carried—the free path of nuclei and electrons—is considerably smaller than that of radiation; their velocity is also smaller, since radiation carries energy at the speed of light. It follows from this that practically the entire transport of energy from the interior of the star to the surface is effected by radiation.

This general principle was first clearly elucidated by E. C. Pickering in 1894 (Mém. R. A. S. 51, p. 123), but its practical application was hindered by the erroneous law of radiation that he had adopted. Twelve years later Schwarzschild independently expressed the same idea (Gött. Nachr., p. 41, 1906): he showed that the temperature of a certain element inside a star must be determined by the condition that this element receives just as much radiation as it emits, and he gave exact equations for radiative equilibrium; these equations also served as the basis for all subsequent considerations of the problem.

Configuration of a Star in Equilibrium

As a consequence of the fact that radiation completely displaces material carriers in the transport of energy to the surface of a star, the structure of the latter is completely determined by the values of \(k\)—the absorption coefficient inside the star. If this coefficient everywhere

is equal to zero—the star is perfectly transparent and cannot retain heat; this is a star of zero temperature and, consequently, of infinite extent. If, on the other hand, \(k\) is everywhere infinite, the star is perfectly opaque; the radiation is gathered where it is produced until the temperature becomes infinite; this is the case of a star with infinite temperature but vanishingly small radius. Of practical interest, of course, are intermediate values of \(k\); the two limiting cases indicated show only that the structure of a star depends completely on the value of the coefficient of absorption. All attempts to investigate the structure of stars before the coefficient \(k\) became known can be regarded only as speculations.

Eddington’s first attempt to compute \(k\) theoretically in 1922 (Mon. Not. R. A. S. 83, p. 32) proved unsuccessful and was abandoned. In the following year Kramers (Phil. Mag. 46, p. 836) developed the now generally accepted theory of absorption. Using the coefficient of absorption given by this theory, one can fully determine the structure of a star of given mass and with given energy. In this way I showed (Mon. Not. R. A. S. 85, pp. 196 and 394) that a star of given mass can remain in equilibrium at any radius from zero to infinity, with different radii corresponding to different rates of energy generation in the star, from zero to infinity. A star changes its radius according to the rate of energy emission, to which correspond its surface temperature and spectral type. If the rate of energy generation suddenly changes, the star will expand or contract to the radius and temperature corresponding to the new value of the rate of energy emission. Contrary to the usual opinion, an increase in the rate of energy generation in a star causes it to contract and its temperature to rise; conversely, a weakening of the rate of emission is accompanied by expansion and cooling. Thus, for example, giant red stars, such as Betelgeuse, owe their enormous size not to the radiation of too great an energy, but, on the contrary, of too little. Indeed, comparatively compact stars, such as, for example, Plaskett’s star and V Puppis, radiate considerably more in relation to their masses. The general theoretical principle can be verified by studying stellar pairs of approximately equal mass, such as, for example, the two pairs in the following table. The surface temperature is derived here directly from the observed spectra, and the radii were computed by the method explained earlier (see the table on p. 9).

Evolution of Stars.

The rate of energy emission apparently does not change abruptly in actual stars. There is a slow secular decrease, connected with the slow secular decrease of stellar mass, occurring as a result—

the action of continuous radiation. For example, 90,000 calories of radiation per minute from \(1\ \mathrm{cm}^2\) of the solar surface corresponds to a loss of mass of \(4 \cdot 10^{-9}\ \mathrm{g}\); hence it is easy to calculate that the mass of the Sun decreases every minute by 250 million tons. After many millions of years such an expenditure of mass will amount to the gigantic mass of the Sun. In order to trace the changes in the radius and temperature of an actual star, we must study the successive configurations resulting from the change of mass and the release of energy. In this way I found (Mon. Not. R. A. S., January 1925) that a normal star must first decrease in size and become hotter, but then, in the end, expand and cool. This result gives a simple dynamical interpretation of the sequence of “ascending and descending temperatures,” first indicated by Lockyer and constituting the principal consequence of Russell’s theory of stellar evolution (1913), although our interpretation is very different from Russell’s theory.

Atomic weight of stellar matter.

In the simplest case, when energy is produced uniformly throughout the entire mass of the star, the surface temperature \(T\) of a star of mass \(M\) and given luminosity (with a given rate of energy release) is determined by the equation:

\[ \text{Luminosity of the star} = C \cdot \left(\frac{N^2}{A}\right)^{-0.3} T^{0.8}\mu^{6.8} f(M): \]

here \(C\) is a known constant, \(N\) and \(A\) are the atomic number and atomic weight of the stellar atoms, \(\mu\) is the effective molecular weight (about 2) of the dissociated stellar substance, \(T\) is the surface temperature of the star, and \(f(M)\) is a function which I have computed and for which I compiled a table; this function depends only on the mass of the star (Mon. Not. R. A. S. 85, p. 395).

The quantity \(\dfrac{N^2}{A}\) necessarily appears in the written formula, since the coefficient of absorption, which determines the whole structure of the star,

is proportional to \(\dfrac{N^{2}}{A}\). If Maxwell’s demon could divide each atomic nucleus in a piece of matter into two equal parts, then \(N\) and \(A\), and likewise \(\dfrac{N^{2}}{A}\), would be reduced by half, and the substance would become twice as transparent as before. Hence it is clear that a large accumulation of matter in the form of massive nuclei absorbs X-rays considerably more strongly than a large number of small nuclei of the same total mass. For this reason the physicist and the physician choose lead as a material for protection from X-rays: a ton of lead is considerably more reliable, with respect to protection from undesirable X-rays, than a ton of wood or iron. If we know the power of the X-ray apparatus and the total weight of the shielding material around it, then we can very accurately determine the atomic weight of the material of which the shield is made, by measuring the quantity of X-radiation passing through it.

A very similar method may be applied to determining the atomic weight of the atoms of which a star is composed. A star is in reality nothing other than a gigantic X-ray apparatus. We know the total mass of many stars and can easily calculate the rate of formation of X-rays in them; this rate is simply the emission of radiant energy into space. If it were possible to send our Maxwellian demon into a star and make him split each atomic nucleus in half, leaving the mass of the star and the emission of radiation unchanged, he would reduce the absorption coefficient of the star by half. As a result, the structure of the star would change; its radius would increase fourfold, and the surface energy would decrease by half. We can follow the demon’s progress by observing changes in the surface temperature of the star. Thus, by observing the surface temperature of any star of known mass and luminosity, it is possible to determine the atomic weight of the atoms of which the star is composed. The formula given above makes it possible to do this.

I should perhaps point out in passing that Eddington and others approached this question from the other end, assigning values to \(\dfrac{N^{2}}{A}\) by conjecture on the basis of our knowledge of the elements in the atmospheres of the Sun and the stars. Such a path, however, is very risky. The stellar spectrum gives no indication of which elements should be chosen as those located inside; at the very least, it is possible to say a priori that the elements inside a star are quite different from the elements on the surface. What error would an observer on another heavenly body make if he supposed that on the earth there are no chemical elements other than those found in the atmosphere!

But suppose we have taken the risk and assigned such values of \(\dfrac{N^{2}}{A}\); all the quantities entering into the formula for luminosity are known; there remains

the only question is whether the calculated luminosities agree with those observed directly through the telescope. They do not agree.

It is clear that the value \(\dfrac{N^{2}}{A}\) must be corrected in such a way that agreement is obtained. This also corresponds to a direct determination of \(\dfrac{N^{2}}{A}\) from the luminosity formula. Having done this for a number of stars, I found (Mon. Not. R. A. S., June 1926) that two very important facts become clear. First, most of the values determined in this way turn out to be greater than for uranium, the heaviest element on earth. Second, the various values of \(\dfrac{N^{2}}{A}\) are systematically arranged so that the youngest stars give the largest values for \(\dfrac{N^{2}}{A}\); as the stars age, the numbers decrease.

The second result has extensive consequences. Contrary to the views of earlier spectroscopists, and also, apparently, to the opinion still prevailing today, the atoms of a star become simpler the older it is; evolution proceeds from the complex to the simple, and not from the simple to the complex, as in biology. At present there are no direct experimental data on this question, except for radioactivity, where evolution undoubtedly proceeds from the complex to the simple: atoms with lower atomic weight are continually produced as a result of the disappearance of heavy atoms.

The data of astrophysics, indicating the evolution of matter in the same direction, compel us to suppose that the general evolution of matter in the universe may also proceed in this way, being a generalization of radioactive processes on earth.

The data obtained are wholly based on Kramers’s theory of the absorption of X-rays. This theory, as was found, agrees very well with the absorption of radiation observed in laboratories at approximately the same wavelengths as inside stars. The theoretical foundations were examined thoroughly and critically by Eddington, Milne, and others, and they were unable to point out the necessity of any substantial changes. However, if the data from Kramers’s formula are the only ones, then our conclusions, though based on a firm foundation, rest on only a single foundation. In fact, there are many other arguments, as we shall now see.

Distribution of the chemical elements in a star.

A star is inevitably arranged so that the greatest concentration of matter is at its center. This is the first consequence of the inverse-square law of gravitation, although the law of absorption also has some significance here. According to Kramers’s formula for absorption, the distri-

the distribution of matter in a star is such that the density at the center exceeds the mean density by 100 times or more; at least 90 or 95 percent of the star’s total mass is concentrated in a sphere of half the radius, i.e., in one-eighth of the volume. But the degree of condensation at the center is very insensitive to changes in the formula for absorption; any rational formula will likewise give a very high condensation at the center. A rigorous mathematical consideration of this circumstance (Mon. Not. R. A. S. June 1926, p. 561) compels us to exclude the possibility of convection currents mixing the interior of a star, as boiling water is mixed in a kettle. Convection in a kettle occurs because the water at the bottom has a lower density than the less hot water above; there is no convection in a star, because the incandescent matter near the center, despite the intense heat, is many times denser than the cold matter at the surface. Thus the mixture of matter inside a star does not resemble the lower layers of an atmosphere, where the constituent gases are mixed by winds and storms, but rather resembles a calm upper atmosphere, in which the lightest elements float upward and the heaviest sink downward under the action of gravity.

These considerations at once suggest that the elements discovered from spectra in the outer regions of the Sun and stars are only the lightest in the series of elements existing in the star. Naturally, the Earth, having formed from the outer layers of the Sun, contains the same chemical elements as this outer layer; but it is now clear that there must be heavier elements inside. The calculation indicating that the atomic numbers of stellar matter are higher than that of uranium no longer seems suspicious and paradoxical; it begins to seem natural and almost inevitable.

The Origin of Stellar Energy.

A further indication that the atomic weights of stellar atoms are greater than those of any known terrestrial atoms may be obtained from considering the release of energy inside a star. The Sun radiates about 2 ergs per second per gram of mass; the same amount of energy, at the same rate, must arise within it. According to our most reliable data, the Sun has generated and radiated energy in the same quantity for several million million years. Could the Sun possess such a capacity for radiation if it consisted internally of ordinary terrestrial elements: calcium, iron, silicon, etc.?

The first impulse is to answer: no. Even if the Sun were built of pure uranium, its radiating capacity would amount to only, approximately, half the observed value; this energy would suffice for only an insignificant fraction of what we regard as the life of the Sun. A Sun of pure radium would radiate more than is needed for

of the present moment, but the life of such a Sun would be limited to a few millennia. No possible combination of terrestrial elements can give the high radiation and stability that we observe in the Sun and the stars.

We must, however, remember that within the stars there reign pressures and temperatures unattainable in our laboratories. Will our terrestrial elements behave quite differently under stellar conditions? Is it possible, for example, that the interior of the Sun consists of ordinary terrestrial elements, and that the enormous release of energy is connected only with high temperature and pressure?

A general consideration of the astronomical material sheds considerable light on this question. We find at once that the stars which radiate most energetically (per unit mass) are not, generally speaking, the hottest and densest. Some of the hottest and densest stars are completely put to shame, as regards radiation, by very cold stars of low density, such as Antares and Betelgeuse. If the stars are arranged in order of the magnitude of their radiation per unit mass, it turns out that they are distributed not in order of temperatures or densities, but rather accurately in order of ages; the youngest stars radiate most energetically; irrespective of their internal temperature and density, the older stars seem exhausted.

This general tendency is shown in the following table.

It is asked whether such high densities can actually exist at the center of stars. The answer has been obtained from the companion of Sirius (Sirius B). Direct observation has shown that the average density of this star is about 53,000, and, consequently, the density at the center must be still greater. Incidentally, as noted

Eddington, here we have convincing confirmation of our view that the matter of stars consists of atoms that have decomposed into their principal constituent parts. It is impossible to compress matter consisting of whole atoms of radius \(10^{-8}\) cm or more to such densities; this difficulty, however, disappears with respect to the negligibly small nuclei and electrons, whose dimensions are of the order of \(10^{-13}\) cm.

It should be noted that many of the data in the table are only unreliable guesses and do not claim great accuracy. Many astronomers would prefer other figures in this table; however, I doubt that anyone would seriously dispute the general proposition that a star’s capacity to generate energy depends above all on its age, and not on its central temperature and density.

Of course, there may be exceptions to the general rule. The Earth and the Sun are extreme examples of this. The matter of both is of one and the same limiting age; however, they radiate very different amounts of energy per unit mass. This can be explained simply by the fact that the heavy atoms which determine the energy of the Sun sank deep inside and therefore did not enter into the composition of the Earth and the planets; the same explanation can be given for the different radiative capacity of the components of binary systems. These exceptions are the result of special conditions in individual cases; they do not violate the general law that a star’s output is not determined by its density and temperature.

The table shows that the law is well confirmed by observational astronomy; it can also be obtained by a theoretical study of the actual process of energy formation in a star. A multitude of data, most of them dynamical, indicate that stars must have existed for millions of millions of years. Here is an example: recently formed binary stars have circular, or almost circular, orbits; this is a consequence of the manner of their formation. Every gravitational perturbation of a circular orbit tends to make it more elliptical; therefore, the older a binary star is, the more elliptical its orbit should be. In reality this is just what happens. On the basis of data on the number and masses of stars wandering about in space, one can determine the rate at which the ellipticity of the orbits of binary stars should increase; from this, conversely, one can determine the ages of actual stars. This is a purely dynamical problem. The answer is obtained in millions of millions of years.

It is now possible to determine the quantity of radiation emitted by individual stars over the course of millions of millions of years of their existence. With the exception of the very youngest stars, the total mass of radiated energy proves to be considerably greater than the mass of the star itself.

in its present state. The mass of a star at the time of its birth is obtained by adding together the mass of the radiated energy and the remaining mass of the star. Thus, the mass of the star at its inception was much greater than it is now. But at any moment the mass of a star consists chiefly of the mass of the matter of which the star is built; we see, therefore, that a large part of the substance that was in the star at first has ceased to exist as substance: it has been annihilated and, having been transformed into radiation, has flown away into space. As early as 1904 (Natur, 70, p. 101), I expressed the supposition that energy is created as a result of the annihilation of matter; now it is indeed necessary to believe that herein lies the source of the energy radiated by the Sun and the stars. Electrons and protons inside the star must from time to time collide and mutually annihilate one another; the corresponding energy is emitted in the form of radiation.

The energy of such a process is colossal; it can impart to both masses participating in the process velocities amounting to 0.866 of the speed of light. There is no other way by which matter could release energy in such quantity; for example, the ordinary burning of a ton of coal gives energy sufficient to move an express locomotive for an hour, whereas the complete conversion of a ton of coal into energy would be accompanied by the release of energy sufficient for the heating, lighting, mechanical work, and transport of all Great Britain for a century.

The annihilation of each proton, or atom, is accompanied by flashes of radiant energy wandering inside the star until, as a result of innumerable absorptions and emissions, the energy reaches the surface and flies away into space. Such flashes of radiant energy are similar to the flashes produced by radioactive materials in a scintariscope, but they are many thousands of times more powerful. The enormous energy of these flashes is compensated to some extent by their rarity. For example, on the Sun only one atom out of \(10^{17}\) is annihilated in the course of an hour. In \(1\ \mathrm{cm}^{3}\) of solar mass there are, approximately, \(10^{22}\) atoms, of which about 100,000 disappear every hour. Thus the energy arising in \(1\ \mathrm{cm}^{3}\) of solar mass is not very great: it is equal to approximately 9400 ergs, or 0.00022 calories per hour. The power of the energy flux from the surface of the Sun is determined by the fact that all the energy formed in a cone 695,000 km deep must pass out through the aperture of this cone.

Such, in a few words, is the mechanism of the formation of stellar energy. Immediately after this there arises the question: does the formation of energy proceed more vigorously, do electrons and protons collide more often inside the star under conditions of enormous temperatures and densities?

It is known from experiment that ordinary radioactive processes remain unaffected and are not intensified at those high temperatures which are attainable in the laboratory; quantum theory explains this circumstance. Einstein showed that the formation of subatomic energy can occur in only two ways: spontaneously or under the influence of external radiation. It is easy to calculate the temperature at which the latter factor can become appreciable. The quantum of radiation at this temperature must be equal to the energy released in the given subatomic process. Thus, the temperature required for the decomposition of uranium proves to be approximately equal to 120,000 million degrees. Hence it is clear why heating uranium in the laboratory cannot accelerate its decay. The same calculation shows that the temperature needed to accelerate the rate of subatomic self-destruction of matter is of the order of 7,500,000 million degrees. It may be noted that at lower temperatures, insufficient for the actual destruction of matter, other subatomic processes may nevertheless be accelerated. This is true with respect to the instantaneous radiation of a star, but such processes cannot have a lasting effect on the radiation. All processes affected by a temperature below 7.5 million million degrees leave the total number of electrons and protons in the star unchanged. Meanwhile, astronomical data indicate that the number of electrons and protons in a star is continuously decreasing.

These considerations show that the relatively low temperatures of stars, which are less than billions of degrees, prove to be almost ineffectual with respect to the formation of stellar energy; the heat of the most incandescent stars cannot exert any greater influence on the process of the destruction of energy than the warmth of a summer day on the process of the decomposition of uranium. Thus it is sufficiently clear that the destruction of matter in stars is determined neither by heat nor by cold, nor by high or low density, but simply by the passage of time.

Nevertheless, Russell (Nature, Aug. 8, 1925), and then Eddington (Nature, May 1, 1926), while agreeing that the final source of stellar radiation is the destruction of matter, suppose, however, that such destruction can occur if the temperature of ordinary matter reaches a certain critical value of 30–40 million degrees. According to Russell, up to this critical temperature matter is inert, but as soon as it is reached, an unhindered transformation of matter into radiation suddenly takes place.

Apart from violating the physical principles set forth above, this proposition is also connected with the following difficulty: the formation of energy which arises according to this assumption occurs not only without hindrance, but also without limit; if it has begun, it cannot be stopped. According to the hypothesis of Russell and Eddington, matter becomes thermodynamically unstable at stellar temperatures; it

acquires the properties of an explosive substance at the point of explosion. If stellar matter has somewhere reached the critical point, then the resulting destruction of matter will be accompanied by the release of such heat that the neighboring layers of matter will also reach the critical temperature, and the whole star will almost instantly have to explode and turn into radiation. We would not see permanent luminaries in the sky, but only successive appearances of new stars of the most terrifying type, as various stars reached the critical point and in turn “blew up.” Despite the high position occupied in astronomical science by the father and stepfather of this hypothesis, I consider it unacceptable not only because it contradicts the general principles of physics, but also because the stars themselves speak against it by their peaceful appearance.

A general mathematical consideration of the problem of stability shows that a star constructed of matter whose energy emission is entirely unaffected by changes in temperature and density will be dynamically stable. However, the degree of stability is small. If the properties of stellar matter are such that, with an increase in temperature, the emission of energy increases, then this last reserve of stability disappears. Any substantial influence in this direction will make the star dynamically unstable.

Combining this purely dynamical result with the physical principles set forth, we arrive at the conclusion that, at least in a first approximation, an increase in the temperature of stellar matter does not increase the emission of energy.

Stellar radiation must arise either in matter of the terrestrial type, or in matter of some other type, unknown to us. If it is accepted that high temperature and density cannot accelerate the emission of radiation by ordinary matter, then stellar radiation must arise from matter of a type unknown on earth. Other types of matter must exist; and although in recent years physics and chemistry have gone badly astray, nevertheless it may be asserted that these new types can only be elements with higher atomic weights than uranium. The significance now becomes clear of the calculations which showed that stellar atomic weights are in most cases greater than that of uranium.

Comparison and Interpretation of the Results

By three different paths we have come to the conclusion that the atomic weights of stellar atoms must in most cases exceed the atomic weight of uranium: 1) by direct calculation according to Kramers’ formula; 2) from the consideration that atoms near the center of a star must be considerably heavier than near the surface; 3) on the basis that atoms with atomic weight less than that of uranium do not

cannot be produced by any heating and compression of the intense and prolonged radiation that is emitted by stars.

It has turned out that the atomic weights of stellar atoms are not only greater than that of uranium, but that they vary systematically from star to star. In short, the youngest stars reveal the greatest atomic weights, and this key brings order into the former chaos.

We suppose that in the initial stage matter consists of a mixture of elements with different atomic weights. The heaviest ones especially readily and spontaneously annihilate themselves, turning into radiant energy; the duration of their existence is the shortest. These elements disappear first as the star ages; their disappearance lowers the average atomic weight of the star and the average rate of emission of radiation per unit mass, since the heavy elements are the most energetic radiators. Just as on the shore the hardest rocks withstand the destructive onslaught of the sea longest of all, so on a star the lightest elements resist longest of all the destructive action of time. In the end only the lightest elements remain on the star, and it loses its radiating capacity. Our terrestrial elements are capable of spontaneous transformations to so slight a degree that they may rightly be called “permanent.” Calculation shows that if these elements underwent a noticeable transformation over periods comparable with the age of the stars (approximately \(10^{13}\) years), then the independent production of heat by the terrestrial mass would heat it to such a degree that it would become uninhabitable for man. The radioactive elements, of course, are an exception; they are probably the last survivals of the original, more turbulent matter and, thus, form a bridge between the permanent elements and the short-lived elements of the stars.

It is interesting to know whether heavy atoms turn into radiation at once or through successive stages of transformations. Astronomical data definitely indicate that the most massive stars contain a greater variety of atoms than our Sun, although the variations of stellar masses are wider than the variations of the atomic weights of their atoms. Since with time these stars decrease to the mass of the Sun, the process of evolution must evidently be accompanied by the actual destruction of atoms; it is not enough to postulate a gradual decrease in the atomic weight of each atom until it becomes permanent. Radioactivity shows that the latter process may also occur, but the data of astronomy argue that this is, at best, a secondary process.

The number of “permanent” atoms in a massive star, for example, Antares or V Puppis, cannot decrease appreciably in the next \(10^{13}\) years, so that they all must survive to the final stage of the star with a mass,

component may be one fiftieth of the present one. Thus, approximately 98% of the present masses of these stars must consist of inconstant atoms. In other words, the present mass of such stars as Antares and V Puppis must consist, by 98%, of atoms doomed to transform into radiation, and only by 2% of atoms that cannot pass into radiation. It is clear that the primordial matter of the universe must be of an inconstant type; our terrestrial atoms are only the residues of an untransformable foam. Like bacteria in a drop of rain, gazing at Niagara, we see that our physics and chemistry are only the border of a vast science; beyond the coast explored in our laboratories lies an ocean whose existence we are only beginning to suspect.

We come, therefore, to the conclusion that the youngest stars consist of a substance which is practically entirely unknown on Earth and has an atomic weight greater than that of uranium. This substance can spontaneously be destroyed, the energy thereby liberated appearing in the form of radiation. The rate of energy output, determined from the luminosity of the youngest stars, is of the order of 1,000 ergs per gram per second. The complete destruction of 1 g of matter is accompanied by the liberation of \(9 \cdot 10^{20}\) ergs; consequently, stellar matter must have a “period of decay” of \(9 \cdot 10^{17}\) seconds, or 30,000 million years. As a star grows older and less transformable matter remains, the period of decay is correspondingly lengthened. The matter of the Sun, radiating 2 ergs per gram per second, must have a period of decay of 15,000,000 million years. These periods of decay determine the rate of evolution and the duration of the life of stars. Roughly speaking, a star lives as long as the atoms composing it, and the lifetimes of atoms are constants of nature.

Let us note that the periods of decay of stellar atoms are long in comparison with the periods of ordinary radioactive decay; this indicates that the radioactive elements are only transitory formations in evolving matter.

CRITICAL CENTRAL TEMPERATURE.

A priori one might expect that in a group of stars with approximately equal masses—for example, the Sun, Procyon, and the two components of \(\alpha\) Centauri—the rate of energy output would be very different and that, consequently, these stars might have very different surface and central temperatures. Indeed, at first sight, such stars might have any temperatures from zero to infinity. In fact, however, the surface temperatures of the four indicated stars, as well as of all other stars with the same mass, lie within the narrow limits from 3,700 to 8,300 degrees; their central tempe-

temperatures probably vary within the range from 15 to 100 million degrees. For stars with other masses the limits are different, and considerably wider for stars with large masses. But stars of a definite mass always reveal a definite upper limit, both of the surface and of the central temperature. These limits are never exceeded, and the majority of stars of a given mass tend toward them. The existence of one limit, of course, compels us to assume the existence of the other also, and apparently the limiting central temperature is the more essential one. Stars with a mass like that of our Sun never have central temperatures above 80 million degrees, and the majority have central temperatures not very far from 80 million degrees. For stars with masses 20 times greater than the solar mass, the corresponding limit is probably about 300 million degrees; intermediate limits are possessed by stars with intermediate masses.

This, of course, is one of the fundamental facts of astrophysics. What does it mean? The normal course of events for a star of the type of V Puppis, as it loses mass and its radiation diminishes, ought to consist in a gradual contraction of its dimensions, accompanied by a continuous rise of the central temperature. What stops this normal course of evolution as soon as the central temperature reaches 300 million degrees?

Recently I suggested that the upper temperature limit for any star corresponds simply to that temperature at which its central atoms lose all, or almost all, of their electrons. This is calculated very simply, but one must assume that the atoms at the center of the star have high atomic weights, which agrees with the preceding considerations. For example, a temperature of 300 million degrees is sufficient to strip the last electrons from atoms of atomic weight 300 or more. The decrease of the critical central temperature as the star ages and its mass diminishes is, from this point of view, a direct consequence of the decrease in the atomic weight of the stellar material, occurring as the heaviest atoms are gradually destroyed.

It remains to explain why this temperature constitutes an upper limit, why the star cannot become still hotter after the last electrons have been stripped from its inner atoms. As far as I understand, there is only one possible answer. After the last electrons have been torn from the atom, its capacity for self-annihilation disappears, and the further growth of the emission of radiation ceases. From this moment the central atoms of the star act like the governor of a steam engine, regulating the formation of energy in such a way that the central temperature is kept close to the critical temperature. If the star begins to become hotter, the central atoms in ever greater numbers lose their last electrons and cease generating

energy. Then the star begins to cool, but in the process the atoms are restored and again begin to produce energy, heating the star. The mechanism provides a perfect thermostat, and it is easy to show that its action is stable. As the star ages, the heavier atoms at the center are the first to be transformed into radiation and disappear; their place is taken by lighter atoms; to tear all the electrons from these atoms a lower temperature is sufficient, and therefore the central critical temperature of the star falls.

An interesting confirmation of this hypothesis is provided by the components of recently formed binary stars. They have a recoil velocity per unit mass like that of young stars, but their masses correspond to considerably older stars. It is clear that the “regulating” action must be especially effective in limiting the recoil of these stars, since they must have central temperatures very nearly coinciding with the maximum for their masses. In reality this is indeed so.

All the data available up to the present time indicate that the annihilation of matter is a quantum phenomenon; it is possible that it corresponds to nothing other than an arbitrary fall of an electron onto a zero-quantum orbit. In this way it would be explained why bare nuclei and free electrons are not capable of annihilation and why, consequently, atoms with stripped-off electrons are not transformed into energy.

Penetrating Radiation.

If the earth gives only one end of the chain of chemical elements, then where is the other end to be sought? Moving along the evolutionary ladder, we arrive at the youngest stars, containing elements of ever increasing atomic weight. Passing beyond the stars, we come to the nebulae; here we must find the elements with the highest atomic weights and matter with the greatest radiating capacity.

In outward appearance nebulae are extremely faint objects; their radiation of visible rays per unit mass is approximately the same as that of the Sun. There is, however, an essential difference in the radiation of stars and nebulae. At the moment of its birth the radiation must possess an enormous penetrating power; the simultaneous annihilation of one electron and one proton gives radiation with a wavelength of only \(1.3 \cdot 10^{-13}\) cm. However, the enormous penetrating power of this radiation inside the star is sufficient only for its passage over a distance equal to a small fraction of the star’s radius; subsequent absorptions and emissions soften this radiation owing to a special kind of generalized Compton effect, and it emerges beyond the surface of the star in the form of ordinary temperature radiation. But the density of nebulae is so much less than that of stars that such radiation, once born

in a nebula, passes almost unhindered into space. Along the way this radiation may destroy individual atoms, knocking out electrons with velocities of millions of volts, but the greater part passes unhindered until it encounters a medium with great absorbing power. Thus, one must expect that the atmospheres of stars, the Sun and the Earth, and even the solid body of the Earth are under continuous bombardment by penetrating radiation originating in nebulae.

Such radiation has been discovered in the earth’s atmosphere by Kolhörster, Millikan1 and others, who found that it is of extra-terrestrial origin. If it originates in the stars, then its amount should depend strongly on the position of the Sun. This is not the case; therefore the radiation comes from nebulae, or from other cosmic masses distinct from stars. Quite recently (Nature, October 9, 1926) Kolhörster and von Salis found that the intensity of the radiation varies depending on the position of cosmic masses; the radiation comes chiefly from regions near the Milky Way, especially from the regions of Andromeda and Hercules.

I have calculated that the total amount of penetrating radiation received on the earth is approximately twice as large as could have been obtained from one nebula, [[unclear: Andromeda]] (Nature, December 12, 1925), if it consisted only of matter with the same radiating power as that of the youngest stars. It is clear that the order of magnitude of the observed radiation agrees with this calculation; on the other hand, this radiation is so strong that it is difficult to imagine any other source of its origin. Its penetrating power is, apparently, considerably less than would be expected from the simultaneous annihilation of an electron and a proton, but I think that this difficulty, if it exists, is not insuperable. Quite recently Rosseland (Astr. Journ., May 1926) pointed out that bombardment by this radiation may be the cause of the observed broad lines in stellar spectra. Earlier (Nature, December 12, 1925) I suggested that the glow of irregular nebulae is also explained in this way.

There is a temptation to go further into the physics of nebulae, to try to understand the properties of matter in its primordial forms, and perhaps to look into the act of its creation. But this would lead us far into the realm of conjecture and speculation. Up to this point our argument has not depended on conjectures and suppositions. Where at first it seemed possible to choose different paths, on closer examination all paths, except the only one, proved to be forbidden either by observed facts or by well-established principles of physics or dynamics; there was never any need to choose. For this reason the obtained

conclusions, although they are undoubtedly new and, perhaps, unexpected, seem to me in their main outlines inevitable. I see no way in which they can be avoided.

Life and the Universe.

A survey of the results obtained by cosmic physics has compelled us to suppose that the physics of terrestrial laboratories is only the outskirts of general physics. The primary physical process in the universe is the transformation of matter into radiation, of which on Earth we knew nothing until, approximately, 1904. The primary matter of the universe consists of extremely dissociated atoms—a state of matter of which we did not even think before 1917. The primary radiation of the universe is not visible light, but radiation with short waves and a hardness that would have seemed incredible at the beginning of our century. All our knowledge of the actual fundamental physical conditions of the universe in which we live is the result of the work of the last quarter-century.

The simple explanation of this is that life quite naturally begins the investigation of nature with the study of the conditions immediately surrounding it. The general conditions of the universe as a whole are a considerably more difficult task for life on our planet, and we are only approaching it. The physical conditions under which life is possible are only an insignificant fraction of the scale of the physical conditions of the universe as a whole. The concept of life presupposes duration in time; there can be no life where atoms change their form millions of times a second and not a single pair of atoms can combine. Life also requires a certain mobility in space. These two requirements limit a small interval of physical conditions in which the liquid state is possible. Our survey has shown how small these limits are in comparison with what occurs in the universe as a whole. Primary matter must be transformed into radiation over the course of millions of millions of years in order for an vanishingly small quantity of inert ash to result, upon which life can exist. And even here this ash must not be too hot or too cold, otherwise life will be impossible. It is difficult to imagine life of any higher order except on planets warmed by a Sun. Even if a star lives out its millions of millions of years, the probability that it will prove to be a Sun surrounded by planets is, insofar as we can calculate it, approximately one hundred-thousandth. In every respect—space, time, and physical conditions—life is limited to existence only in an insignificantly small corner of the universe.

What, then, is life? Is it the final goal toward which everything moves, for which, over millions of millions of years, matter is transformed in uninhabited stars and nebulae, and mighty radiation

is sent into the desert spaces? Is all this merely a splendid preparation for life? Or is it only an accidental and altogether insignificant by-product of natural processes that have their own, more astonishing aims? Or—an even more modest point of view—is life not a kind of disease of its own sort, afflicting matter in its old age, when it has lost its high temperature and the ability to generate high-frequency radiation, by means of which younger and stronger matter would at once have destroyed life? Or, casting aside humility, must we say that life is the only reality, creating itself, instead of being created by gigantic masses of stars and nebulae over immeasurable intervals of astronomical time? It is difficult even to enumerate the ways in which the results obtained may be interpreted. There is, however, I believe, no way of avoiding them.

1. Cf. U. F. N. 6, p. 1, 1926. Ed. ↩↩↩↩↩

2. Cf. U. F. N. 5, 457, 1925. Translator’s note. ↩