Worlds in the making: The evolution of the universe

by Svante Arrhenius

We must look for another explanation. It occurred to Helmholtz, one of the most eminent investigators in the domain of the mechanical theory of heat, that, instead of the meteorites, parts of the sun itself might fall towards its centre, or, in other words, that the sun was shrinking. Owing to the high gravitation of the sun (27.4 times greater than on the surface of the earth), the shrinkage would liberate a great amount of heat. Helmholtz calculated that, in order to cover the heat expenditure of the sun, a shrinkage of its diameter by 60 m. annually would be required. If the sun’s diameter should only be diminished by one-hundredth of one per cent.—a change which we should not be able to establish—the heat loss would be covered for more than 2000 years. That seems at first satisfactory. But if we proceed with our estimate, we find that if the sun went on losing as much heat as at present for seventeen million years it would have to contract within this period to a quarter of its present volume, and would therefore acquire a density like that of the earth. Long before that, however, the radiation from the sun would have been decreased so powerfully that the temperature on the earth’s surface would no longer rise above freezing-point. Helmholtz, on this argument, limited the further existence of the earth to about six million years. That is less satisfactory. But we know nothing of the future and must be content with possibilities. Not so, however, if we calculate back with the aid of Helmholtz’s theory. According to this theory, and according to Helmholtz’s own data, a state like the present cannot have existed for more than ten million years. Since, now, geologists have come to the conclusion that the petrefactions which we find in the fossil-bearing strata of the earth have needed at least a hundred million years for their formation, and more probably a thousand million years, and since, moreover, the still more ancient formations—the so-called precambrian strata—have been deposited in equally long or still longer periods, we see that the theory of Helmholtz is unsatisfactory.

A somewhat peculiar way out of the dilemma has been suggested by a few scientists. We know that one gramme of the wonderful element radium emits about 120 calories per hour, or in the course of a year, in round numbers, a million calories. This radiation seems to continue unimpaired for years. If we now assume that each kilogramme of the mass of the sun contains only two milligrammes of radium, that amount would be sufficient to balance the heat expenditure of the sun for all future ages. Without some further auxiliary hypothesis, we can, however, not listen to this suggestion. It presupposes that heat is created out of nothing. Some scientists, indeed, believe that radium may absorb a radiation, coming from space, in some unknown manner and convert it into heat. Before we enter seriously into a discussion of this explanation we shall have to answer the questions where that radiation comes from and where it takes its store of energy.

We must, therefore, again search for another source of heat energy for the sun. Before we can hope to find it, we had better study the sun itself a little.

All scientists are agreed that the sun is of the same constitution as the thousands of luminous stars which we see in the sky. According to the color of the light which they emit, stars are classified as white, yellow, and red stars. The differences in their light become much more distinct when we examine them spectroscopically. In the white stars the helium and hydrogen lines predominate decidedly; the helium stars contain, in addition, oxygen. Metals are comparatively little represented; but they play a main part in the spectra of the yellow stars, in which, further, some bands become visible. In the spectra of the red stars we notice many bands which indicate that chemical compounds are present in the outer portions. Everybody knows that the platinum wire or the filament of an incandescent lamp which has been heated to incandescence by the electric current first shines reddish, then yellow when the current is increased, and finally more and more white. At the same time the temperature rises. We can estimate the temperature from the brightness of the glow. If we know the wave-length of the radiations of that color which emits the greatest amount of heat in the spectrum (it should be a normal spectrum), it is easy to calculate the temperature of the star from Wien’s law of displacements. We need only divide 2.89 by the respective wave-length expressed in mm. to find the absolute temperature of the star; by deducting 273 from the result, we obtain the temperature in degrees Cent. on the ordinary scale. For the sun the maximum of heat radiation lies near wave-length 0.00055 (in the greenish-yellow light), and therefore the absolute temperature of the radiating disk of the sun, the so-called photosphere, should be 5255° absolute, or nearly 5000° Cent. But our atmosphere weakens the sunlight, and it also causes a displacement of the maximum radiation in the spectrum. The same applies to the sun’s own atmosphere, so that we have to adopt a higher estimate than 5000° Cent. By means of Stefan’s law of radiation, the solar temperature has been estimated at about 6200°, which would correspond to a wave-length of about 0.00045 mm. This correction is therefore significant. About half of it has to be ascribed to the influence of the solar atmosphere, the other half to the terrestrial atmosphere. A Hungarian astronomer, Harkányi, has determined in the same way the temperature of several white stars (Vega and Sirius), and found it to be about 1000° higher than that of the sun, while the red star Betelgeuse, the most prominent star in Orion, would have a temperature by 2500° lower than that of the sun.

It must expressly be stated that in making these estimates we understand by the temperature of the star in this case the temperature of a radiating body which emits the same light as that which reaches us from the star. But the stellar light undergoes important changes on its way to us. We learn from observing new stars that a star may be surrounded by a cloud of cosmical dust which sifts the blue rays out and permits the red ones to pass. The star then shines with a less brilliantly white light than in the absence of the cloud. The consequence is that we estimate the temperature lower than it really is. In the red stars bands have been noticed, indicating, as we have already said, the presence of chemical compounds. The most interesting of these are the compounds of cyanogen and of carbon, probably with hydrogen, which appear to resemble those observed by Swan in the spectrum of gas flames and which were named after him. It was formerly thought that the presence of these compounds implied lower temperature. But we shall see that this conclusion is not firmly established. Hale has found during eclipses of the sun that exactly the same compounds occur immediately above the luminous clouds of the sun. They are probably more numerous below the clouds, where the temperature is no doubt higher, than above them.

However that may be, we have reason to assume that the now yellow sun was once a white star like the brilliant Sirius, that it has slowly cooled down to its present appearance, and that it will some day shine with the reddish light of Betelgeuse. The sun will then only radiate a seventh of the heat which it emits now, and it is very likely that the earth will have been transformed into a glacial desert long before that time.

It has already been pointed out that the atmospheres of both the sun and of the earth produce a strong absorption of the solar rays, and especially of the blue and white rays. It is for this reason that the light of the sun appears more red in the evening than at noon, because in the former case it has to pass through a thicker layer of air, which absorbs the blue rays. For the same reason the limb of the sun appears more red in spectroscopic examinations than the centre of the sun. This weakening of the sun’s light is due to the fine dust pervading the atmospheres of the earth and the sun. When the products of strong volcanic eruptions, like the eruptions of Krakatoa in 1883 and of Mont Pelée in 1902, filled the atmosphere with a fine volcanic dust, the sun appeared distinctly red when standing low in the horizon. It was this dust that caused the red glow.

When we examine an image of the sun which has been thrown on a screen by the aid of a lens or a system of lenses, we notice on the sun’s disk a mottling of characteristic darker spots. These spots struck the attention of Galileo, and they were discovered almost simultaneously by him, by Fabricius, and by Scheiner (1610-1611). These spots have since been the most diligently studied features of the sun. We carefully determine their number and sizes, and combine these two data to make the so-called sun-spot numbers. These numbers change from year to year in a rather irregular way, the period amounting on an average to 11.1 years. The spots appear in two belts on the sun, and they glide over the disk in the course of thirteen or fourteen days. Sometimes they reappear after another thirteen or fourteen days. It is therefore believed that they lie comparatively quiet on the surface of the sun, and that the sun rotates about its own axis in about twenty-seven days, so that after that period the same points are again opposite the earth. This is the so-called synodical period. The great interest which attaches to the study of these features lies in the fact that simultaneously with these spots several other phenomena seem to vary which attain their maxima at the same time. Such are, in the first instance, the polar lights and the magnetic variations, and, to a lesser degree, the cirrus clouds and temperature changes, as well as several other meteorological phenomena (compare Chapter V.).

About the sun-spots we notice the so-called faculæ—portions which are much brighter than their surroundings. When we carefully examine a strongly magnified image of the sun, we find that it has a granulated appearance (Fig. 18). Langley compares the disk to a grayish-white cloth almost hidden by flakes of snow. The less bright portions are designated "pores," the brighter portions "granules." It is generally assumed that the granules correspond to clouds which rise like the clouds of our atmosphere on the top of ascending convection currents. But while the terrestrial clouds are formed of drops of rain or of crystals of ice, the granules consist probably of soot—that is to say, condensed carbon—and of drops of metals, iron, and others. The smallest granule which we are able to discern has a diameter of about 200 km. (130 miles).