i010Fig. 10. SOLAR PROMINENCE
Fig. 10. SOLAR PROMINENCE
Fig. 10. SOLAR PROMINENCE
i011Fig. 11. STAR CLUSTER ω CENTAURI
Fig. 11. STAR CLUSTER ω CENTAURI
Fig. 11. STAR CLUSTER ω CENTAURI
On the whole it is steady and quiescent, although, as the prominence flames show, it is liable to be blown sky-high by violent outbursts. The conclusions about the calcium chromosphere that I am going to describe rest on a series of remarkable researches by Professor Milne.
How does an atom float on a sunbeam? The possibility depends on the pressure of light to which we have already referred (p. 26). The sunlight travelling outwards carries a certain outward momentum; if the atom absorbs the light it absorbs also the momentum and so receives a tiny impulse outwards. This impulse enables it to recover the ground it was losing in falling towards the sun. The atoms in the chromosphere are kept floating above the sun like tiny shuttlecocks, dropping a little and then ascending again from the impulse of the light. Only those atoms which can absorb large quantities of sunlight in proportion to their weight will be able to float successfully. We must look rather closely into the mechanism of absorption of the calcium atom if we are to see why it excels the other elements.
The ordinary calcium atom has two rather loose electrons in its attendant system; the chemists express this by saying that it is a divalent element, the two loose electrons being especially important in determining the chemical behaviour. Each of these electrons possesses a mechanism for absorbing light. But under the conditions prevailing in the chromosphere one of the electrons is broken away, and the calcium atoms are in the same smashed state that gives rise to the ‘fixed lines’ in the interstellar cloud. The chromospheric calcium thus supports itself on what sunlight it can gather in with the one loose electron remaining. To part with this would be fatal; the atomwould no longer be able to absorb sunlight, and would drop like a stone. It is true that after two electrons are lost there are still eighteen remaining; but these are held so tightly that sunlight has no effect on them and they can only absorb shorter waves which the sun does not radiate in any quantity. The atom therefore could only save itself if it restored its main absorbing mechanism by picking up a passing electron; it has little chance of catching one in the rarefied chromosphere, so it would probably fall all the way to the sun’s surface.
There are two ways in which light can be absorbed. In one the atom absorbs so greedily that it bursts, and the electron scurries off with the surplus energy. That is the process of ionization which was shown inFig. 5. Clearly this cannot be the process of absorption in the chromosphere because, as we have seen, the atom cannot afford to lose the electron. In the other method of absorption the atom is not quite so greedy. It does not burst, but it swells visibly. To accommodate the extra energy the electron is tossed up into a higher orbit. This method is called excitation (cf.p. 59). After remaining in the excited orbit for a little while the electron comes down again spontaneously. The process has to be repeated 20,000 times a second in order to keep the atom balanced in the chromosphere.
The point we are leading up to is, Why should calcium be able to float better than other elements? It has always seemed odd that a rather heavy element (No. 20 in order of atomic weight) should be found in these uppermost regions where one would expect only the lightest atoms. We see now that the special skill demanded is to be able to toss up an electron 20,000 times a second without ever making the fatal blunder of dropping it. That is not easy even for an atom. Calcium[23]scoresbecause it possesses a possible orbit of excitation only a little way above the normal orbit so that it can juggle the electron between these two orbits without serious risk. With most other elements the first available orbit is relatively much higher; the energy required to reach this orbit is not so very much less than the energy required to detach the electron altogether; so that we cannot very well have a continuous source of light capable of causing the orbit-jumps without sometimes overdoing it and causing loss of the electron. It is the wide difference between the energy of excitation and the energy of ionization of calcium which is so favourable; the sun is very rich in ether-waves capable of causing the first, and is almost lacking in ether-waves capable of causing the second.
The average time occupied by each performance is ¹⁄₂₀₀₀₀th of a second. This is divided into two periods. There is a period during which the atom is patiently waiting for a light-wave to run into it and throw up the electron. There is another period during which the electron revolves steadily in the higher orbit before deciding to come down again. Professor Milne has shown how to calculate from observations of the chromosphere the durations of both these periods. The first period of waiting depends on the strength of the sun’s radiation. But we focus attention especially on the second period, which is more interesting because it is a definite property of the calcium atom, having nothing to do with local circumstances. Although we measure it for ions in the sun’s chromosphere, the same result must apply to calcium ions anywhere. Milne’s result is that an electron tossed into the higherorbit remains there for an average time of a hundred-millionth of a second before it spontaneously drops back again. I may add that during this brief time it makes something like a million revolutions in the upper orbit.
Perhaps this is a piece of information that you were not particularly burning to know. I do not think it can be called interesting except to those who make a hobby of atoms. But it does seem to me interesting that we should have to turn a telescope and spectroscope on the sun to find out this homely property of a substance which we handle daily. It is a kind of measurement of immense importance in physics. The theory of these atomic jumps comes under the quantum theory which is still the greatest puzzle of physical science; and it is greatly in need of guidance from observation on just such a matter as this. We can imagine what a sensation would be caused if, after a million revolutions round the sun, a planet made a jump of this kind. How eagerly we should try to determine the average interval at which such jumps occurred! The atom is rather like a solar system, and it is not the less interesting because it is on a smaller scale.
There is no prospect at present of measuring the time of relaxation of the excited calcium atom in a different way. It has, however, been found possible to determine the corresponding time for one or two other kinds of atoms by laboratory experiments. It is not necessary that the time should be at all closely the same for different elements; but laboratory measurements for hydrogen also give the period as a hundred-millionth of a second, so there is no fault to find with the astronomical determination for calcium.
The excitation of the calcium atom is performed by light of twoparticular wave-lengths, and the atoms in the chromosphere support themselves by robbing sunlight of these two constituents. It is true that after a hundred-millionth of a second a relapse comes and the atom has to disgorge what it has appropriated; but in re-emitting the light it is as likely to send it inwards as outwards, so that theoutflowingsunlight suffers more loss than it recovers. Consequently, when we view the sun through this mantle of calcium the spectrum shows gaps or dark lines at the two wave-lengths concerned. These lines are denoted by the letters H and K. They are not entirely black, and it is important to measure the residual light at the centre of the lines, because we know that it must have an intensity just strong enough to keep calcium atoms floating under solar gravity; as soon as the outflowing light is so weakened that it can support no more atoms it can suffer no further depredations, and so it emerges into outer space with this limiting intensity. The measurement gives numerical data for working out the constants of the calcium atom including the time of relaxation mentioned above.
The atoms at the top of the chromosphere rest on the weakened light which has passed through the screen below; the full sunlight would blow them away. Milne has deduced a consequence which may perhaps have a practical application in the phenomena of explosion of ‘new stars’ or novae, and in any case is curiously interesting. Owing to the Doppler effect a moving atom absorbs a rather different wave-length from a stationary atom; so that if for any cause an atom moves away from the sun it will support itself on light which is a little to one side of the deepest absorption. This light, being more intense than that which provided a balance, will make the atom recede faster. The atom’s ownabsorption will thus gradually draw clear of the absorption of the screen below. Speaking rather metaphorically, the atom is balanced precariously on the summit of the absorption line and it is liable to topple off into the full sunlight on one side. Apparently the speed of the atom should go on increasing until it has to climb an adjacent absorption line (due perhaps to some other element); if the line is too intense to be surmounted the atom will stick part-way up, the velocity remaining fixed at a particular value. These later inferences may be rather far-fetched, but at any rate the argument indicates that there is likely to be an escape of calcium into outer space.
By Milne’s theory we can calculate the whole weight of the sun’s calcium chromosphere. Its mass is about 300 million tons. One scarcely expects to meet with such a trifling figure in astronomy. It is less than the tonnage handled by our English railways each year. I think that solar observers must feel rather hoaxed when they consider the labour that they have been induced to spend on this airy nothing. But science does not despise trifles. And astronomy can still be instructive even when, for once in a way, it descends to commonplace numbers.
This story has not much to do with atoms, and scarcely comes under the title of these lectures; but we have had occasion to allude to Betelgeuse as the famous example of a star of great size and low density, and its history is closely associated with some of the developments that we are studying.
No star has a disk large enough to be seen with our present telescopes. We can calculate that a lens or mirror of about 20 feet aperture wouldbe needed to show traces even of the largest star disk. Imagine for a moment that we have constructed an instrument of this order of size. Which would be the most hopeful star to try it on?
Perhaps Sirius suggests itself first, since it is the brightest star in the sky. But Sirius has a white-hot surface radiating very intensely, so that it is not necessary that it should have a wide expanse. Evidently we should prefer a star which, although bright, has its surface in a feebly glowing condition; then the apparent brightness must be due to large area. We need, then, a star which is both red and bright. Betelgeuse seems best to satisfy this condition. It is the brighter of the two shoulder-stars of Orion—the only conspicuous red star in the constellation. There are one or two rivals, including Antares, which might possibly be preferred; but we cannot go far wrong in turning our new instrument on Betelgeuse in the hope of finding the largest or nearly the largest star disk.
You may notice that I have paid no attention to the distances of these stars. It happens that distance is not relevant. It would be relevant if we were trying to find the star of greatest actual dimensions; but here we are considering the star which presents the largest apparent disk,[24]i.e. covers the largest area of the sky. If we were at twice our present distance from the sun, we should receive only one-quarter as much light; but the sun would look half its present size linearly, and its apparent area would be one-quarter. Thus the light per unit area of disk is unaltered by distance. Removing the sun to greaterand greater distance its disk will appear smaller but glowing not less intensely, until it is so far away that the disk cannot be discriminated.
By spectroscopic examination we know that Betelgeuse has a surface temperature about 3,000°. A temperature of 3,000° is not unattainable in the laboratory, and we know partly by experiment and partly by theory what is the radiating power of a surface in this state. Thus it is not difficult to compute how large an area of the sky Betelgeuse must cover in order that the area multiplied by the radiating power may give the observed brightness of Betelgeuse. The area turns out to be very small. The apparent size of Betelgeuse is that of a half-penny fifty miles away. Using a more scientific measure, the diameter of Betelgeuse predicted by this calculation is 0·051 of a second of arc.
No existing telescope can show so small a disk. Let us consider briefly how a telescope forms an image—in particular how it reproduces that detail and contrast of light and darkness which betrays that we are looking at a disk or a double star and not a blur emanating from a single point. This optical performance is called resolving power; it is not primarily a matter of magnification but of aperture, and the limit of resolution is determined by the size of aperture of the telescope.
To create a sharply defined image the telescope must not only bring light where there ought to be light, but it must also bring darkness where there ought to be darkness. The latter task is the more difficult. Light-waves tend to spread in all directions, and the telescope cannot prevent individual wavelets from straying on to parts of the picture where they have no business. But it has this oneremedy—for every trespassing wavelet it must send a second wavelet by a slightly longer or shorter route so as to arrive in a phase opposite to the first wavelet and cancel its effect. This is where the utility of a wide aperture arises—by affording a wider difference of route of the individual wavelets, so that those from one part of the aperture may be retarded relatively to and interfere with those from another part. A small object-glass can furnish light; it takes a big object-glass to furnish darkness in the picture.
Now we may ask ourselves whether the ordinary circular aperture is necessarily the most efficient for giving the wavelets the required path-differences. Any deviation from a symmetrical shape is likely to spoil the definition of the image—to produce wings and fringes. The image will not so closely resemble the object viewed. But on the other hand we may be able to sharpen up the tell-tale features. It does not matter how widely the image-pattern may differ from the object, provided that we can read the significance of the pattern. If we cannot reproduce a star-disk, let us try whether we can reproduce something distinctive of a star-disk.
A little reflection shows that we ought to improve matters by blocking out the middle of the object-glass, and using only the extreme regions on one side or the other. For these regions the difference of light-path of the waves is greatest, and they are the most efficient in furnishing the dark contrast needed to outline the image properly.
But if the middle of the object-glass is not going to be used, why go to the expense of manufacturing it? We are led to the idea of using two widely separated apertures, each involving a comparatively small lens or mirror. We thus arrive at an instrument after the pattern of arangefinder.
This instrument will not show us the disk of a star. If we look through it the main impression of the star image is very like what we should have seen with either aperture singly—a ‘spurious disk’ surrounded by diffraction rings. But looking attentively we see that this image is crossed by dark and bright bands which are produced by interference between the light-waves coming from the two apertures. At the centre of the image the waves from the two apertures arrive crest on crest since they have travelled symmetrically along equal paths; accordingly there is a bright band. A very little to one side the asymmetry causes the waves to arrive crest on trough, so that they cancel one another; here there is a dark band. The width of the bands decreases as the separation of the two apertures increases, and for any given separation the actual width is easily calculated.
Each point of the star’s disk is giving rise to a diffraction image with a system of bands of this kind, but so long as the disk is small compared with the finest detail of the diffraction image there is no appreciable blurring. If we continually increase the separation of the two apertures and so make the bands narrower, there comes a time when the bright bands for one part of the disk are falling on the dark bands for another part of the disk. The band system then becomes indistinct. It is a matter of mathematical calculation to determine the resultant effect of summing the band systems for each point of the disk. It can be shown that for a certain separation of the apertures the bands will disappear altogether; and beyond this separation the system should reappear though not attaining its original sharpness. The complete disappearance occurs when the diameter of the star-disk is equal to1⅕ times the width of the bands (from the centre of one bright band to the next). As already stated, the bandwidth can be calculated from the known separation of the apertures.
The observation consists in sliding apart the two apertures until the bands disappear. The diameter of the disk is inferred at once from their separation when the disappearance occurred. Although we measure the size of the disk in this way we neverseethe disk.
We can summarize the principle of the method in the following way. The image of a point of light seen through a telescope is not a point but a small diffraction pattern. Hence, if we look at an extended object, say Mars, the diffraction pattern will blur the fine detail of the marking on the planet. If, however, we are looking at a star which is almost a point, it is simpler to invert the idea; the object, not being an ideal point, will slightly blur the detail of the diffraction pattern. We shall only perceive the blurring if the diffraction pattern contains detail fine enough to suffer from it. Betelgeuse on account of its finite size must theoretically blur a diffraction pattern; but the ordinary diffraction disk and rings produced with the largest telescope are too coarse to show this. We create a diffraction image with finer detail by using two apertures. Theoretically we can make the detail as fine as we please by increasing the separation of the two apertures. The method accordingly consists in widening the separation until the pattern becomes fine enough to be perceptibly blurred by Betelgeuse. For a smaller star-disk the same effect of blurring would not be apparent until the detail had been made still finer by further separation of the apertures.
This method was devised long ago by Professor Michelson, but it was only in 1920 that he tried it on a large scale with a great 20-foot beam across the 100-inch reflector at Mount Wilson Observatory. After many attempts Pease and Anderson were able to show that the bright and dark bands for Betelgeuse disappeared when the apertures were separated 10 feet. The deduced diameter is 0·045 a second of arc in good enough agreement with the predicted value (p. 78). Only five or six stars have disks large enough to be measured with this instrument. It is understood that the construction of a 50-foot interferometer is contemplated; but even this will be insufficient for the great majority of the stars. We are fairly confident that the method of calculation first described gives the correct diameters of the stars, but confirmation by Michelson’s more direct method of measurement is always desirable.
To infer the actual size of the star from its apparent diameter, we must know the distance. Betelgeuse is rather a remote star and its distance cannot be measured very accurately, but the uncertainty will not change the general order of magnitude of the results. The diameter is about 300 million miles. Betelgeuse is large enough to contain the whole orbit of the earth inside it, perhaps even the orbit of Mars. Its volume is about fifty million times the volume of the sun.
There is no direct way of learning the mass of Betelgeuse because it has no companion near it whose motion it might influence. We can, however, deduce a mass from the mass-brightness relation inFig. 7. This gives the mass equal to 35 x sun. If the result is right, Betelgeuse is one of the most massive stars—but, of course, not massive in proportion to its bulk. The mean density is aboutone-millionth of the density of water, or not much more than one-thousandth of the density of air.[25]
There is one way in which we might have inferred that Betelgeuse is less dense than the sun, even if we had had no grounds of theory or analogy for estimating its mass. According to the modern theory of gravitation, a globe of the size of Betelgeuse and of the same mean density as the sun would have some remarkable properties:
Firstly, owing to the great intensity of its gravitation, light would be unable to escape; and any rays shot out would fall back again to the star by their own weight.
Secondly, the Einstein shift (used to test the density of the Companion of Sirius) would be so great that the spectrum would be shifted out of existence.
Thirdly, mass produces a curvature of space, and in this case the curvature would be so great that space would close up round the star, leaving us outside—that is to say,nowhere.
Except for the last consideration, it seems rather a pity that the density of Betelgeuse is so low.
It is now well realized that the stars are a very important adjunct to the physical laboratory—a sort of high-temperature annex where the behaviour of matter can be studied under greatly extended conditions. Being an astronomer, I naturally put the connexion somewhat differently and regard the physical laboratory as a low-temperature station attached to the stars. It is the laboratory conditions which should be counted abnormal. Apart from the interstellar cloud which is at themoderate temperature of about 15,000°, I suppose that nine-tenths of the matter of the universe is above 1,000,000°. Underordinaryconditions—you will understand my use of the word—matter has rather simple properties. But there are in the universe exceptional regions with temperature not far removed from the absolute zero, where the physical properties of matter acquire great complexity; the ions surround themselves with complete electron systems and become the atoms of terrestrial experience. Our earth is one of these chilly places and here the strangest complications can arise. Perhaps strangest of all, some of these complications can meet together and speculate on the significance of the whole scheme.