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 own absorption 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.
[The Story of Betelgeuse]
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 would be 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 greater and 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 one remedy—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.