in a position to make an estimate of the amount of matter remaining
unaggregated in space. An ordinary region where there is no observable
nebulosity is the highest vacuum existing--within the limits of the
stellar system at least--but there still remains about _one atom in
every cubic inch_. It depends on our point of view whether we regard
this as an amazing fullness or an amazing emptiness of space. Perhaps
it is the fullness that impresses us most. The atom can find no place
of real solitude within the system of the stars; wherever it goes it
can nod to a colleague not more than an inch away.
Let us approach the same subject from a different angle.
In the ‘Story of Algol’ I referred to the way in which we measure the
velocity of rotation of the sun. We point the spectroscope first on one
limb of the sun and then on the other. Taking any one of the dark lines
of the spectrum, we find that it has shifted a little between the two
observations. This tells us that the material which imprinted the line
was moving towards or away from us with different velocities in the two
observations. That is what we expected to find; the rotation of the
sun makes solar material move towards us on one side of the disk and
away from us on the other side. But there are a few dark lines which
do not show this change. They are in just the same position whether
we observe them on the east or on the west of the sun. Clearly these
cannot originate on the sun. They have been imprinted on the light
after it left the sun and before it reached our telescope. We have
thus discovered a medium occurring somewhere between the sun and our
telescope; and as some of the lines are recognized as belonging to
oxygen, we can infer that it is a medium containing oxygen.
This seems to be the beginning of a great discovery, but it ends in a
bathos. It happens that we were already aware of a medium containing
oxygen lying somewhere between our telescope and the sun. It is a
medium essential to our existence. The terrestrial atmosphere is
responsible for the ‘fixed’ lines seen in the sun’s spectrum.
Just as the spectroscope can tell us that the sun is turning round (a
fact already familiar to us from watching the surface markings), so
it can tell us that certain stars are wandering round an orbit, and
therefore are under the influence of a second star which may or may
not be visible itself. But here again we sometimes find ‘fixed’ lines
which do not change with the others. Therefore somewhere between the
star and the telescope there exists a stationary medium which imprints
these lines on the light. This time it is not the earth’s atmosphere.
The lines belong to two elements, calcium and sodium, neither of which
occur in the atmosphere. Moreover, the calcium is in a smashed state,
having lost one of its electrons, and the conditions in our atmosphere
are not such as would cause this loss. There seems to be no doubt that
the medium containing the sodium and ionized calcium--and no doubt
many other elements which do not show themselves--is separate from the
earth and the star. It is the ‘fullness’ of interstellar space already
mentioned. Light has to pass one atom per cubic inch all the way from
the star to the earth, and it will pass quite enough atoms during its
journey of many hundred billion miles to imprint these dark lines on
its spectrum.
At first there was a rival interpretation. It was thought that the
lines were produced in a cloud attached to the star--forming a kind
of aureole round it. The two components travel in orbits round each
other, but their orbital motion need not disturb a diffuse medium
filling and surrounding the combined system. This was a very reasonable
suggestion, but it could be put to the test. The test was again
_velocity_. Although either component can move periodically to
and fro within the surrounding cloud of calcium and sodium, it is
clear that its average approach to us or recession from us taken over
a long time must agree with that of the calcium and sodium if the star
is not to leave its halo behind. Professor Plaskett with the 72-inch
reflector at the Dominion Observatory in British Columbia carried out
this test. He found that the secular or average rate of approach of
the star[20] was in general quite different from the rate shown by the
fixed calcium or sodium lines. Clearly the material responsible for
the fixed lines could not be an appendage of the star since it was not
keeping pace with it. Plaskett went farther and showed that whereas
the stars themselves had all sorts of individual velocities, the
material of the fixed lines had the same or nearly the same velocity
in all parts of the sky, as though it were one continuous medium
throughout interstellar space. I think there can be no doubt that this
research demonstrates the existence of a cosmic cloud pervading the
stellar system. The fullness of interstellar space becomes a fact of
observation and no longer a theoretical conjecture.
The system of the stars is floating in an ocean--not merely an ocean
of space, not merely an ocean of ether, but an ocean that is so far
material that one atom or thereabouts occurs in each cubic inch. It is
a placid ocean without much relative motion; currents probably exist,
but they are of a minor character and do not attain the high speeds
commonly possessed by the stars.
Many points of interest arise, but I will only touch on one or two.
Why are the calcium atoms ionized? In the calm of interstellar space
we seem to have passed away from the turmoil which smashed the calcium
atoms in the interior of a star; so at first it seems difficult to
understand why the atoms in the cloud should not be complete. However,
even in the depths of space the breaking-up of the atom continues;
because there is always starlight passing across space, and some of
the light-waves are quite powerful enough to wrench a first or second
electron away from the calcium atom. It is one of the most curious
discoveries of modern physics that when a light-wave is attenuated
by spreading, what it really suffers from is _laziness_ rather
than actual loss of power. What is weakened is not the power but the
probability that it will display the power. A light-wave capable of
bursting an atom still retains the power when it is attenuated a
million-fold by spreading; only it is a million times more sparing in
the exercise of the power. To put it another way, an atom exposed to
the attenuated waves will on the average have to wait a million times
longer before a wave chooses to explode it; but the explosion when it
does occur will be of precisely the same strength however great the
attenuation. This is entirely unlike the behaviour of water-waves; a
wave which is at first strong enough to capsize a boat will, after
spreading, become too weak. It is more like machine-gun fire which is
more likely to miss a given object at greater distance but is equally
destructive if it hits. The property here referred to (the quantum
property) is the deepest mystery of light.
Thus in interstellar space electrons are still being torn from calcium
atoms, only very infrequently. The other side of the question is the
rate of repair, and in this connexion the low density of the cosmic
cloud is the deciding factor. The atom has so few opportunities for
repair. Roving through space the atom meets an electron only about
once a month, and it by no means follows that it will capture the first
one it meets. Consequently very infrequent smashing will suffice to
keep the majority of the atoms ionized. The smashed state of the atoms
inside a star can be compared to the dilapidation of a house visited by
a tornado; the smashed state in interstellar space is a dilapidation
due to ordinary wear and tear coupled with excessive slackness in
making repairs.
A calculation indicates that most of the calcium atoms in interstellar
space have lost two electrons; these atoms do not interfere with the
light and give no visible spectrum. The ‘fixed lines’ are produced by
atoms temporarily in a better state of repair with only one electron
missing; they cannot amount at any moment to more than one-thousandth
of the whole number, but even so they will be sufficiently numerous to
produce the observed absorption.
We generally think of interstellar space as excessively cold. It is
quite true that any thermometer placed there would show a temperature
only about 3° above the absolute zero--if it were capable of
registering so low a reading. Compact matter such as a thermometer, or
even matter which from the ordinary standpoint is regarded as highly
diffuse, falls to this low temperature. But the rule does not apply
to matter as rarefied as the interstellar cloud. Its temperature is
governed by other considerations, and it will probably be not much
below the surface-temperature of the hottest stars, say 15,000°.
Interstellar space is at the same time excessively cold and decidedly
hot.[21]
_The Sun’s Chromosphere_
Once again we shift the scene, and now we are back in the outer parts
of the sun. Fig. 10[22] shows one of the huge prominence flames which
from time to time shoot out of the sun. The flame in this picture was
about 120,000 miles high. It went through great changes of form and
disappeared in not much more than twenty-four hours. This was rather an
exceptional specimen. Smaller flames occur commonly enough; it seems
that the curious black marks in Fig. 1, often looking like rifts,
are really prominences seen in projection against the still brighter
background of the sun. The flames consist of calcium, hydrogen, and
several other elements.
We are concerned not so much with the prominences as with the layer
from which they spring. The ordinary atmosphere of the sun terminates
rather abruptly, but above it there is a deep though very rarefied
layer called the chromosphere consisting of a few selected elements
which are able to float--float, not on the top of the sun’s atmosphere,
but on the _sunbeams_. The art of riding a sunbeam is evidently
rather difficult, because only a few of the elements have the necessary
skill. The most expert is calcium. The light and nimble hydrogen atom
is fairly good at it, but the ponderous calcium atom does it best.
The layer of calcium suspended on the sunlight is at least 5,000 miles
thick. We can observe it best when the main part of the sun is hidden
by the moon in an eclipse; but the spectroheliograph enables us to
study it to some extent without an eclipse.
[Illustration: Fig. 10. SOLAR PROMINENCE]
[Illustration: 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 atom
would 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
in Fig. 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] scores
because 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 higher
orbit 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 two
particular 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
the _outflowing_ sunlight 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 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.