20,000 to 200,000 light years. Is there anything yet more remote? It
has long been suspected that the spiral nebulae,[29] which seem to be
exceedingly numerous, are outside our stellar system and form ‘island
universes’. The evidence for this has become gradually stronger, and
now is believed to be decisively confirmed. In 1924 Hubble discovered
a number of Cepheid variables in the great Andromeda nebula which is
the largest and presumably one of the nearest of the spirals. As soon
as their periods had been determined they were available as standard
candles to gauge the distance of the nebula. Their apparent magnitude
was much fainter than that of the corresponding Cepheids in globular
clusters, showing that they must be even more remote. Hubble has since
found the distance of one or two other spirals in the same way.
With the naked eye you can see the Andromeda nebula as a faint patch of
light. When you look at it you are looking back 900,000 years into the
past.
_The Contraction Hypothesis_
The problem of providing sufficient supplies of energy to maintain the
sun’s output of light and heat has often been debated by astronomers
and others. In the last century it was shown by Helmholtz and
Kelvin that the sun could maintain its heat for a very long time by
continually shrinking. Contraction involves an approach or fall of
the matter towards the centre; gravitational potential energy is thus
converted and made available as heat. It was assumed that this was
the sole resource since no other supply capable of yielding anything
like so large an amount was known. But the supply is not unlimited,
and on this hypothesis the birth of the sun must be dated not more
than 20,000,000 years ago. Even at the time of which I am speaking the
time-limit was found to be cramping; but Kelvin assured the geologists
and biologists that they must confine their outlines of terrestrial
history within this period.
About the beginning of the present century the contraction theory was
in the curious position of being generally accepted and generally
ignored. Whilst few ventured to dispute the hypothesis, no one seems to
have had any hesitation, if it suited him, in carrying back the history
of the earth or moon to a time long before the supposed era of the
formation of the solar system. Lord Kelvin’s date of the creation was
treated with no more respect than Archbishop Ussher’s.
The serious consequences of the hypothesis become particularly
prominent when we consider the diffuse stars of high luminosity; these
are prodigal of their energy and squander it a hundred or a thousand
times faster than the sun. The economical sun could have subsisted
on its contraction energy for 20,000,000 years, but for the high
luminosity stars the limit is cut down to 100,000 years. This includes
most of the naked-eye stars. Dare we believe that they were formed
within the last 100,000 years? Is the antiquity of man greater than
that of the stars now shining? Do stars in the Andromeda nebula run
their course in less time than their light takes to reach us?
It is one thing to feel a limitation of time-scale irksome, ruling out
ideas and explanations which are otherwise plausible and attractive; it
is another thing to produce definite evidence against the time-scale.
I do not think that astronomers had _in their own territory_ any
weapon for a direct attack on the Helmholtz-Kelvin hypothesis until
the Cepheid variables supplied one. To come to figures: δ Cephei emits
more than 700 times as much heat as the sun. We know its mass and
radius, and we can calculate without difficulty how fast the radius
must contract in order to provide this heat. The required rate is one
part in 40,000 per annum. Now δ Cephei was first observed carefully
in 1785, so that in the time it has been under observation the radius
must have changed by one part in 300 if the contraction hypothesis is
right. You remember that we have in δ Cephei a very sensitive indicator
of any changes occurring in it, viz. the period of pulsation; clearly
changes of the above magnitude could not occur without disturbing this
indicator. Does the period show any change? It is doubtful; there is
perhaps sufficient evidence for a slight change, but it is not more
than ¹⁄₂₀₀th of the change demanded by the contraction hypothesis.
Accepting the pulsation theory, the period should diminish 17 seconds
every year--a quantity easily detectable. The actual change is not
more than one-tenth of a second per year. At least during the Cepheid
stage the stars are drawing on some source of energy other than that
provided by contraction.
On such an important question we should not like to put implicit
trust in one argument alone, and we turn to the sister sciences for
other and perhaps more conclusive evidence. Physical and geological
investigations seem to decide definitely that the age of the
earth--reckoned from an epoch which by no means goes back to its
beginnings as a planet--is far greater than the Helmholtz-Kelvin
estimate of the age of the solar system. It is usual to lay most stress
on a determination of the age of the rocks from the uranium-lead ratio
of their contents. Uranium disintegrates into lead and helium at a
known rate. Since lead is unlike uranium in chemical properties the two
elements would not naturally be deposited together; so that the lead
found with uranium has presumably been formed by its decomposition.[30]
By measuring how much lead occurs with the uranium we can determine
how long ago the uranium was deposited. The age of the older rocks
is found to be about 1,200 million years; lower estimates have been
urged by some authorities, but none low enough to save the contraction
hypothesis. The sun, of course, must be very much older than the earth
and its rocks.
We seem to require a time-scale which will allow at least
10,000,000,000 years for the age of the sun; certainly we cannot
abate our demands below 1,000,000,000 years. It is necessary to look
for a more prolific source of energy to maintain the heat of the
sun and stars through this extended period. We can at once narrow
down the field of search. No source of energy is of any avail unless
it liberates heat in the deep interior of the star. The crux of the
problem is not merely the provision for radiation but the maintenance
of the internal heat which keeps the gravitating mass from collapsing.
You will remember how in the first lecture we had to assign a certain
amount of heat at each point in the stellar interior in order to keep
the star in balance. But the internal heat is continually running away
towards the cooler outside and then escaping into space as the star’s
radiation. This, or its equivalent, must be put back if the star is to
be kept steady--if it is not to contract and evolve at the rate of the
Kelvin time-scale. And it is no use to put it back at the surface of
the star--by bombarding the star with meteors, for example. It could
not flow up the temperature-gradient, and so it would simply take the
first opportunity of escaping as additional radiation. You cannot
maintain a temperature-gradient by supplying heat at the bottom end.
Heat must be poured in at the top end, i. e. in the deep interior of
the star.
Since we cannot well imagine an extraneous source of heat able to
release itself at the centre of a star, the idea of a star picking up
energy as it goes along seems to be definitely ruled out. _It follows
that the star contains hidden within it the energy which has to last
the rest of its life_.
Energy has mass. Many people would prefer to say--energy _is_
mass; but it is not necessary for us to discuss that. The essential
fact is that an erg of energy in any form has a mass of 1·1. 10^-21
grammes. The erg is the usual scientific unit of energy; but we can
measure energy also by the gramme or the ton as we measure anything
else which possesses mass. There is no real reason why you should not
buy a pound of light from an electric light company--except that it
is a larger quantity than you are likely to need and at current rates
would cost you something over £100,000,000. If you could keep all this
light (ether-waves) travelling to and fro between mirrors forming a
closed vessel, and then weigh the vessel, the observed weight would be
the ordinary weight of the vessel plus 1 lb. representing the weight of
the light. It is evident that an object weighing a ton cannot contain
more than a ton of energy; and the sun with a mass of 2.000 quadrillion
tons (p. 24) cannot contain more than 2.000 quadrillion tons of energy
at the most.
Energy of 1·8. 10^{54} ergs has a mass 2. 10^{33} grammes which is the
mass of the sun; consequently that is the sum total of the energy which
the sun contains--the energy which has to last it all the rest of its
life.[31] We do not know how much of this is capable of being converted
into heat and radiation; if it is all convertible there is enough to
maintain the sun’s radiation at the present rate for 15 billion years.
To put the argument in another form, the heat emitted by the sun each
year has a mass of 120 billion tons; and if this loss of mass continued
there would be no mass left at the end of 15 billion years.
_Subatomic Energy_
This store of energy is, with insignificant exception, energy of
constitution of atoms and electrons; that is to say, subatomic energy.
Most of it is inherent in the constitution of the electrons and
protons--the elementary negative and positive electric charges--out
of which matter is built; so that it cannot be set free unless these
are destroyed. The main store of energy in a star cannot be used for
radiation unless the matter composing the star is being annihilated.
It is possible that the star may have a long enough life without
raiding the main energy store. A small part of the store can be
released by a process less drastic than annihilation of matter, and
this might be sufficient to keep the sun burning for 10,000,000,000
years or so, which is perhaps as long as we can reasonably require.
The less drastic process is transmutation of the elements. Thus we
have reached a point where a choice lies open before us; we can either
pin our faith to transmutation of the elements, contenting ourselves
with a rather cramped time-scale, or we can assume the annihilation of
matter, which gives a very ample time-scale. But at present I can see
no possibility of a third choice. Let me run over the argument again.
First we found that energy of contraction was hopelessly inadequate;
then we found that the energy must be released in the interior of the
star, so that it comes from an internal, not an external, source; now
we take stock of the whole internal store of energy. No supply of
any importance is found until we come to consider the electrons and
atomic nuclei; here a reasonable amount can be released by regrouping
the protons and electrons in the atomic nuclei (transmutation of
elements), and a much greater amount by annihilating them.
Transmutation of the elements--so long the dream of the alchemist--is
realized in the transformation of radio-active substances. Uranium
turns slowly into a mixture of lead and helium. But none of the known
radio-active processes liberate anything like enough energy to maintain
the sun’s heat. The only important release of energy by transmutation
occurs at the very beginning of the evolution of the elements.
We must start with hydrogen. The hydrogen atom consists simply of a
positive and negative charge, a proton for the nucleus plus a planet
electron. Let us call its mass 1. Four hydrogen atoms will make a
helium atom. If the mass of the helium atom were exactly 4, that would
show that all the energy of the hydrogen atoms remained in the helium
atom. But actually the mass is 3·97; so that energy of mass a 0·03
must have escaped during the formation of helium from hydrogen. By
annihilating 4 grammes of hydrogen we should have released 4 grammes of
energy, but by transmuting it into helium we release 0·03 grammes of
energy. Either process might be used to furnish the sun’s heat though,
as we have already stated, the second gives a much smaller supply.
The release of energy occurs because in the helium atom only two of the
four electrons remain as planet electrons, the other two being cemented
with the four protons close together in the helium nucleus. In bringing
positive and negative charges close together you cause a change of
the energy of the electric field, and release electrical energy which
spreads away as ether-waves. That is where the 0·03 grammes of energy
has gone. The star can absorb these ether-waves and utilize them as
heat.
We can go on from helium to higher elements, but we do not obtain much
more release of energy. For example, an oxygen atom can be made from 16
hydrogen atoms or 4 helium atoms; but as nearly as we can tell it has
just the weight of the 4 helium atoms, so that the release of energy
is not appreciably greater when the hydrogen is transmuted into oxygen
than when it is transmuted into helium.[32] This becomes clearer if
we take the mass of a hydrogen atom to be 1·008, so that the mass of
helium is exactly 4 and of oxygen 16; then it is known from Dr. Aston’s
researches with the mass-spectrograph that the atoms of other elements
have masses which are very closely whole numbers. The loss of 0·008 per
hydrogen atom applies approximately whatever the element that is formed.
The view that the energy of a star is derived by the building up of
other elements from hydrogen has the great advantage that there is no
doubt about the possibility of the process; whereas we have no evidence
that the annihilation of matter can occur in Nature. I am not referring
to the alleged transmutation of hydrogen into helium in the laboratory;
those whose authority I accept are not convinced by these experiments.
To my mind the existence of helium is the best evidence we could desire
of the possibility of the _formation_ of helium. The four protons
and two electrons constituting its nucleus must have been assembled at
some time and place; and why not in the stars? When they were assembled
the surplus energy must have been released, providing a prolific supply
of heat. Prima facie this suggests the interior of a star as a likely
locality, since undoubtedly a prolific source of heat is there in
operation. I am aware that many critics consider the conditions in the
stars not sufficiently extreme to bring about the transmutation--the
stars are not hot enough. The critics lay themselves open to an obvious
retort; we tell them to go and find a _hotter place_.
But here the advantage seems to end. There are many astronomical
indications that the hypothesis attributing the energy of the stars
to the transmutation of hydrogen is unsatisfactory. It may perhaps be
responsible for the rapid liberation of energy in the earliest (giant)
stages when the star is a large diffuse body radiating heat abundantly;
but the energy in later life seems to come from a source subject to
different laws of emission. There is considerable evidence that as a
star grows older it gets rid of a large fraction of the matter which
originally constituted it, and apparently this can only be contrived
by the annihilation of the matter. The evidence, however, is not very
coherent, and I do not think we are in a position to come to a definite
decision. On the whole the hypothesis of annihilation of matter seems
the more promising; and I shall prefer it in the brief discussion of
stellar evolution which I propose to give.
The phrase ‘annihilation of matter’ sounds like something supernatural.
We do not yet know whether it can occur naturally or not, but there is
no obvious obstacle. The ultimate constituents of matter are minute
positive charges and negative charges which we may picture as centres
of opposite kinds of strain in the ether. If these could be persuaded
to run together they would cancel out, leaving nothing except a splash
in the ether which spreads out as an electromagnetic wave carrying off
the energy released by the undoing of the strain. The amount of this
energy is amazingly large; by annihilating a single drop of water we
should be supplied with 200 horsepower for a year. We turn covetous
eyes on this store without, however, entertaining much hope of ever
discovering the secret of releasing it. If it should prove that the
stars have discovered the secret and are using this store to maintain
their heat, our prospect of ultimate success would seem distinctly
nearer.
I suppose that many physicists will regard the subject of subatomic
energy as a field of airy speculation. That is not the way in which
it presents itself to an astronomer. If it is granted that the stars
evolve much more slowly than on the contraction-hypothesis, the
measurement of the output of subatomic energy is one of the commonest
astronomical measurements--the measurement of the heat or light of the
stars.[33] The collection of observational data as to the activity of
liberation of subatomic energy is part of the routine of practical
astronomy; and we have to pursue the usual course of arranging the
measurements into some kind of coherence, so as to find out how the
output is related to the temperature, density, or age of the material
supplying it--in short, to discover the laws of emission. From this
point onwards the discussion may be more or less hypothetical according
to the temperament of the investigator; and indeed it is likely that in
this as in other branches of knowledge advances may come by a proper
use of the scientific imagination. Vain speculation is to be condemned
in this as in any other subject, and there is no need for it; the
problem is one of induction from observation with due regard to our
theoretical knowledge of the possibilities inherent in atomic structure.
I cannot pass from this subject without mentioning the penetrating
radiation long known to exist in our atmosphere, which according
to the researches of Kohlhörster and Millikan comes from outer
space. Penetrating power is a sign of short wave-length and intense
concentration of energy. Hitherto the greatest penetrating power
has been displayed by Gamma rays originated by subatomic processes
occurring in radio-active substances. The cosmic radiation is still
more penetrating, and it seems reasonable to refer it to more energetic
processes in the atom such as those suggested for the source of
stellar energy. Careful measurements have been made by Millikan, and
he concludes that the properties accord with those which should be
possessed by radiation liberated in the transmutation of hydrogen; it
is not penetrating enough to be attributed to a process so energetic as
the annihilation of protons and electrons.
There seems to be no doubt that this radiation is travelling downwards
from the sky. This is shown by measurements of its strength at
different heights in the atmosphere and at different depths below the
surface of mountain lakes; it is weakened according to the amount of
air or water that it has had to traverse. Presumably its source must be
extra-terrestrial. Its strength does not vary with the sun’s altitude,
so it is not coming from the sun. There is some evidence that it varies
according to the position of the Milky Way, most radiation being
received when the greatest extension of the stellar system is overhead.
It cannot come from the _interior_ of the stars, the penetrating
power being too limited; all the hottest and densest matter in the
universe is shut off from us by impenetrable walls. At the most it
could come only from the outer rind of the stars where the temperature
is moderate and the density is low; but it is more likely that its main
source is in the diffuse nebulae or possibly in the matter forming the
general cloud in space.[34]
We must await further developments before we can regard the supposed
subatomic origin of this radiation as other than speculative; we
mention it here only as a possible opening for progress. It will be of
great interest if we can reach by this means a more direct acquaintance
with the processes which we assume to be the source of stellar energy;
and the messages borne to us by the cosmic rays which purport to
relate to these processes deserve the closest attention. Our views
of stellar energy are likely to be affected on one crucial point.
Hitherto we have usually supposed that the very high temperature in the
interior of a star is one of the essential conditions for liberation of
subatomic energy, and that a reasonably high density is also important.
Theoretically it would seem almost incredible that the building up of
higher elements or the annihilation of protons and electrons could
proceed with any degree of vigour in regions where encounters are rare
and there is no high temperature or intense radiation to wake the atoms
from apathy; but the more we face the difficulties of all theories of
the release of subatomic energy the less inclined we are to condemn
any evidence as incredible. The presence of sodium and calcium in
the cosmical cloud, of helium and nebulium in the diffuse nebulae,
of titanium and zirconium in large quantities in the atmospheres of
the youngest stars, bears witness that the evolution of the elements
is already far advanced during the diffuse prestellar stage--unless
indeed our universe is built from the debris of a former creation.
From this point of view it is fitting that we should discern symptoms
of subatomic activity in open space. But the physicist may well shake
his head over the problem. How are four protons and two electrons to
gather together to form a helium nucleus in a medium so rare that the
free path lasts for days? The only comfort is that the mode of this
occurrence is (according to present knowledge) so inconceivable under
any conditions of density and temperature that we may postulate it in
the nebulae--on the principle that we may as well be hung for a sheep
as for a lamb.
_Evolution of the Stars_
Twenty years ago stellar evolution seemed to be very simple. The stars
begin by being very hot and gradually cool down until they go out.
On this view the temperature of a star indicated the stage of evolution
that it had reached. The outline of the sequence was sufficiently
indicated by the crude observation of colour--white-hot, yellow-hot,
red-hot; a more detailed order of temperature was ascertained by
examining the light with a spectroscope. The red stars naturally
came last in the sequence; they were the oldest stars on the verge
of extinction. Sir Norman Lockyer strongly opposed this scheme and
to a considerable extent anticipated the more modern view; but most
astronomers pinned their faith to it up to about 1913.
Ten years ago more knowledge had been gained of the densities of
stars. It seemed likely that density would be a more direct criterion
of evolutionary development than temperature. Granted that a star
condenses out of nebulous material, it must in the youngest stage be
very diffuse; from that stage it will contract and steadily increase in
density.
But this necessitates an entire rearrangement of the scheme of
evolution, because the order according to density is by no means the
same as the order according to surface temperature. On the former
view all the cool red stars were old and dying. But a large number of
them are now found to be extremely diffuse--stars like Betelgeuse,
for instance. These must be set down as the very youngest of the
stars; after all it is not unnatural that a star just beginning to
condense out of nebulous material should start at the lowest stage of
temperature. Not all the red stars are diffuse; there are many like
Krueger 60 which have high density, and these we leave undisturbed
as representing the last stage of evolution. Both the first and last
periods of a star’s life are characterized by low temperature; in
between whiles the temperature must have risen to a maximum and fallen
again.