27.1: The Problem
The conclusion was reached in Part Three that a cosmological model based
on Symmetrical Impermanence would contain spiral nebulae. In this respect
it would resemble actuality. But it did not seem to do so in another respect,
for no reason could be found why the nebulae should contain discrete
stars. It seemed that they must consist only of a more or less diffuse gas.
For many years this conclusion led me to doubt the validity of Symmetrical Impermanence. It seemed to lead to a false model. But it will be
shown below that what was at fault was not Symmetrical Impermanence
but the traditional theory of gravitation. If one adopts the new theory
that has been presented in Chapter 25, one arrives at a model in which the
nebulae do contain discrete stars.
The difficulty of arriving at the correct model with the traditional
theory is, it will be remembered, that, according to this theory, the gravitational pull on particles of gas in a cosmic cloud would always be towards
the centre of gravity of the whole cloud. But stars would not form if
movement were exclusively towards the common centre. The result would
be one single, compact mass. For stars to separate out there must be
movement towards local centres; some particles must move outwards,
away from the centre of gravity of the whole cloud and towards the centres
of the incipient stars. So star formation would require the setting up of
parochial fields of force strong enough to compete successfully with the
gravitational field common to the whole cloud.
Of course one could save the traditional theory of gravitation by inventing additional hypotheses. Perhaps, one might say, some other kind
of force operates to cause stars to condense out of a cloud of gas. Perhaps
the stars have not condensed out of a cloud of gas at all but have beer
assembled by some quite different and unknown process. Perhaps the
Cosmic Statute Book contains a law to say that particles shall congregate
to form stars and they obediently do so. But 'perhaps' as the basis of an
explanation is a word that should be avoided in physics whenever possible,
An hypothesis that cannot be inferred from the Principle of Minimum
Assumption has, I should like to insist once again, no place in physics.
But it will be shown below that no ad hoc hypothesis is needed to explain
the formation of stars.
27.2: In a Tenuous Cloud Gravitational Pulses are Intermittent
The explanation of star formation lies in the simple fact that the gravitational force is, like light, intermittent. Around any appreciable concentration of matter the discontinuity is no more observable than the discontinuity in a beam of radiation, which, nevertheless, consists of a bundle of
discrete photons. But when the quantity of mass in a given place is quite
small, there must be a significant interval of time between successive
In a gas so diffuse that scattered atoms are well separated from each
other the sites for extinctions must be few and far between. According to
the new theory of gravitation, it has to be remembered, these isolated
atoms do not exercise any gravitational effect at all so long as they continue to exist. It is only when, here and there, an atom becomes extinct
that a gravitational pulse is emitted. The effect of such intermittent extinctions is very different from a steady pull in any one direction.
After there has been an extinction in one particular place there may
not be another in the vicinity for an appreciable time. The next nearest
extinction may be a great distance away if the gas is very diffuse. Such
infrequent extinctions will impart spasmodic jerks to all matter that comes
under their influence. During the intervals of time between them there will
be no forces at all except those that arise from still more remote extinctions; and as the pulses diminish in intensity according to the inverse
square law the more remote sources of quanta of gravitation will have a
relatively feeble effect.
In such conditions it is rather meaningless to speak of a centre of
gravity for the whole cloud. There is a geometric centre, but the gravitational pull is by no means always and everywhere directed towards it.
The pulls are random; they arise from scattered sources and operate in all
directions. At most one can say that there are, on the average, more pulls
in the direction where there is most mass, namely towards the geometric
centre, than away from it.
27.3: Incipient Concentrations
Let us consider in the light of the above remarks what must happen
to particles in the cloud that has begun to form around an astronomical
summit. The density of such a cloud, it has to be remembered, is by
terrestrial standards very low. A gramme occupies a vast region.
Let us first consider extinctions. These produce pulses of gravitation.
So long as such a passing pulse of gravitation lasts, all particles in the cloud
that are reached by it experience an acceleration towards the site. When
the pulse is over there is no more acceleration, but the particles have
acquired a finite velocity and are therefore converging from all directions
on to the site. Origins have an opposite effect. As these are distributed
almost uniformly in space, the dispersals occasioned by them are on the
average as much away from as towards any particular direction. They must
create a little turbulence in the gas, but do not have any lasting effect on
the distribution of its particles. They may, however, break up concentrations that are beginning to form. For after an extinction has caused
particles to converge on to the site, a subsequent origin in the same place
will send the particles back to where they came from. This will prevent
every extinction from leading to a lasting concentration. But one can infer
that some of the incipient concentrations will not be dispersed before they
have established themselves. The establishing of at least some follows from
The probability of an extinction anywhere is directly proportional to
the gas density there. When, therefore, the particles have begun to crowd
together around the site of a recent extinction, it becomes a little more
probable that another extinction will occur near the previous one. When
this does happen the converging particles will receive an additional
acceleration in roughly the same direction in which they are moving
already. They will then not be so easily scattered as before.
The second extinction will cause the crowd to thicken and make a
third extinction there yet more probable. If this occurs, the crowd of
particles will be rendered still more dispersal-proof. So it must go on. After
a concentration has got well underway it must steadily increase.
The process just described is of the kind that can be achieved in
engineering with the help of devices that provide what is called 'positive
feedback'. But no such devices are needed to maintain the process of
forming concentrations in extragalactic space. The laws of probability
suffice to explain what happens. When the process has continued for long
enough, the result is a very big and massive concentration. We call it a
star. Here, incidentally, is an example of a process that tends not to a
stable equilibrium, as with negative feedback, but to increase its cause.
27.4: Incipient Stars have an Irregular Structure
Probability considerations lead one to expect an increase in the
number of extinctions around the geometric centre of an incipient star
during the very earliest stage of its formation; but these extinctions may
be near to or far from the geometric centre. Each will form its own
incipient concentration so that the structure of the incipient star must be
far from homogeneous. Within this structure there must be numerous
parochial concentrations. But as the star becomes more dense and pulses
of gravitation within it more frequent, conditions must gradually change
so that the general effect is as though all the pulses emanated from the
common centre. The intervals between pulses will become so short that
particles will never have time to move far towards the parochial centre
before they are accelerated away from it towards the centre of gravity of
the whole star.
Before this happens the incipient star must have a quite irregular
shape. But as extinctions within it become numerous enough to be practically continuous, it will be gradually pulled together into the shape of a
27.5. Double and Multiple Stars
As the thickening of the gas extends to a substantial distance from the
incipient star, there must be many occasions when an extinction at a
substantial distance forms the beginning of a second star. If this happens
while pulses from the original incipient star are still significantly intermittent, the second star will be able to form, competing for hydrogen
successfully with its slightly more developed neighbour. More than one
star may thus form at a certain distance from the first star. The consequence
will be one of the double or multiple stars that are rather numerous.
It should be noted that the components of double or multiple stars
must, according to the new theory, all begin at about the same time. If
one of them had become well-established it would be so massive that it
would attract all surrounding particles to itself; a later incipient concentration would not stand a chance of surviving.
The component stars must also be of approximately the same size
during their period of growth. For if any one of them were much less
massive than its neighbours it would be absorbed by them. Small differences
in mass need not, however, prevent double or multiple stars from growing
side by side during the time while they remain very tenuous.
Later, however, when the difference between gain by capture and loss
by extinction becomes very narrow a small reduction in income from
capture can lead to a change from growing to dwindling. One should
therefore expect the two components of a double star to have unequal later
histories. When both have reached the size at which income and loss
balance one should expect the slightly larger one to maintain, even somewhat increase, its mass while the smaller one would lose mass at an ever
increasing rate. In other words, neighbouring stars of the size at which
income and loss nearly balance are in competition for new matter and the
smaller ones lose the battle. The consequence of this will be discussed in
27.6: At What Gas Density do Stars Form?
The gas density at which stars can form would seem to be a quantity of
some significance in cosmology. Knowledge of it might help us to estimate
the stage in the evolution of a spiral nebula at which star formation occurs.
But at present it is only possible to say that there must be an upper and a
That there is a lower limit is obvious, for no stars can form where the
density is zero. The density must be at least such that the conditions for
the effective crowding together of particles are met. These conditions are
that the particles are able to acquire a significant average velocity from
one single quantum of gravitation and that there is a significant number of
such particles. But the velocity cannot be significant if the nearest particles
to the site of an extinction are a long way off. The pulse of gravitation can
only produce such a velocity if it has not become too weak; and its effect
diminishes with the square of distance.
Hence the pulse can only significantly affect the movement of particles
within a limited range. If the number of particles within this range is small,
the effect on the local density will be negligible.
It has to be remembered that the scattering effect produced by origins
is independent of density. There are as many quanta of anti-gravitation
per unit volume in a high vacuum as in a dense medium. But a large number
of particles moving at a high velocity are not so easily dispersed by a single
quantum of anti-gravitation as a small number moving slowly. For this
reason the chance of becoming dispersal-proof increases up to some limit
as the density increases.
The upper density limit is reached when particles are so close together
that extinctions in the near vicinity follow each other in close succession,
The particles will then be accelerated towards the region of the greatest
number of extinctions, which means towards the geometric centre of the
system. The effect of the whole mass predominates at a certain density
over the parochial effect of nearby particles.
Once star formation has become established in a cloud it must become
increasingly difficult for new stars to begin. The competition of the established ones must be too great. One should therefore expect most of the
stars in the core of a spiral nebula to begin at about the same time. The
possibility, however, of the occasional formation of new stars on
astronomical summits within a spiral nebula ought not to be disregarded.
The history of the stars in the spiral arms may be a little different. The
density at which the original population of stars begins must be very low;
so one should not preclude the possibility that stars may begin to form
while the spokes of the cloud are still lying on the astronomical shoulders
and long before these have poured into the rotating core to form the spiral
arms. Indeed, there are considerations that point in this direction.
After the pouring has occurred there must be considerable turbulence,
The spokes have entered the core from an enormous height and must stir
things up considerably as they splash into the core. I have already suggested
in Chapter 20 that this turbulence ought to be picked up by a radio-telescope. Now it is not easy to believe that the little crowds of particles that are
assembled around the site of a recent extinction could ever survive such a
bufieting. From this I am inclined to conclude that the crowds have become
fairly massive in the calm atmosphere of the spokes as these rest sluggishly
on the astronomical shoulders. They must be large and compact enough to
be the sites of concentrated extinctions. Only so can they be dispersal-proof, even from the violence of the agitated gas in which they find themselves after the pouring process.
On the other hand, the concentrations can hardly yet approach the
massiveness of stars before the pouring process. If they did, they would be
only slightly delayed in their fall by impact with the gas of the core.
They would all fall deep into the interior and one should not expect to
observe any stars in the spiral arms.
The tangential effect of the gas in the core would, moreover, be no
greater than the radial effect. Not only would massive stars fail to stay near
the surface, if they did they would not be entrained.
Thus we are led to the conclusion that star formation probably begins
in the central core at an early date and later also in the spokes, far out
beyond the limits of the future nebula. Formation of these stars is completed in the spiral arms.
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