by     Reginald O. Kapp


Chapter 18 - The Early Shape and Structure of An Extragalactic Cloud

18.1: Variations in Density
Though very tenuous everywhere, the cloud cannot have a uniform density throughout. Let us consider in broad outline how the density must vary from the centre outwards.

As in the earth's atmosphere, any gas in the cloud that bears the weight of higher layers must be compressed. So the greatest density must be at the centre of the cloud.

A space traveller who moved outwards from this centre would be rising against the cloud's gravitational field and would be entering an increasingly rarified atmosphere as he did so. After a while he would find himself climbing up the inner slope of the ridge that formed the lip of the crater around the astronomical summit. This ridge or reversal zone, it will be remembered, is moving outwards as the cloud grows in mass. A little earlier the place where the space traveller is at the moment was on an outward slope. Gas was falling away from it into further space and is now falling in the reverse direction towards the core. So it is safe to assume that none of the gas that was there originally can have remained. The only gas that the space traveller encounters must be new particles that have originated but recently. On the inner slope of the crater the gas density must be as near to zero as it can be anywhere in space.

On crossing the ridge the space traveller reaches a very gentle gradient that slopes downwards away from the centre of the cloud. During the first stage of growth gas is originating in this region faster than it falls down the slope and the traveller enters once again into a region that is less depleted. The density is here much as it was on the summit at the still earlier stage, when the cloud first began to form as a small sphere.

As the ridge moves steadily outwards, the picture changes. What has just been on the top of the ridge finds itself on the inner slope and falls backwards on to the core in the hollow of the crater. The change goes on until the ridge has reached the fringe of the cloud and the first stage of growth has been completed.

Thus there must be a period during the first stage of growth when the cloud has a central core, which may already be fairly dense at its centre and is very tenuous in its outer layers. Around this there must be a region where there would be no gas whatever if it were not for new origins within the region. It is easy to show from the inverse square law that the potential gradient must be relatively steep in this region and so the new origins fall quickly out of it.

Beyond the region of the near-perfect vacuum there must be more cloud. It must extend a long way out into space and be very tenuous; for its density must be below the critical value for cloud formation. The potential gradient becomes steeper as one proceeds from the crater outwards and so the gas density must also diminish with distance from the core.

It will be found later that the large vacuous region around the core plays an important part in the evolution of galaxies and so it needs to have a name. I propose to call it the 'depleted region'.

18.2: Rotation of the Core
Stars and galaxies are known to rotate, but it is far from easy to say why. I doubt whether it is generally appreciated how difficult it is to find an explanation. Any explanation that is found must conform to established principles of mechanics and it is desirable that it should not require the invention of ad hoc hypotheses. I doubt whether a satisfying explanation can be based at all on accepted notions about gravitation. The difficulty, together with a tentative solution of the problem, will be discussed in Chapter 28. It cannot be usefully discussed until after a discussion of the nature of gravitation has been undertaken. In the meantime it must suffice to note the bare fact that galaxies are observed to rotate.

18.3. The Physics of the Core
It would be a mistake to seek much resemblance between the core of the extragalactic cloud and a star. Apart from the facts that both spin and consist mostly of hydrogen, they can have little in common.

The core is very new at the time we are considering, i.e. before the reversal zone reaches the rim of the cloud. The time that it takes for the zone to traverse to this has been found to be probably no more than some hundreds of thousands of years. The time taken to travel far enough to leave a core behind must then be reckoned, perhaps, in tens of thousands. The extent of the core is enormous; it could contain many millions of stars. So the journey travelled by those molecules that contribute to the shrinking is a long one. After a hundred thousand years or so the core must still be large enough to be very tenuous. It can have no property that one could think of as rigidity. Collisions between molecules must be rare by terrestrial standards. The quantity of heat generated per unit volume by collisions must be small.

In such a core one should not expect the conditions to exist that cause the synthesis of hydrogen into helium; this can only happen with pressures and temperatures such as occur inside the sun. The heat generated inside the core does not seem to have any other source at this time than the gravitational potential energy of the molecules of hydrogen, which is very small compared with the energy released by the synthesis of helium. The temperature in the core can therefore only be the result of the small amount of heat generated by collisions. The core must be a very cold body.

This must have a significant effect on the rate of shrinking. In a star the helium synthesis produces intense internal radiation. Its pressure is so great that it balances the star's own gravitational field. In other words, pressure of radiation supports the weight of the outer shell and prevents it from falling towards the centre. When this pressure ceases, as sometimes happens, the star collapses rapidly and with a great increase in the rate of spin.

As it does not seem possible to postulate the restraint of internal pressure of radiation for the core during its early life, one must assume that the penetration of molecules into the core is restricted only by collisions; and as, in view of the core's tenuousness, these are rare, penetration must be deep. The rate of shrinking must therefore be great.

18.4: Retardation of Spin
From this one might at first be inclined to infer that the angular velocity of the core would rise to the point where centrifugal force balanced gravitation. If this were to happen, there would be no shrinking. But there is also a retarding influence that we have to consider.

While the cloud is shrinking and becoming more dense by reduction in its volume, it is also becoming more dense by the acquisition of new matter, and this from two distinct sources.

The first of these is new origins within the region occupied by the cloud. The new particles would appear to an observer to be at rest relative to a given frame of reference. The existing particles must collide with the new ones and entrain them. Hence the new particles come to participate in the general rotatory motion. The angular momentum of the core remains constant, but the angular velocity becomes less as the mass increases.

The other source of new matter is the gas that finds itself within the reversal zone as this moves outwards. This gas, which has hitherto been falling away from the centre of the cloud, now falls towards it across the depleted region. It has to fall a long way across this steep part of the inner slope where, as has been mentioned above, there is a high vacuum. During this falling it acquires a substantial momentum and must penetrate deep into the core. Like the originating matter, it is entrained and causes retardation.

It would be interesting to know more about the physics of the core. How does its density vary from the centre, where the only force is the weight of the gas around it, to the periphery, where centrifugal force opposes the weight? How does the angular velocity vary with time? Does it increase at first up to a maximum and then decrease as the retarding effect of additional mass becomes more pronounced? To what extent is the core flattened by rotation? Is it disc-shaped at first, and does it become spherical later when pressure of radiation from helium synthesis blows out, as it were? When, if at all, does helium synthesis begin? But such questions must be put to various specialists in astrophysics. They are beyond the scope of this elementary study.

18.5: The Spokes It has been pointed out in Chapter 10, entitled 'The Astronomical Landscape', that the potential gradient around an astronomical summit cannot be at all uniform. There must be shoulders and valleys and these must stretch out into space in several directions in all three dimensions The shoulders descend gently for a long while and eventually reach those places that have been called astronomical passes. The valleys descend more steeply and end in the deep wells that represent the neighbouring galaxies The number of pronounced shoulders, it will be remembered, cannot be great. A typical number is likely to be six; and these will spread out from the summit like rods pushed through the faces of a cube. If all surrounding galaxies were arranged in a regular cubic pattern, the six astronomical shoulders would be at right-angles to each other.

The cloud can only form where the potential gradient is below this critical value. This must occur along a gentle shoulder at a time when the valley next to it is so steep that no gas can accumulate there. The cloud cannot therefore have the form of a simple sphere. Its shape must be very different. Hydrogen must be accumulating on a shoulder while it is rapidly pouring down the side into the deeper valley below. It must also be pouring down this towards the neighbouring galaxy.

This shows that the inner cloud must, during its early stages, be surrounded by a collection of spokes that extend away from the summit in all directions and far out into space. The spokes must be roughly cylindrical and must become more tenuous towards their tips, where the potential gradient is greatest.

As space expands, the landscape is flattening in all directions and so the spokes must grow in diameter as well as in length. They must also acquire a gravitational field of their own. In other words, they must carve out shallow troughs for themselves along the shoulders. They may be thought of as lying in these and attracting hydrogen towards their axes, Hydrogen in the outer regions of a spoke must fall inwards towards its axis and thereby collide with hydrogen that is already there. It will give rise to some turbulence. But I should not like to claim that the turbulence would be enough to have any significant effect. To all intents and purposes one may perhaps regard the spokes like inert slugs lying motionless along their supporting shoulders.

Though I have called them spokes, they are not spatially arranged like the spokes of a wheel. They are not all in one plane but point in each direction of three dimensional space; and they are not connected to a central hub. The wide depleted region separates them from the inner core of the cloud.

The picture that we have been led to infer differs substantially, as I have said already, from that presented by the spiral nebulae.

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