The Findings of De Sitter

Calculating the radius of the universe in the theory which bears his name, that is, ignoring the presence of matter and introducing into the formulas the value T subH given by the observation of the expansion, he obtained a result which scarcely differs from that which is obtained, in Einstein’s totally different theory of the universe, by introducing into the formulas the observed value of the density of matter.

This coincidence is caused, according to our interpretation of the clusters of nebulae, by the fact that for a value of the radius which is a dozen times the radius of equilibrium, the last term in Friedmann’s formula greatly prevails over the others.

The constant T which figures in it is therefore practically equal to the observed value T subH.

But since the clusters are a fragment of Einstein’s universe, we can use the relationship existing between the density and the constant T for them.

For T = TH one finds, as we have seen, that the density in the clusters must be 10(27) gram per cubic centimeter, which is the value given by observation.

This observation is based on counts of nebulae and on the estimate of their mass indicated by their spectroscopic velocity of rotation.

My theory explains why the clusters do not show any marked central condensations and have vague forms, with irregular extensions.

These would be difficult to explain if they formed dynamic structures controlled by dominant forces, as is manifestly the case for the starclusters or the elliptical and spiral nebulae.

My theory also takes into account the large fluctuations of density in the distribution of the nebulae, even outside the clusters.

This means that the universe has just passed through a state of unstable equilibrium, a whole gamut of transition between the properly-termed clusters which are still in equilibrium, while passing through regions where the expansion, without being arrested, has nevertheless been retarded, in such a manner that these regions have a density which is greater than the average.

This interpretation permits the value of the radius at the moment of equilibrium to be determined at a billion light-years, and thus 10(10) lightyears for the present value of the radius.

Since American telescopes prospect the universe as far as half a billion light-years, one sees that this observed region already constitutes a sample of a size which is not at all negligible compared to all space.

Hence, the values of the coefficient of expansion TH and of the density, obtained for this restricted domain, are representative of the whole.

The only deficiency of my theory is the approximation of equilibrium since expansion depends on this value.

Perhaps it will be possible to estimate this value through statistical considerations regarding the relative frequency of the clusters, compared to the isolated nebulae.

The Proper Motion Of Nebulae

How were nebulae formed?

The characteristic velocities, or the relative velocities of gaseous clouds, which cross one another in the same place, must have been very large.

Since certain of them, because of a density which is a little too large, form a nucleus of condensation, they will be able to retain the clouds which have about the same velocity as this nucleus.

The proper velocity of the cloud so formed will hence be determined by the velocity of the nucleus of condensation.

The nebulae formed by such a mechanism must have large relative velocities. in fact, that is what is observed in the clusters of nebulae.

In the one which has been best studied, that of Virgo, the dispersion of the velocities about the mean velocity is 650 kilometers per second.

The proper velocity must have been the proper velocity of all the nebulae at the moment of passage through equilibrium. For isolated nebulae, this velocity has been reduced to about one-twelfth, as a result of expansion, by the same mechanism which we have explained with reference to the formation of gaseous clouds.

The Formation Of Stars

The density of the clouds is, on the average, the density of equilibrium 10(27). For this density of distribution, a mass such as the Sun would occupy a sphere of one hundred light-years in radius.

These clouds have no tendency to contract. in order that a contraction due to gravitation can be initiated, their density must be notably increased.

This is what can occur if two clouds happen to collide with great velocities. Then the collision will be an inelastic collision, giving rise to ionization and emission of radiation.

The two clouds will flatten one another out, while remaining in contact, the density will be easily doubled and condensation will be definitely initiated.

It is clear that a solar system or a simple or multiple star may arise from such a condensation, through known mechanisms. That which characterizes the mechanism to which we are led is the greatness of the dimensions of the gaseous clouds, the condensation of which will form a star.

This circumstance takes account of the magnitude of the angular momentum, which is conserved during the condensation and whose value could only be nil or negligible if the initial circumstances were adjusted in a wholly improbable manner.

The least initial rotation must give rise to an energetic rotation in a concentrated system, a rotation incompatible with the presence of a single body but assuming either multiple stars turning around one another or, simply, one star with one or several large planets turning in the same direction.

The Distribution Of Densities Of Nebulae

Here is the manner in which we can picture for ourselves the evolution of the regions of condensation. The clouds begin by falling toward the center, and by describing a motion of oscillation following a diameter from one part and another of the center. in the course of these oscillations, they will encounter one another with velocities of several hundreds of kilometers per second and will give rise to stars.

At the same time, the loss of energy due to these inelastic collisions will modify the distribution of the clouds and stars already formed in such a manner that the system will be further condensed. it seems likely that this phenomenon could be submitted to mathematical analysis.

Certain hypotheses will naturally have to be introduced, in such a way as to simplify the model, so as to render the calculation possible and also so as artificially to eliminate secondary phenomena. There is scarcely any doubt that there is a way of thus obtaining the law of final distribution of the stars formed by the mechanism described above. Since the distribution of brilliance is known for the elliptical nebulae and from that one can deduce the densities in these nebulae, one sees that such a calculation is susceptible of leading to a decisive verification of the theory.

One of the complications to which i alluded, a moment ago, is the eventual presence of a considerable angular momentum. in excluding it, we have restricted the theory to condensations respecting spherical symmetry, that is, nebulae which are spherical or slightly elliptical. it is easy to see what modification will bring about the presence of considerable angular momentum. it is evident that one will obtain, in addition to a central region analogous to the elliptical nebulae, a flat system analogous to the ring of Saturn or the planetary systems, in other words, something resembling the spiral nebulae. in this theory, the spiral or elliptical character of the nebula is a matter of chance; it depends on the fortuitous value of the angul~ momentum in the region of condensation. it can no longer be a question of the evolution of one type into another. Moreover, the same thing obtains for stars where the type of the star is determined by the accidental value of its mass, that is, of the sum of the masses of the clouds whose encounter produced the star.