20-2
282, 283]
315
Triple and Multiple Systems
had evolved by fission would shew the observed arrangement, but the argu
ment is not reversible and the investigation does not prove that no other
origin could result in close and wide pairs.
Considerations of another kind make it unlikely that the normal triple or
multiple system can have been formed by repeated fission of the type we
have had under consideration. The table on p. 312 shews that with the
mass ratios normally observed in binaries, there would have to be a thou
sand-fold increase in density between the first and second fission, and if a
third fission should occur, a further thousand-fold increase between the second
and third fission, making a million-fold increase in all. The observed range
of stellar densities, wide though it may be, does not encourage us to postulate
increases of this order in the densities of ordinary stars. Further, we have seen
that rotational fission can only occur in masses which approximate to the
liquid state; in a gaseous mass in equilibrium the central condensation of
density is too great for fission to occur at all, and it is difficult to imagine two
liquid stars with their liquid densities in the ratio of a million to one.
Let us imagine two adjacent condensations in a nebula, which are destined
ultimately to form separate stars, failing to get clear of one another’s gravi
tational fields, and so describing elliptic orbits about one another. After a
time it seems likely that their periods of rotation and revolution will approxi
mately coincide. As soon as this happens, the system becomes dynamically
indistinguishable from one which has originated by fission. The dynamical
investigation just given may be supposed to begin at this stage, and we see
that one further fission will result in the production of a normal triple
system.
Even this fails to explain the existence of systems in which three separa
tions have occurred in succession, or of triple systems in which the close pair
has too long a period for it to have originated by fission.
To explain these we probably have to consider the shrinkage of a condensa
tion which has been formed out of a tenuous nebula and is contracting until
its density is great enough to ensure stability. Although the details require
working out, it may be that during the process of shrinkage the density
remains far more uniform than would be the case if the mass were in
equilibrium throughout, and the central condensation of mass may be so
slight that fission can occur in the manner in which it occurs in a liquid
of uniform density. A succession of fissions of this kind, all occurring during
the actual act of shrinkage, before equilibrium had been attained, would
account for all observed varieties of triple and multiple systems.