SOLUTION OF THE EQUATIONS
143
(103-5) the whole energy must increase as increases in order to maintain
equilibrium. The star cannot obtain this extra energy at a moment’s
notice; hence K + H is below the value required to maintain equilibrium.
This means that there is too little heat and the pressures p G and p R are
insufficient to support the weight of the material. Thus a further contrac
tion ensues and the star deviates further and further from equilibrium.
We have said that the star cannot at a moment’s notice secure the
extra energy required to save it. If the star is being supplied with ex
traneous energy it is quite possible that the changing physical conditions
may stimulate the supply; but this effort to prevent the collapse is too
dilatory. In a star like the sun the heat stored up represents about
40 million years’ supply of radiation and therefore (if the radiation is
supplied by liberation of subatomic energy) is equal to the subatomic
energy released in 40 million years. If the rate of release is doubled when
the collapse starts, it will take a year to increase H + K by 1 part in
40 million; whereas the threatened collapse due to withdrawal of pressure
support is a matter of days or hours. It is important not to confuse this
condition of stability with another condition to be investigated later.
We shall find in § 211 that the supply of subatomic energy must satisfy
certain conditions in order that the star may be stable; these conditions
are independent of, and additional to, the condition here found that
r > I; also the threat to the star which violates them is a lingering fate
and not the swift doom here contemplated.
It may perhaps be suggested that some extra source of energy could
exist which is immediately releasable as heat when the temperature and
density change. But immediately releasable heat is not “extra”; it is
by definition part of the specific heat and must be taken account of in
y and, by (103-4), in K. Energy of ionisation is of this type. Energy
which is very slowly released such as radio-active and other kinds of sub
atomic energy is, of course, not reckoned in the total heat K + H ; it is
treated as a non-realisable asset in the star’s balance sheet which is neg
lected unless we are dealing with long periods of time.
There appears to be no objection to y falling below f in a limited region
of the star provided that the general average is above |. Circulating
convection currents will be set up in this region (§ 70), since the convection
process produces mechanical energy when y < f, instead of dissipating
it. Presumably viscous forces will not allow the movement to increase
indefinitely, and in any case the local instability can scarcely lead to
consequences affecting the star as a whole.
The constant y is least when the ratio of the energy of ionisation to the
translatory energy is greatest. It is conceivable that in the course of
evolution a star may reach a stage at which further contraction will
involve a great deal of fresh ionisation, the stage being critical for the