204
VARIABLE STARS
the period depends mainly on the density, there is a particular density
at which this star becomes a Cepheid; at higher or lower densities it is
static. The close agreement of all stars with the period-luminosity curve
(checked especially in the star clusters) shows that the range of density
is a rather narrow one, but I daresay the density may change in the ratio
1 to 3 or 4 and the internal temperature by 50 per cent, between the
beginning and end of the Cepheid stage.
This suggests that the lowering of the exponent is a transitory feature
in the development of the star synchronising with some important change
in the internal condition. The only kind of change that we have been able
to think of is a step in the ionisation of some element predominating in the
constitution of the star. If this is the explanation the step must almost
certainly be the loss of the L electrons reducing the element from a neon
like to a helium-like ion. This ionisation is rather sudden, and the tempera
ture range required for its completion corresponds roughly to the probable
duration of the Cepheid stage.
Undoubtedly there would be an abnormal change of absorption with
temperature during this ionisation—that is to say, the reduction with tem
perature would be less than normal. But so far as we can see it would not
be great enough for our purpose. There are extra electrons to be captured
and captures occur at the deeper levels now vacant so that emission is
increased and absorption must keep pace with it. But not much of this
increase is reflected in the opacity coefficient, when account is taken
of Rosseland’s correction. The increased absorption is chiefly of high-
frequency radiation forming an inconsiderable part of the whole.
It is evidently necessary that the predominant element should be in
a critical stage of ionisation for all the Cepheids, or at least all those which
seem to fall into continuous series. Since temperature is the main factor in
determining ionisation the Cepheids should have nearly the same internal
temperature. There would be a slight increase of central temperature (to
counteract the increased density) as we pass down the list in Table 25,
but not nearly so much as is shown in that Table. Various sources of
systematic error may render the progression of T c with temperature in
Table 25 rather unreliable and probably as there shown it is a little
exaggerated. But we do not feel able to make such changes in the data
as would give the practically constant central temperature that the theory
demands.
If the central temperature were strictlv constant we should have
by (99-2)
Tì oc Mi (1 - |8)i,
so that T e oc Jf* (1 — /f) T L
Accordingly, the effective temperature should increase slightly with
