392
Variable Stars
[oh. XV
correspond to alternations of stability and instability in the temperature-*
luminosity diagram shewn in fig. 12 (p. 159). Fission can only commence
when the star has a liquid or semi-liquid centre, and for this reason stars in
process of fission are on or near the left-hand edges of the regions of stability,
while spectroscopic binaries, which are permanent structures, must of course
be actually on the bands of stability.
The foregoing consideration would seem to suggest that the long-period
variables may be of the same nature as Cepheids, namely stars in which the
process of fission is either about to start or is under way. There is a certain
difficulty, however, in supposing that the long periods of these variables can be
those of the rotation of Jacobian ellipsoids. Corresponding to a period of 300
days, we have seen that equation (360T) requires a density of only 0*00002.
This hardly suggests matter in a sufficiently liquid state for ellipsoidal con
figurations, although it must not be overlooked that eclipsing binaries exist,
such as W Crucis, in which both components are giants of low density, and
these must, so far as we can tell, have broken up by fission. Moreover, there
are two distinct types of long-period variables; in one of these, the regular
variables, the light-curve repeats itself indefinitely with perfect regularity, as
in the Cepheid variables, but in the other types the light-curve is irregular
both in period and shape. It seems possible that the fission theory may
adequately account for the former. But the irregular variables do not shew
the features to be expected in a star breaking up by fission.
Irregular Variables.
365 . The irregular long-period variables give various indications which
suggest that they are in a state of pulsation. The diameter of Betelgeux has
already been found by interferometer observations to vary from 0*047" to 0*034".
Moreover in most of the irregular long-period variables which have been
studied in detail, the spectrum and effective temperature appear to vary exactly
in phase with the visual luminosity.
From an exhaustive study of o Ceti, Joy* finds an approximately linear
relation between the spectral type (ranging from Mo to M 9*5) and the
logarithm of the visual magnitude (ranging from 0*45 to 1*0). Vogtf has given
observational curves for R Scuti in which the maxima and minima of the
effective temperature agree exactly with those of the visual magnitude.
If this is accepted as being generally true of long-period variables, then
equation (360*2) shews that R, the radius of the star, must be in phase with
both the spectral type and the magnitude, which is precisely what is required
of a pulsating star. It is true that Joy finds that the displacements of spectral
lines of o Ceti, if interpreted as radial velocities, would indicate changes
in the star’s radius which are out of phase with both these quantities, but
* Astrophys. Journ. lxiii. (1926), p. 290.
f Heidelberg ( Konigsstuhl ) Obs. vm. (1926) No. 5.