divided into an outer part (radius R 1 , mass m 1 , mean density ρ 1 ) and an inner core
(radius R
0 , mass m
0 , mean density ρ
0 ). Point C indicates the center of mass of the
whole system. By setting m 1 /m ¼ α and P the period of revolution of the eccentric
nucleus around C, Shinjo (1922a) derived the relation
P
2
¼
1
4
3 πρ 0
α
1 þ α
:
ð2:3Þ
On the Cepheid variables, Harlow Shapley (1914) had already developed the
pulsation model, according to which the pulsation period is related to the mean
density of stars in the form
P
2
¼
1
4
3 π ρ
:
ð2:4Þ
In his theory, Shinjo obtained a proportional relation similar to Shapley’s, and he
claimed the priority of his model in two points.
First, the period of a Cepheid variable may be regarded as the fundamental mode
of oscillation in the pulsation theory. If the Cepheids are radial oscillators, some of
them would show some higher order of oscillation. However, there is no evidence of
such higher-order oscillations among the Cepheids. On the other hand, the Cepheids
should always be of a single period in his eccentric-nucleus model, which is in
good agreement with observations. (For higher-order oscillations, see Chap. 7,
Sect. 7.3.1).
Second, the eccentric-nucleus model is applicable to all types of variable stars
except Algols. Furthermore, this model describes the basic process of stellar evolution, as shown in the next subsection.
Fig. 2.12 Shinjo’s
eccentric-nucleus model
(Shinjo 1922a)
34
2 Astronomy from Meiji to Taisho Period 1868–1926