first and second approximations are illustrated in Fig. 5.9, along with observed data
for comparison (Hitotuyanagi 1941a, b).
In addition, based on his theory of model atmosphere (Hitotuyanagi 1944, 1947),
Hitotuyanagi and Inaba derived the center-limb variation of the sodium D line. The
line profile is sensitive to the distribution of stellar temperature and sodium abundance. By comparing these findings with previous works of C. W. Allen (1940) and
W. Priester (1953), Hitotuyanagi derived a new plausible abundance of sodium in
the solar atmosphere (Hitotuyanagi and Inaba 1954).
5.3.4 Galactic Astronomy
After the war, Hitotuyanagi, together with his young colleagues, promoted theoretical studies of galaxies.
In the 1960s, the main subjects were the formation of spiral arms in galaxies and
the dynamical structure of barred galaxies (Oki et al. 1965).
1. Formation of spiral arms in Galaxies
In 1958–1962, various models were proposed on the formation of spiral arms
based on the magneto gas dynamical point of view. A. G. Pacholczyk and J. S.
Stodolkiewicz (1958), F. Hoyle and J. G. Ireland (1961), J. Tassoul (1962), and
A. Elvius, N. Herlofson, and P. O. Lindblad (1961) proposed different models.
Following the publication of these works, Hitotuyanagi’s group considered the
formation of spiral arms. They assumed that the initial gravitational field was
determined by stars alone and unchanged thereafter, since the total mass of gas is
too small compared to the mass of stars. They considered a two-dimensional model
of a galaxy and approximately solved the magneto-hydrodynamic equations of gas
and magnetic field (Oki et al. 1965).
As the initial conditions, they supposed that the gas was distributed in a circular,
homogeneous thin layer and that the magnetic field was also homogeneously
extended through galactic and intergalactic space. Under regular galactic rotation,
the formation of spiral arms begins and develops as delineated in Fig. 5.10, where
the structure of arms is represented at four time intervals t, measured in units of
2 Â 10
8 years, which corresponds to around one rotation period of the galaxy. Arms
are traced as the curves of maximum density ρ max relative to the mean density ρ 0 . In
Fig. 5.10, full lines represent the region for ρ max/ ρ 0. >1.5 and dotted lines for <1.5.
A serious difficulty arose in this solution concerning the time scale of spirals.
When winding curves in Fig. 5.10 are compared with observations, the age of arms
can be estimated such as t %6 for our Galaxy, and t % 4 for M81.Thereafter arms
wind up toward the galactic center. These values were evidently much smaller than
the actual age of the galaxies, t % 100 or even more. To avoid this difficulty, they
assumed that once a spiral arm formed, the arm and other physical conditions in a
galaxy remained nearly stationary state for a time interval comparable with the age of
the galaxy. The formation of spiral arms will be considered again in Chap. 7.
5.3 Hitotuyanagi Zyuiti and Astrophysics
133
for comparison (Hitotuyanagi 1941a, b).
In addition, based on his theory of model atmosphere (Hitotuyanagi 1944, 1947),
Hitotuyanagi and Inaba derived the center-limb variation of the sodium D line. The
line profile is sensitive to the distribution of stellar temperature and sodium abundance. By comparing these findings with previous works of C. W. Allen (1940) and
W. Priester (1953), Hitotuyanagi derived a new plausible abundance of sodium in
the solar atmosphere (Hitotuyanagi and Inaba 1954).
5.3.4 Galactic Astronomy
After the war, Hitotuyanagi, together with his young colleagues, promoted theoretical studies of galaxies.
In the 1960s, the main subjects were the formation of spiral arms in galaxies and
the dynamical structure of barred galaxies (Oki et al. 1965).
1. Formation of spiral arms in Galaxies
In 1958–1962, various models were proposed on the formation of spiral arms
based on the magneto gas dynamical point of view. A. G. Pacholczyk and J. S.
Stodolkiewicz (1958), F. Hoyle and J. G. Ireland (1961), J. Tassoul (1962), and
A. Elvius, N. Herlofson, and P. O. Lindblad (1961) proposed different models.
Following the publication of these works, Hitotuyanagi’s group considered the
formation of spiral arms. They assumed that the initial gravitational field was
determined by stars alone and unchanged thereafter, since the total mass of gas is
too small compared to the mass of stars. They considered a two-dimensional model
of a galaxy and approximately solved the magneto-hydrodynamic equations of gas
and magnetic field (Oki et al. 1965).
As the initial conditions, they supposed that the gas was distributed in a circular,
homogeneous thin layer and that the magnetic field was also homogeneously
extended through galactic and intergalactic space. Under regular galactic rotation,
the formation of spiral arms begins and develops as delineated in Fig. 5.10, where
the structure of arms is represented at four time intervals t, measured in units of
2 Â 10
8 years, which corresponds to around one rotation period of the galaxy. Arms
are traced as the curves of maximum density ρ max relative to the mean density ρ 0 . In
Fig. 5.10, full lines represent the region for ρ max/ ρ 0. >1.5 and dotted lines for <1.5.
A serious difficulty arose in this solution concerning the time scale of spirals.
When winding curves in Fig. 5.10 are compared with observations, the age of arms
can be estimated such as t %6 for our Galaxy, and t % 4 for M81.Thereafter arms
wind up toward the galactic center. These values were evidently much smaller than
the actual age of the galaxies, t % 100 or even more. To avoid this difficulty, they
assumed that once a spiral arm formed, the arm and other physical conditions in a
galaxy remained nearly stationary state for a time interval comparable with the age of
the galaxy. The formation of spiral arms will be considered again in Chap. 7.
5.3 Hitotuyanagi Zyuiti and Astrophysics
133