Prog. Theor. Phys. Vol. 55 No. 5 (1976) pp. 1419-1431

[ Full Text PDF : FREE ACCESS (834K) ]

Nonlinear Modulation of Density Wave in Self-Gravitating Systems

— Gas Dynamical Description —

Satoru Ikeuchi and Takashi Nakamura

Department of Physics, Kyoto University, Kyoto 606

(Received October 21, 1975)

Abstract:

Nonlinear modulation of density wave in self-gravitating systems is studied by the reductive perturbation method. Using gas dynamical equations, an infinitely long rotating cylinder and an infinitesimally thin disk are considered. In the former system, both one-dimensional and two-dimensional modulations, the so-called self-focusing, are found to be stable for all wave number when the carrier wave propagates perpendicularly to rotational axis. In the latter system, amplitude modulation becomes unstable for large wave number. This unstable amplitude modulation grows to the envelope solitary wave in a time of the order of rotational one even if the amplitude of carrier wave is as low as one hundredth of zeroth order quantity.
It is concluded that nonlinear effects cannot be neglected in the density wave theory of spiral arms. The conjecture is proposed that this nonlinear modulationally unstable mode can be identified with the spiral arms of S-type galaxies.

URL : http://ptp.ipap.jp/link?PTP/55/1419/
DOI : 10.1143/PTP.55.1419

References:

C. C. Lin and F. H. Shu, Astrophys. J. 140 (1964), 646[CrossRef].
F. H. Shu, Astrophys. J. 160 (1970), 99[CrossRef].
W. W. Roberts, Astrophys. J. 158 (1968), 123[CrossRef].
“The Spiral Structure of Our Galaxy,” IAU Symp. No. 38 (D. Reidel Publ. Dordrecht-Holland, 1970).
A. Toomre, Astrophys. J. 158 (1969), 899[CrossRef].
A. J. Kalnajs, Astrophys. Lett. 11 (1972), 41.
W. W. Roberts and F. H. Shu, Astrophys. Lett. 12 (1972), 49.
S. Kato, Publ. Astron. Soc. Jpn. 25 (1973), 231.
F. Takahara, S. Ikeuchi and T. Nakamura, Prog. Theor. Phys. 55 (1976), 1743[PTP].
G. Contopoulos, `Galaxies and Relativistic Astrophysics' (Springer-verlag, Berlin, Heidelberg and New York, 1974), p. 120.
T. Nakamura and S. Ikeuchi, Prog. Theor. Phys. 54 (1975), 910[PTP].
T. Taniuti, Prog. Theor. Phys. Suppl. No. 55 (1974), 1[PTP].
N. Asano, T. Taniuti and N. Yajima, J. Math. Phys. 10 (1969), 2020[CrossRef].
A. Toomre, Astrophys. J. 139 (1964), 1217[CrossRef].
T. Taniuti and N. Yajima, J. Math. Phys. 10 (1969), 1369[CrossRef].
T. Nakamura and S. Ikeuchi, (in preparation).

Citing Article(s) :

Progress of Theoretical Physics Vol. 57 No. 4 (1977) pp. 1239-1254 :
Resonant Three-Wave Interactions of Density Waves in a Self-Gravitating Disk

Satoru Ikeuchi