1. Spiral Structure of the Milky Way

With Professor C.C. Lin, I have established the overall spiral structure of the Milky Way in late 60's and early 70's for the first time. This spiral structure was achieved by comparing the density wave theory and various observations: from optical to radio, from stars to gas, from astrometry to kinematics. It has had significant impact on the modern astronomy: (1) The consistency between the theory and observations, on a wide range of observing aspects, has constituted a convincing evidence for the validity of the theory. (2) The spiral structure and the pattern speed of spiral waves determined then are still widely used in the astronomy community until today.

Representative papers:
(1). C.C. Lin, Yuan, C., and F.H. Shu, "On the Spiral Structure of Disk i Galaxies III. Comparison with Observations",
Ap.J. 155, 721 (1969). (SCI)

(2). Yuan, C.,"Application of Density-Wave Theory to the Spiral Structure of the Milky Way System I. Systematic Motion of Neutral Hydrogen", Ap.J., 158, 871 (1969). (SCI)

(3). Yuan, C.,"Application of Density Wave Theory to the Spiral Structure of the Milky Way System II. Migration of Stars", Ap. J. 158, 889 (1969). (SCI)

(4). C.C. Lin, Yuan, C., and W.W. Roberts, "On the Stellar Streaming Motions and the Observational Determination of
Structural Constant of the Galaxy", Astron. Astrophys. 69, 181-198 (1978). (SCI)

2. Galactic Magnetic Field

I used the fact that magnetic field and momentum flux of the gas are both the divergent free in the frame rotating with the pattern speed of the spiral density waves and thus made them proportional to each other, i.e., B ~ u, and solved the doubly periodic shock problem with the magnetized interstellar medium (ISM) with Dr. Bill Roberts and showed the magnetic shock coincides with the shock of ISM as well as the dust lanes in 1970. The next year, Mathewson, van der Kruit and Brouw (1972) discovered the enhancement of the synchrotron radiation along the dust lane of M51, confirming the density wave theory. This galactic model is still one of the best models describing the
overall configuration of galactic magnetic field in the galactic plane.

(5) W.W. Roberts, Yuan, C., "Application of Density-Wave Theory to the Spiral Structure of the Milky Way System III. Galactic Magnetic Field", Ap.J. 161, 887 (1970). (SCI)

3. The "3-kpc Arm" Phenomenon

In 1983, I proposed that a fast rotating bar in the center of the Milky Way is responsible for the "3-kpc Arm" phenomenon, which had puzzled astronomer for a quarter of a century since its discovery in late 50's. Both the linear and non-linear theory were carried out to show that a small bar field can resonantly excite spiral density waves with a non-linear radial outward streaming motions of 53 km/s, as seen in the observations. The existence of the central bar of the Milky Way was confirmed in 1991 (Blitz and Spergel) in almost the same orientation as I proposed.

(6) Yuan, C., "On the '3-kpc' Arm: Resonance Excitation of Linear and non-linear Waves by an Oval Distortion in the Central Region," Ap. J. 281, 600 (1984). (SCI)

(7) Yuan, C., and Ye Cheng, "Resonance Excitation: A Possible Interpretation of the 3-kpc Arm", in The Outer Galaxy,
Ed. L. Blitz and J. Lochman, Springer-Verlag, 144-148 (1987).

4. Saturn's Rings and Proto-stellar Disks

Dr. Frank Shu and I developed a non-linear asymptotic theory of resonance excitation and successfully applied it to the
interpretation of the structure of Saturn's rings. Extending the theory for Saturn's Rings by including the stress tensor for pressure and viscosity, I re-formulated the problem, and with Dr. Pat Cassen, we applied the theory to the proto-stellar disk, to examine the principal spiral modes which are excited resonantly by a giant proto-planet in the disk and the consequences of the disk-planet interaction.

(8) F.H. Shu, Yuan, C., and J.J. Lissauer, "Non-Linear Spiral Density Waves: an Inviscid Theory", Ap. J., 291, 356-376 (1985). (SCI)

(9) Yuan, C., and Pat Cassen, "Resonantly Driven Non-linear Density Waves in Protostellar Disks", Ap.J., 436, 338 (1994) (SCI)

5. Resonance Excitation and Spiral Structure in the Galactic Central Regions

This is a first step of my long-term research to understand the mechanism of fuelling AGNs and starburst rings in the galactic center. I believe the bar-disk interaction plays the central role in this. I use (1) the non-linear asymptotic theory to study the bar-driven density waves in the gas-dust disk in galactic central regions, (2) the wavelet analysis to probe the hidden spiral-bar structure of the HST observations, and (3) the gasdynamic codes, which we have developed, to study the evolution of disks driven by a rotating bar potential. The main results are not published yet. But my early work has sufficiently reflected this trend. They are:

(10) Yuan, C., and Chao-Lin Kuo, "Bar-driven Spiral Density Waves in Gaseous Disks", Ap.J., 486, 750 (1997). (SCI)

(11) Chao-Lin Kuo and Yuan, C., "Resonantly Excited Waves in Gaseous Disks: Asymptotic Theory vs. Numerical Hydrodynamics", Ap.J., 512, 79 (1999). (SCI)

6. Kinetic Theory of Disk Systems

Uri Griv and I have made a systematic study of disk systems in search for Landau type of instabilities. We took a different approach from the rest: (1) to consider of local gradients of density and mean dispersion velocities in addition to the differential rotation, and (2) to carry out second order epicyclic approximation; thus perturbation velocity squares are included. We found various instabilities and a wide range of implications. In particular, spiral density waves can be self-excited at the corotation in a wave-disk interaction. Another important result is that the critical dispersion velocity for disk instability is equal to 2 / time Toomre's value.

(12) Griv, E., Yuan, C., & Gedalin, M., "Dynamics of Disk-shaped Stellar System: Resonant self-excitation/Absorption of Density Waves", MNRAS, 307, 1 (1999). (SCI)