\relax \@writefile{toc}{\contentsline {chapter}{\numberline {1}Rotation Curve vs. Central Spiral-bar Structure in the Nearby Galaxies}{1}} \@writefile{toc}{\contentsline {section}{\numberline {1.1}Introduction}{1}} \@writefile{toc}{\contentsline {section}{\numberline {1.2}The Theory}{2}} \@writefile{toc}{\contentsline {section}{\numberline {1.3}The Observations}{2}} \@writefile{lof}{\contentsline {figure}{\numberline {1.1}{\ignorespaces The spirals excited by a fast bar and a slow bar at OLR and ILR respectively at $r=1.5\mskip \thickmuskip kpc$. The fast bar is necessarily a nuclear or central bar. The slow bar can be a nuclear or central bar, or a major bar of the galaxy, as long as it provides a doubly periodic forcing at ILR. }}{3}} \@writefile{lof}{\contentsline {figure}{\numberline {1.2}{\ignorespaces Spirals excited at ILR propagate towards the center. The two examples shown above have the same viscosity and both are excited at $r=1.5\mskip \thickmuskip kpc$. The left one has a flat rotation curve and the right has flat rotation curve from $r=1\mskip \thickmuskip kpc$ outward and connected to a rigid-body rotation curve from $r=0.8\mskip \thickmuskip kpc $ to the center. On the left the waves go all the way to the center and on the right, waves are stopped immediately at the rigid-body region, which defines a wave forbidden region. It happens when $D={\kappa }^{2}-4(\Omega -{\Omega }_{p})^{2}>0$, where ${\kappa }$ is the epicyclic frequency, ${\Omega }$, the angular speed of the disk, and ${\Omega }_{p}$, the rotating speed of the bar. The rotation curves and the $D-r$ are shown on the right.}}{3}} \@writefile{toc}{\contentsline {section}{\numberline {1.4}Concluding Remarks}{3}} \@writefile{lof}{\contentsline {figure}{\numberline {1.3}{\ignorespaces The spiral patterns excited at ILR are sensitively dependent on the rotation curves. We make the ILR's all at $r=1.5\mskip \thickmuskip kpc$. The results vary considerably as how far the rotation curve rises. The slower the rotation curve rises, the more open the spirals become. We plot the results in the above. Two values of kinematic viscosity ($\nu $, or Nu) are used for each spiral patterns, to demonstrate the effect of viscosity. The rotation curves and the $D$-curves are also shown for comparison. Please note the leading spirals at the center are waves excited at the inner inner Lindblad resonance (IILR).}}{4}} \@writefile{lof}{\contentsline {figure}{\numberline {1.4}{\ignorespaces Central spiral structure and rotation curves of 7 nearby galaxies. The rotation curves are all rapidly rising from the center. Spirals are believed to be excited by a fast nuclear bar at OLR. The top two rows are wavelet analysis results and the bottom row shows the rotation curves, taken from various sources. See text.}}{4}} \bibcite{}{1} \bibcite{}{2} \bibcite{}{3} \bibcite{}{4} \bibcite{}{5} \bibcite{}{6} \bibcite{}{7} \bibcite{}{8} \@writefile{lof}{\contentsline {figure}{\numberline {1.5}{\ignorespaces Central spirals and rotation curves of 3 nearby galaxies. Their rotation curves are slowly rising from the center. The central spirals are all relatively open. Some of them can be traced all the way to the center. They are believed to be excited at ILR either by a slowly rotating nuclear bar. Wavelet results of the central region are shown in the first two rows. The rotation curves are depicted in the bottom row.}}{5}} \@writefile{toc}{\contentsline {schapter}{{\normalfont \rmfamily References}}{5}}