Aside from the grand-design stellar spirals appearing in the disk of M81, a pair of stellar spiral arms situated well inside the bright bulge of M81 has been recently discovered by Kendall et al. (2008). The seemingly unrelated pairs of spirals pose
a challenge to the theory of spiral density waves. To address this problem, we have constructed a three component model for M81, including the contributions from a stellar disk, a bulge, and a dark matter halo subject to observational constraints. Given this basic state for M81, a modal approach is applied to search for the discrete unstable spiral modes that may provide an understanding for the existence of both spiral arms. It is found that the apparently separated inner and outer spirals can be interpreted as a single trailing spiral mode. In particular, these spirals share the same pattern speed 25.5 km s$^{-1}$ kpc$^{-1}$ with a corotation radius of 9.03 kpc. In addition to the good agreement between the calculated and the observed spiral pattern, the variation of the spiral amplitude can also be naturally reproduced.
NGC 1097 is a nearby barred spiral galaxy believed to be interacting with the elliptical galaxy NGC 1097A located to its northwest. It hosts a Seyfert 1 nucleus surrounded by a circumnuclear starburst ring. Two straight dust lanes connected to the ri
ng extend almost continuously out to the bar. The other ends of the dust lanes attach to two main spiral arms. To provide a physical understanding of its structural and kinematical properties, two-dimensional hydrodynamical simulations have been carried out. Numerical calculations reveal that many features of the gas morphology and kinematics can be reproduced provided that the gas flow is governed by a gravitational potential associated with a slowly rotating strong bar. By including the self-gravity of the gas disk in our calculation, we have found the starburst ring to be gravitationally unstable which is consistent with the observation in citet{hsieh11}. Our simulations show that the gas inflow rate is 0.17 M$_sun$ yr$^{-1}$ into the region within the starburst ring even after its formation, leading to the coexistence of both a nuclear ring and a circumnuclear disk.
NGC 4945 is a Seyfert 2 galaxy at a distance of 3.82 Mpc. Its relative proximity has permitted a detailed SMA study of the circumnuclear molecular gas in a galaxy exhibiting an AGN. Based on an analysis of the high-resolution velocity field of the ce
ntral region (20 X 20, 1 = 19 pc), we demonstrate that the S-shaped structure of the isovelocity contours is well reproduced by the numerical results of a two dimensional hydrodynamical simulation. In particular, the velocity structure is represented by the bending produced by a shock along the spiral density waves, which are excited at the outer-inner Lindblad resonance by a fast rotating bar. The simulated density map reveals a pair of tightly wound spirals in the center which pass through most of the ring-like (claimed to be a circumnuclear starburst ring by other authors) high intensity region in the observations as well as intersect several Pa$alpha$ emission line knots located outside the ring-like region. The calculated mass inflow rate at a scale of 50 pc is about three times the inferred mass accretion rate of the AGN of NGC 4945. We find that self-gravity of the gas is important and should be included in our model for NGC 4945. The model is compared with the gas orbit model discussed in Lim et al. (2009), and it is shown that the hydrodynamic model provides a better match to the observed position-velocity diagram and, hence, provides a more reliable prediction of the outer inner Lindblad resonance position.
NGC 6782 is an early-type barred spiral galaxy exhibiting a rich and complex morphology with multiple ring patterns. To provide a physical understanding of its structure and kinematical properties, two-dimensional hydrodynamical simulations have been
carried out. Numerical calculations reveal that the striking features in NGC 6782 can be reproduced provided that the gas flow is governed by the gravitational potential associated with a slowly rotating strong bar. In particular, the response of the gaseous disk to the bar potential leads to the excitation of spiral density waves at the inner Lindblad resonance giving rise to the appearance of a nearly circular nuclear ring with a pair of dust lanes. For a sufficiently strong bar potential, the inner 4:1 spiral density waves are also excited. The interaction of the higher harmonic waves with the waves excited at the inner Lindblad resonance and confined by the outer Lindblad resonance results in the observed diamond-shaped (or pointy oval) inner ring structure. The overall gas morphology and kinematical features are both well reproduced by the model provided that the pattern speed of the bar is $sim 25$ km s$^{-1}$ kpc$^{-1}$.
