The inner regions of barred galaxies contain substructures such as off-axis shocks, nuclear rings, and nuclear spirals. These substructure may affect star formation, and control the activity of a central black hole (BH) by determining the mass inflow rate. We investigate the formation and properties of such substructures using high-resolution, grid-based hydrodynamic simulations. The gaseous medium is assumed to be infinitesimally-thin, isothermal, and non-self-gravitating. The stars and dark matter are represented by a static gravitational potential with four components: a stellar disk, the bulge, a central BH, and the bar. To investigate various galactic environments, we vary the gas sound speed c_s as well as the mass of the central BH M_BH. Once the flow has reached a quasi-steady state, off-axis shocks tend to move closer to the bar major axis as c_s increases. Nuclear rings shrink in size with increasing c_s, but are independent of M_BH, suggesting that ring position is not determined by the Lindblad resonances. Rings in low-c_s models are narrow since they are occupied largely by gas on x2-orbits and well decoupled from nuclear spirals, while they become broad because of large thermal perturbations in high-c_s models. Nuclear spirals persist only when either c_s is small or M_BH is large; they would otherwise be destroyed completely by the ring material on eccentric orbits. The shape and strength of nuclear spirals depend sensitively on c_s and M_BH such that they are leading if both c_s and M_BH are small, weak trailing if c_s is small and M_BH is large, and strong trailing if both c_s and M_BH are large. While the mass inflow rate toward the nucleus is quite small in low-c_s models because of the presence of a narrow nuclear ring, it becomes larger than 0.01 Msun/yr when c_s is large, providing a potential explanation of nuclear activity in Seyfert galaxies.
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