Circumnuclear Dust in Nearby Active and Inactive Galaxies. II. Bars, Nuclear Spirals, and the Fueling of Active Galactic Nuclei

(Abridged) We present a detailed study of the relation between circumnuclear dust morphology, host galaxy properties, and nuclear activity in nearby galaxies. We use our sample of 123 nearby galaxies with visible--near-infrared colormaps from the Hubble Space Telescope to create well-matched, "paired" samples of 28 active and 28 inactive galaxies, as well as 19 barred and 19 unbarred galaxies, that have the same host galaxy properties. Comparison of the barred and unbarred galaxies shows that grand design nuclear dust spirals are only found in galaxies with a large-scale bar. Tightly wound nuclear dust spirals, in contrast, show a strong tendency to avoid galaxies with large-scale bars. Comparison of the AGN and inactive samples shows that nuclear dust spirals, which may trace shocks and angular momentum dissipation in the ISM, occur with comparable frequency in both active and inactive galaxies. The only difference between the active and inactive galaxies is that several inactive galaxies appear to completely lack dust structure in their circumnuclear region, while none of the AGN lack this structure. The comparable frequency of nuclear spirals in active and inactive galaxies, combined with previous work that finds no significant differences in the frequency of bars or interactions between well-matched active and inactive galaxies, suggests that no universal fueling mechanism for low-luminosity AGN operates at spatial scales greater than ~100 pc radius from the galactic nuclei. The similarities instead suggest that the lifetime of nuclear activity is less than the characteristic inflow time from these spatial scales. An order-of-magnitude estimate of this inflow time is the dynamical timescale. This sets an upper limit of several million years to the lifetime of an individual episode of nuclear activity.