2006AJ....131.1377B

We complement our Hubble Space Telescope (HST) observations of the inner ring of the galaxy NGC 3081 using an analytical approach and n-body simulations. We find that a gas cloud inner (r) ring forms under a rotating bar perturbation with very strong azimuthal cloud crowding where the ring crosses the bar major axis. Thus, star formation results near to and ``downstream'' of the major axis. From the dust distribution and radial velocities, the disk rotates counterclockwise (CCW) on the sky like the bar pattern speed. We explain the observed CCW color asymmetry crossing the major axis as due to the increasing age of stellar associations inside the r ring major axis. These move faster than the pattern speed. The exterior point of the r ring at the bar major axis has an orbital rate equal to the pattern speed. We show how the perturbation strength can be estimated from the ring shapes and relative spacing over the inner through outer ring regions. The bar strength (maximum tangential/radial force) appears to be constant from 6 to 15 kpc. We derive how the perturbation, the fractional long wavelength m=2 intensity, and the rotation curve can be used to calculate the disk surface mass density versus radius. The disk surface density at 7 kpc is 13 M<sub>☉</sub>/pc2 rising to 19 at 13 kpc. The latter is insufficient by a factor of seven to generate the observed rotation curve, implying halo domination. The surface density may have been reduced at 7 kpc due to inner ring gas cloud scattering. The surface density plus the observed surface brightness gives a disk mass-to-light (M/L) ratio which increases from 7 kpc through 13 kpc, contradicting the usual assumption in bar strength calculations. The simulation ring lifetime of several billion years is consistent with our ∼400 Myr HST estimates. With a sufficiently high gas cloud surface mass density, our simulations form gas cloud ``associations'' near the ends of the bar as observed. Too high a density destroys the ring.