The propagation velocity of the first gas ring in collisional ring galaxies, i.e. the velocity at which the maximum in the radial gas density profile propagates radially in the galactic disk, is usually inferred from the radial expansion velocity of gas in the first ring. Our numerical hydrodynamics modeling of ring galaxy formation however shows that the maximum radial expansion velocity of gas in the first ring ($v_{gas}$) is invariably below the propagation velocity of the first gas ring itself ($v_{ring}$). Modeling of the Cartwheel galaxy indicates that the outer ring is currently propagating at $v_{ring} approx$ 100 km/s, while the maximum radial expansion velocity of gas in the outer ring is currently $v_{gas} approx$ 65 km/s. Modeling of the radial B-V/V-K color gradients of the Cartwheel ring galaxy also indicates that the outer ring is propagating at $v_{ring} ge $ 90 km/s. We show that a combined effect of inclination, finite thickness, and warping of the Cartwheels disk might be responsible for the lack of angular difference in the peak positions found for the azimuthally averaged $Halpha$, K and B surface brightness profiles of the Cartwheels outer ring. Indeed, the radial $Halpha$ surface brightness profiles obtained along the Cartwheels major axis, where effects of inclination and finite thickness are minimized, do peak exterior to those at K- and B-bands. The angular difference in peak positions implies $v_{ring}$ = 110 km/s, which is in agreement with the model predictions. We briefly discuss the utility of radio continuum emission and spectral line equivalent widths for determining the propagation velocity of gas rings in collisional ring galaxies.
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