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 ^ { -1 } , while the maximum radial expansion velocity of gas in the outer ring is currently v _ { gas } \approx 65 km s ^ { -1 } .
The latter value is in marginal agreement with the measurements of Higdon ( [ 1996 ] ) based on HI kinematics .
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 } \geq 90 km s ^ { -1 } for the adopted distance to the galaxy of 140 Mpc .
On the other hand , the azimuthally averaged H \alpha surface brightness profile of the Cartwheel ’ s outer ring does not peak exterior to those in K- and B -bands , contrary to what would be expected for such a high propagation velocity .
We show that a combined effect of 41 ^ { \circ } inclination , finite thickness , and warping of the Cartwheel ’ s disk might be responsible for the lack of angular difference in the peak positions .
Indeed , the radial H \alpha surface brightness profiles obtained along the Cartwheel ’ s 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 ^ { -1 } , 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 .