We study the two-dimensional kinematics of the H \alpha -emitting gas in the nearby barred Scd galaxy , NGC 6946 , in order to determine the pattern speed of the primary m = 2 perturbation mode .
The pattern speed is a crucial parameter for constraining the internal dynamics , estimating the impact velocities of the gravitational perturbation at the resonance radii , and to set up an evolutionary scenario for NGC 6946 .
Our data allows us to derive the best fitting kinematic position angle and the geometry of the underlying gaseous disk , which we use to derive the pattern speed using the Tremaine-Weinberg method .
We find a main pattern speed \Omega _ { \mathrm { p } } ^ { \mathrm { P } } = 22 ^ { +4 } _ { -1 } \mbox { km s } ^ { -1 } \mbox { kpc } ^ { -1 } , but our data clearly reveal the presence of an additional pattern speed \Omega _ { \mathrm { p } } ^ { \mathrm { S } } = 47 ^ { +3 } _ { -2 } \mbox { km s } ^ { -1 } \mbox { kpc } ^ { -1 } in a zone within 1.25 kpc of the nucleus .
Using the epicyclic approximation , we deduce the location of the resonance radii and confirm that inside the outer Inner Lindblad Resonance radius of the main oval , a primary bar has formed rotating at more than twice the outer pattern speed .
We further confirm that a nuclear bar has formed inside the Inner Lindblad Resonance radius of the primary bar , coinciding with the inner Inner Lindblad Resonance radius of the large-scale m = 2 mode oval .