Response of the integrals in the Tremaine-Weinberg method to multiple pattern speeds: a counter-rotating inner bar in NGC 2950?

When integrals in the standard Tremaine-Weinberg method are evaluated for the case of a realistic model of a doubly barred galaxy, their modifications introduced by the second rotating pattern are in accord with what can be derived from a simple extension of that method, based on separation of tracers density. This extension yields a qualitative argument that discriminates between prograde and retrograde inner bars. However, the estimate of the value of inner bars pattern speed requires further assumptions. When this extension of the Tremaine-Weinberg method is applied to the recent observation of the doubly barred galaxy NGC 2950, it indicates that the inner bar there is counter-rotating, possibly with the pattern speed of -140 +/- 50 km/s/arcsec. The occurrence of counter-rotating inner bars can constrain theories of galaxy formation.