Using the Tremaine - Weinberg method to measure pattern speeds from H α velocity maps

The Tremaine-Weinberg method is a well-known model independent technique for measuring density wave pattern speeds in spiral galaxies. Here we show how it can be applied to the data cubes (maps of surface brightness and velocity) obtained in Hα emission using a Fabry-Perot spectrometer. One of the main difficulties, the discontinuity of the Hα emission, is resolved using the neighbouring stellar continuum delivered by the data cube. We argue from symmetry that the motions not associated with the density wave should cancel. We show that our pattern speeds are reasonable by computing corotation radii, and comparing them to measured bar lengths. Simulations including star forming gas also add credibility to our results. Nevertheless it will be necessary to compare them with results using the spectra of the stellar components to quantify any systematic deviations from valid pattern speed values.