2011ApJ...736...70S

The Tremaine-Weinberg equations are solved for a pattern speed that is allowed to vary with radius. The solution method transforms an integral equation for the pattern speed to a least-squares problem with well-established procedures for statistical analysis. The method applied to the H I spiral pattern of the barred, grand-design galaxy NGC 1365 produces convincing evidence for a radial dependence in the pattern speed. The pattern speed behaves approximately as 1/r and is very similar to the material speed. There are no clear indications of corotation or Lindblad resonances. Tests show that the results are not selection biased, and that the method is not measuring the material speed. Other methods of solving the Tremaine-Weinberg equations for shearing patterns are found to produce results in agreement with those obtained using the current method. Previous estimates that relied on the assumptions of the density-wave interpretation of spiral structure are inconsistent with the results obtained using the current method. The results are consistent with spiral structure theories that allow for shearing patterns, and contradict fundamental assumptions in the density-wave interpretation that are often used for finding spiral arm pattern speeds. The spiral pattern is winding on a characteristic timescale of ∼500 Myr.