On the Tremaine-Weinberg method: how much can we trust gas tracers to measure pattern speeds?

Pattern speeds are a fundamental parameter of the dynamical features (e.g. bars, spiral arms) of a galaxy, setting resonance locations. Pattern speeds are not directly observable, so the Tremaine-Weinberg (TW) method has become the most common method used to measure them in galaxies. However, it has not been tested properly whether this method can straightforwardly be applied to gas tracers, despite this being widely done in the literature. When applied to observations, the TW method may return invalid results, which are difficult to diagnose due to a lack of ground truth for comparison. Although some works applying the TW method to simulated galaxies exist, only stellar populations have been tested. Therefore, here we explore the applicability of the TW method for gas gracers, by applying it to hydrodynamical simulations of galaxies, where we know the true value of the bar pattern speed. We perform some simple tests to see if the TW method has a physically reasonable output. We add different kinds of uncertainties (e.g. in position angle or flux) to the data to mock observational errors based on the magnitude of uncertainty present in the observations. Second, we test the method on 3D simulations with chemical networks. We show that in general, applying TW to observations of gas will not recover the true pattern speed. These results have implications for many "pattern speeds" reported in the literature, and based on these tests we also give some best practices for measuring pattern speeds using gas tracers going forwards.