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Fig. 2.

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Top: Illustration showing the expectations for a non-exhaustive list of three scenarios that explain spiral structure: a quasi-stationary density wave (constant pattern speed), multiple overlapping modes (i.e. different pattern speeds across the disc), and material arms (always made up of the same stars, all of which are by definition co-rotating) or dynamical spirals (transient features made up of rather short, unconnected segments). Middle panels: Expected histograms for the distribution of CO-Hα offsets (θ) as well as the expected mean offset. We define offsets such that positive values mean Hα peaks lie ahead of CO peaks in the direction of galactic rotation. For quasi-stationary density waves, we expect such offsets to be positive inside co-rotation and negative outside; however, since we sample mostly the inner parts of galaxies, the net offsets should typically be positive within our fields of view. The right panels indicate whether we should find a significant correlation between offsets and radius or not. Bottom: Illustration of how we measure azimuthal offsets in spiral arms in practice. For each radial bin (an elliptical annulus of width ∼100 pc that accounts for the inclination and PA of the galaxy), we average the CO and Hα intensities in azimuthal bins. We then find the azimuth (ϕ) corresponding to the maximum of both tracers within the footprint of each spiral mask (ϕmax). The angular difference between the bins of peak intensity yields the offset of interest, θ, at that radius. To account for galaxy rotation, if the galaxy rotates anti-clockwise, the offset θ is multiplied by η = −1.

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