LAUSR

A method, which we have developed for determining corotation radii, has allowed us to map in detail the radial resonant structures of barred spiral galaxies. Here, we have combined this information with new determinations of the bar strength and the pitch angle of the innermost segment of the spiral arms to find relationships between these parameters of relevance to the dynamical evolution of the galaxies. We show how (1) the bar mass fraction, (2) the scaled bar angular momentum, (3) the pitch angle, and (4) the shear parameter vary along the Hubble sequence, and we also plot along the Hubble sequence (5) the scaled bar length, (6) the ratio of bar corotation radius to bar length, (7) the scaled bar pattern speed, and (8) the bar strength. It is of interest to note that the parameters (2), (5), (6), (7), and (8) all show breaks in their behaviour at type Scd. We find that bars with high shear have only small pitch angles, while bars with large pitch angles must have low shear; we also find a generally inverse trend of the pitch angle with bar strength. An inference that at first seems counter-intuitive is that the most massive bars rotate most slowly but have the largest angular momenta. Among a further set of detailed results, we pick out here the 2:1 ratio between the number of spiral arms and the number of corotations outside the bar. These results give a guideline to theories of disc–bar evolution.