Properties of Fast and Slow Bars Classified by Epicyclic Frequency Curves from Photometry of Barred Galaxies

We test the idea that bar pattern speeds decrease with time owing to angular momentum exchange with a dark matter halo. If this process actually occurs, then the locations of the corotation resonance and other resonances should generally increase with time. We therefore derive the angular velocity $Ω$ and epicyclic frequency $κ$ as functions of galactocentric radius for 85 barred galaxies using photometric data. Mass maps are constructed by assuming a dynamical mass-to-light ratio and then solving the Poisson equation for the gravitatonal potential. The location of Lindblad resonances and the corotation resonance radius are then derived using the standard precession frequency curves in conjunction with bar pattern speeds recently estimated from the Tremaine-Weinberg method as applied to Integral Field Spectroscopy (IFS) data. Correlations between physical properties of bars and their host galaxies indicate that bar {\it length} and the corotation radius depend on the disk circular velocity while bar {\it strength} and pattern speed do not. As the bar pattern speed decreases, bar strength, length, and corotation radius incease, but when bars are subclassified into fast, medium, and slow domains, no significant change in bar length is found. Only a hint of an increase of bar strength from fast to slow bars is found. These results suggest that bar length in galaxies undergoes little evolution, being instead determined mainly by the size of their host galaxy.