We have developed a new method for determining the corotation radii of density waves in disk galaxies, which makes use of the calculated radial distribution of an azimuthal phase shift between the potential and density wave patterns. The approach originated from improved theoretical understanding of the relation between the morphology and kinematics of galaxies and of the dynamical interaction between density waves and the basic-state disk stars, which results in the secular evolution of disk galaxies. We present the rationales behind the method and the 1st application of it to several representative barred and grand-design spiral galaxies, using near-infrared images to trace the mass distributions and to calculate the potential distributions used in the phase-shift calculations. We compare our results with those from other existing methods and show that the new method both confirms the previously established trends of bar-length dependence on galaxy morphological types and provides new insights into the possible extent of bars in disk galaxies. The method also facilitates the estimation of mass accretion /excretion rates due to bar and spiral density waves, providing an alternative way of quantifying the importance of these features in disk galaxies. A preliminary analysis of a larger sample shows that the phase-shift method is likely to be a generally applicable, accurate, and essentially model- independent method for determining the pattern speeds and corotation radii of single or nested density wave patterns in galaxies. Other implications of the results of this work include that most of the nearby bright disk galaxies appear to possess quasi-stationary spiral modes; that these density wave modes, as well as the associated basic states of the galactic disks, slowly transform over the time span of a Hubble time due to a collective dissipation process directly related to the presence of the phase shift between the potential and density patterns.
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