We have developed a new method for determining the corotation radii of
density waves in disk galaxies, which makes use of the radial distribution of
an azimuthal phase shift between the potential and density wave patterns. The
approach originated from improved theoretical understandings of the relation
between the morphology and kinematics of galaxies, and on the dynamical
interaction between density waves and the basic-state disk stars which results
in the secular evolution of disk galaxies. In this paper, we present the
rationales behind the method, and the first application of it to several
representative barred and grand-design spiral galaxies, using near-infrared
images to trace the mass distributions, as well as to calculate the potential
distributions used in the phase shift calculations. We compare our results with
those from other existing methods for locating the corotations, and show that
the new method both confirms the previously-established trends of bar-length
dependence on galaxy morphological types, as well as provides new insights into
the possible extent of bars in disk galaxies. Application of the method to a
larger sample and the preliminary analysis of which show 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 this work are: most of the nearby bright disk galaxies appear to possess
quasi-stationary spiral modes; that these density wave modes and the associated
basic state of the galactic disk slowly transform over time; and that
self-consistent N-particle systems contain physics not revealed by the passive
orbit analysis approaches.Comment: 48 pages, 16 figures. Accepted for publication in the Astronomical
Journa
