36x72 poster template

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A New Method for Corotation Determination in
Spiral and Barred Galaxies Xiaolei Zhang (US
Naval Research Laboratory) Ronald J. Buta
(University of Alabama)
ABSTRACT
The approaches proposed in the past for
determining the pattern speeds and corotation
radii of the density waves in spiral and barred
galaxies are mostly limited in their scope of
application, as well as in their accuracy.  In
this work, we have developed and verified a
general approach for the determination of
corotation radii, which is applicable to any
galaxies whose density wave modes have reached
quasi-steady state -- a condition empirically
found to be the case for the majority of nearby
disk galaxies. We describe the dynamical
mechanism underlying this method,  which utilizes
an azimuthal  phaseshift between the potential
and the density distributions for the density
wave modes, the existence and the radial
variations of which are closely related to the
dynamical mechanism leading to the secular
evolution of the basic state of the same disk
galaxies. Preliminary results on the application
of this method to the near-infrared images of
over 100 galaxies in the Ohio State University
Bright Galaxy Survey are summarized and discussed.
Fig. 3. Phaseshift versus radius for the barred
spiral NGC 3513, showing a major positive to
negative crossing at 56 pix radius. The red
circle superposed on the OSUBGS H-band image at
right shows that this crossing lies well beyond
the ends of the bar. The green circle shows that
the bar ends lie near a major negative to
positive crossing.
BACKGROUND
The derivation of galactic density wave pattern
speeds and corotation radii has historically been
difficult. The Tremaine and Weinberg (1984TW)
method uses the continuity equation and
off-nuclear spectra to derive pattern speeds,
from which a corotation radius may be inferred if
the rotation curve is known. Canzian (1993)
proposed a method which uses a residual velocity
field to locate corotation. The numerical
simulation method (Salo et al. 1999 Rautiainen
et al. 2005) is based on transforming a near-IR
image into a potential, and then evolving
collisionless stellar test particles and
inelastically-colliding gas particles in this
potential until the simulated morphology
visually matches the B- and H-band morphologies.
The potential-density phaseshift method
developed in our study has a number of
advantages (1) relatively insensitive to star
formation, M/L variations, and vertical scale
height assumptions (2) can be applied to face-on
galaxies (3) can be applied effectively to all
Hubble types, at least those with a disk shape
(4) multiple pattern speeds are clearly evident
(5) gives corotation radii directly and (6) can
use existing databases of images without the need
for significant investments in new telescope time.
Fig. 4. Phaseshift versus radius for the
early-type barred galaxy NGC 4665, showing a
positive to negative crossing at 31 pix radius.
The red circle superposed on the OSUBGS H-band
image at right shows that this crossing lies
slightly inside the ends of the bar.
APPLICATION OF THE NEW APPROACH
For a self-sustained spiral or bar mode, the
potential-density phaseshift (eq. 1) should
change sign at the corotation radius. This sign
change can be used to locate corotation radii
(Zhang 1996).

eq. 1 Here Sigma1 and V1 are the density
and potential perturbations, respectively, and
phi is the azimuthal angle. NIR images can
be used to measure the phaseshifts because such
images trace the stellar mass distribution better
than do optical images, and may be used to
calculate the gravitational potential. We have
made such calculations for more than 100 OSUBGS
galaxies, and show a few cases here (Figs. 1-5).
The basic assumptions we have made are that the
H-band mass-to-light ratio is constant, the
vertical scale height is a type-dependent
fraction of the radial scale length, and that
galaxies can be deprojected using the shapes of
outer isophotes. The deprojected images we use
are due to Laurikainen et al. (2004).
Figure 5. Comparison of corotation radii (white
circles) derived from the phaseshift method with
corotation bounds determined by the
Tremaine-Weinberg method (hatched regions) for
(left) NGC 4596 (Gerssen et al. 1999) and (right)
M100 (Hernandez et al. 2005). The TW method as
applied to NGC 4596 was used to determine only
the outer pattern corotation radius. The main
disagreement shown is for the bar corotation
location in M100, where we find CR around the
ends of the bar while Hernandez et al. place this
CR out in the arms. Note that the large amount of
star formation in the M100 image does not affect
the phaseshifts. If we remove many of the
star-forming regions, we get almost the same
corotation locations.
Fig. 6 Ratio of phaseshift CR radius to bar
radius for 35 strongly-barred galaxies, based on
bars that have been separated from their spirals
(Buta et al. 2005). (left) Bar radius from
isophote having maximum ellipticity. (right) Bar
radius derived from faintest distinct isophote.
Here, ltr(CR)/r(bar)gt1.29 /- 0.12. In these
plots, T(RC3) is the numerically-coded Hubble
type, where T0 is S0/a, T1 is Sa, T2 is Sab,
etc.
CONCLUSIONS
Fig. 1. Phaseshift versus radius for the ordinary
spiral NGC 5247, showing a major (positive to
negative) crossing at r75 pix. The large red
circle superposed on the OSUBGS H-band image at
right shows that this CR lies in the middle of
the bright spiral.
The phaseshift method is a promising new way of
locating the corotation resonances of normal disk
galaxies. As long as a pattern is
quasi-stationary, the method should be applicable
to any type of spiral or bar, for a wide range of
Hubble types. The locations of CRs inferred for
specific galaxies attests to the accuracy of the
method. We thank E. Laurikainen for the
deprojected images we have used in this study. XZ
acknowledges the support of the Office of Naval
Research. RB acknowledges the support of NSF
grant AST 050-7140 to the University of Alabama.
Funding for the Ohio State University Bright
Galaxy Survey was provided by NSF Grants AST
92-17716 and AST 96-17006, with additional
funding from the Ohio State University.
BIBLIOGRAPHY
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Fig. 2. Phaseshift versus radius for barred
spiral NGC 4314, showing CRs at r5pix and 50 pix
(red circles at right). The inner CR is
associated with central structure (a nuclear
ring/spiral) while the outer CR encircles the
ends of the bar.