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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 nearinfrared images of over 100 galaxies in the Ohio State University Bright
Galaxy Survey are summarized and discussed.
Fig. 3. Phaseshift versus radius for the weakly-barred spiral NGC 4303,
showing multiple positive to negative crossings between 33 and 56 pix
radius. The red circles superposed on the OSUBGS H-band image at
right shows that the inner crossing lies around the ends of the bar
while the outer two crossings lie in the bright spiral. Rautiainen et al.
(2005) were able to reproduce the morphology of NGC 4303 well
with simulations involving a single pattern speed.
BACKGROUND
The derivation of galactic density wave pattern speeds and corotation
radii has historically been difficult. The Tremaine and Weinberg
(1984=TW) method is considered to be the most direct method;
it 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. If a density wave is present,
the residuals will change from a one-armed to a three-armed pattern
across 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.
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.
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.
APPLICATION OF THE NEW APPROACH
For a self-sustained spiral or bar mode, the potential-density
phaseshift should change sign at the corotation radius. This
sign change can be used to locate corotation radii (Zhang 1996).
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, <r(CR)/r(bar)>=1.29 +/- 0.12.
Fig. 1. Phaseshift versus radius for the ordinary spiral NGC 5247,
showing a major (positive to negative) crossing at r=75 pix. The
red circle superposed on the OSUBGS H-band image at right
shows that this CR lies in the middle of the bright spiral.
CONCLUSIONS
The phaseshift method is a promising new way of locating the corotation
resonances of normal disk galaxies. In a future study we will present
calculations of mass inflow rates implied by the observed phaseshift
distributions.
BIBLIOGRAPHY
We thank E. Laurikainen for the deprojected images we have used in
this study. 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 9617006, with additional funding from the Ohio State University.
References:
Fig. 2. Phaseshift versus radius for barred spiral NGC 4314,
showing CRs at r=5pix 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.
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