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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)

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.

The derivation of galactic density wave pattern speeds and corotation radii has historically been difficult. The Tremaine and Weinberg (1984=TW) 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.

For a self-sustained spiral or bar mode, the potential-densityphaseshift (eq. 1) should change sign at the corotation radius. Thissign 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).

ABSTRACT

BACKGROUND

APPLICATION OF THE NEW APPROACH

BIBLIOGRAPHY

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.

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. 1. Phaseshift versus radius for the ordinary spiral NGC 5247, showing a major (positive to negative) crossing at r=75 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.

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.

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.

CONCLUSIONS

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.

Fig. 6: Ratio of phaseshift CR radius to bar radius for 35 strongly-barred galaxies, 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) 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 Bar radius from isophote having maximum ellipticity. (right) Bar radius derived from faintest distinct isophote. Here, <r(CR)/r(bar)>=1.29 +/- 0.12. In these plots, from faintest distinct isophote. Here, <r(CR)/r(bar)>=1.29 +/- 0.12. In these plots, T(RC3) is the numerically-coded Hubble type, where T=0 is S0/a, T=1 is Sa, T=2 is T(RC3) is the numerically-coded Hubble type, where T=0 is S0/a, T=1 is Sa, T=2 is Sab, etc.Sab, etc.

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