The Potential-Density Phase-Shift Method for Determining the Corotation Radii in Spiral and Barred Galaxies

Abstract

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 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. 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; and that self-consistent N-particle systems contain physics not revealed by the passive orbit analysis approaches.

How can double-barred galaxies be long-lived?

“…An in-depth analysis of NGC 1068, based both on multiwavelength observations and numerical simulations, led Emsellem et al (2006) to conclude that 0.19 < ∼ Ω p /Ω s < ∼ 0.26. Zhang & Buta (2007) introduced a potential-density phaseshift method that is able to determine the position of multiple corotations in a galaxy without any kinematical information. This method is thus particularly well suited to double-barred galaxies.…”

Dynamical Evolution of Agn Host Galaxies—gas in/Out-Flow Rates in Seven Nuga Galaxies

“…We have applied the potential density phase shift method (Zhang & Buta 2007) to derive the CR radii for our galaxies. This technique is based on the calculated radial distribution of an azimuthal phase shift between the stellar potential and a stellar density wave pattern which results in a torque action between the wave pattern and the underlying disk matter.…”

“…Overview of the dynamical resonances derived from different methods: the CR radius from our gravity torque study (Column 2), the radius of the bar (Column 3), the CR using the method of Canzian (1993;Column 4), the CR on the basis of the phase-shift method of Zhang & Buta (2007;Column 5) and the associated angular speed of the bar Ω Bar (Column 6), the ILR at Ω Bar = Ω − κ/2 (Column 7), the UHR at Ω Bar = Ω − κ/4 (Column 8), and the OLR at Ω Bar = Ω + κ/2 (Column 9) of the bar. All radii are deprojected.…”

Dynamical Simulations of NGC 2523 and NGC 4245

“…It remains one of the fundamental unknowns of galaxy dynamics. A variety of techniques for determining Ω p have been published (e.g., Canzian 1993;Buta & Combes 1996;Puerari & Dottori 1997;Salo et al 1999;Weiner et al 2001;Egusa et al 2004;Zhang & Buta 2007), though in recent years emphasis has been placed on an observational method developed by Tremaine & Weinberg (1984, hereafter TW). Studies of late that make use of this method have focused on estimating the pattern speed of SB0 galaxies (e.g., Aguerri et al 2003;Corsini et al 2003;Debattista et al 2002).…”