Resonance coupling in spiral arms: Patterns for flat rotation curve

Abstract

To address questions about the physical nature and origin of spiral arms in galaxies, it is necessary to measure their dynamical properties, such as the angular speed, ${\Omega }_p$, or the corotation radius. Observations suggest that galaxies may contain several independent spiral patterns simultaneously. It was shown that so-called non-linear resonance coupling plays an important role in such systems. We aim to identify cases of independent spiral patterns for galaxies with a flat rotation curve and to investigate what relative pattern velocities they might have for all possible cases of coupling between the main resonances. We solved equations for the main resonance positions (1:1, 2:1, 4:1) and estimated the ratio $\varpi$ of the corotation radii for two subsequent patterns. For six close galaxies with flat rotation curves, we collected the measurements of the corotation radii in the literature, using at least three different methods in each case for credibility. We found at least two independent spiral patterns for each galaxy and measured the $\varpi$ ratios. For three cases, we obtained $\varpi >3$, indicating that it would be difficult to fit two or even more spiral patterns in the disc. These ratios have been used to derive the wind-up time for spirals, estimated to be several galactic rotations. We find that three pairs of coupling cases, including those that have been vastly acknowledged in galaxies, namely, $OL{R}_{in}=C{R}_{out}\&C{R}_{in}=IUH{R}_{out}$, have very close $\varpi$ ratios; hence, they ought to be found simultaneously, as observed. We find a strongly confirmed apparent resonance coupling for six galaxies and we show that the observed $\varpi$ is in agreement with theory. In two of them, we identified a previously unreported form of simultaneous coupling, namely, $OL{R}_{in}=OUH{R}_{out}\&OUH{R}_{in}=C{R}_{out}$. This result was also predicted from the proximity of $\varpi$.

Accepted for publication in A&A Letters

References in corpus (13)

• High-Resolution Rotation Curves and Galaxy Mass Models from THINGS
• HyperLEDA. III. The catalogue of extragalactic distances
• Dawes Review 4: Spiral Structures in Disc Galaxies
• The Fundamental Properties of Galaxies and a New Galaxy Classification System
• Geometrically Derived Timescales for Star Formation in Spiral Galaxies
• Radial Dependence of the Pattern Speed of M51
• Slowly Breaking Waves: The Longevity of Tidally Induced Spiral Structure
• The Potential-Density Phase Shift Method for Determining the Corotation Radii in Spiral and Barred Galaxies
• Applying the Tremaine-Weinberg Method to Nearby Galaxies: Stellar Mass-Based Pattern Speeds, and Comparisons with ISM Kinematics
• Fountain-driven gas accretion feeding star formation over the disc of NGC 2403
• Galaxies decomposition with spiral arms -- II: A multiwavelength case study of M 51
• A low density-wave spiral pattern speed, from the tracer separations (age gradient) across a spiral arm in the Milky Way
• Azimuthal propagation of star formation in nearby spiral galaxies: NGC 628, NGC 3726 and NGC 6946

Cited by in corpus (1)

• A Comprehensive Analysis on the Nature of the Spiral Arms in NGC 3686, NGC 4321, and NGC 2403