Lindblad Zones: resonant eccentric orbits to aid bar and spiral formation in galaxy discs

Abstract

The apsidal precession frequency in a fixed gravitational potential increases with the radial range of the orbit (eccentricity). Although the frequency increase is modest it can have important implications for wave dynamics in galaxy discs, which have not been previously explored in detail. One of the most interesting consequences is that for a given pattern frequency, each Lindblad resonance does not exist in isolation, but rather is the parent of a continuous sequence of resonant radii, a Lindblad Zone, with each radius in this zone characterized by a specific eccentricity. In the epicyclic approximation the precession or epicyclic frequency does not depend on epicycle size, and this phenomenon is not captured. A better approximation for eccentric orbits is provided by p-ellipse curves (Struck 2006), which do exhibit this effect. Here the p-ellipse approximation and precession-eccentricity relation are used as tools for finding the resonant radii generated from various Lindblad parent resonances. Simple, idealized examples, in flat rotation curve and near solid-body discs, are used to show that ensembles of eccentric resonant orbits excited in Lindblad Zones can provide a backbone for generating a variety of (kinematic) bars and spiral waves. In cases balancing radius-dependent circular frequencies and eccentricity-dependent precession, a range of resonant orbits can maintain their form in the pattern frame, and do not wind up. Eccentric resonance orbits require a strong perturbation to excite them, and may be produced mostly in galaxy interactions or by strong internal disturbances.

arXiv comment16 pages, 12 figures, MNRAS accepted

References in corpus (16)

• Dynamics of Barred Galaxies
• Rapid formation of exponential disks and bulges at high redshift from the dynamical evolution of clump cluster and chain galaxies
• Secular Evolution in Disk Galaxies
• Galaxy Collisions
• Transient spirals as superposed instabilities
• The regeneration of stellar bars by tidal interactions. Numerical simulations of fly-by encounters
• Adventures of a tidally induced bar
• Manifold-driven spirals in N-body barred galaxy simulations
• Slowly Breaking Waves: The Longevity of Tidally Induced Spiral Structure
• HST Observations of the Interacting Galaxies NGC 2207 and IC 2163
• Tidal-induced lopsidedness in Magellanic-type galaxies
• The symmetries and scaling of tidal tails in galaxies
• LEDA 074886: A remarkable rectangular-looking galaxy
• Simple, Accurate, Approximate Orbits in the Logarithmic and a Range of Power-Law Galactic Potentials
• Natural orbit approximations in single power-law potentials
• A Study of the Orbits of the Logarithmic Potential for Galaxies

Cited by in corpus (4)

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• Orbits in elementary, power-law galaxy bars: 1. Occurence and role of single loops