Which two radii define the stable boundaries for a long-lived spiral structure?

Answer

Inner Lindblad Resonance (ILR) and Outer Lindblad Resonance (OLR)

For a density wave to maintain itself over long periods, the gravitational influence of the wave must effectively compress the matter, requiring the stars to respond appropriately to local density enhancements. This responsiveness is governed by the epicyclic frequency ($\kappa(R)$) of the star's orbit. The theory dictates that this sustained interaction, which reinforces the density wave, can only occur within a specific annulus bounded by two critical radii known as the Lindblad resonances. Outside the Outer Lindblad Resonance (OLR) or inside the Inner Lindblad Resonance (ILR), the wave's influence either occurs too frequently or too infrequently relative to the stellar orbits, preventing the necessary feedback mechanism that sustains the spiral structure.

Which two radii define the stable boundaries for a long-lived spiral structure?

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