What defines the radius where the orbiting matter speed matches the pattern speed ($\Omega_{gp}$)?
Answer
Corotation radius
The corotation radius marks a critical boundary within the galactic disk dynamics. It is specifically defined as the radius where the material—the stars and gas clouds—are orbiting at the exact same angular speed as the spiral density wave pattern itself. Inside this radius, stars move faster than the pattern, and outside this radius, stars move slower than the pattern. This matching speed means there is no net transfer of orbital energy or momentum between the matter and the wave at this specific distance, setting it apart dynamically from regions where the wave must actively push or pull the material to maintain its structure.
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