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I've been learning about the density wave theory of spiral arms, and also how the gravitational potential of galaxies is non-axisymmetric, resulting in a sinusoidal spiral potential.

I've then learnt that the spiral arms/density waves occur at this spiral potential minima. Why is this?

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In general there will be a gravitational force associated with any gradient in potential. The force tends to zero where the potential gradient is zero - at the minimum in potential - and so that's where matter accumulates.

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    $\begingroup$ Of course, the gradient is also zero at the maximum of the potential, but an slight disturbance and you slide off towards the minimum. $\endgroup$
    – Jon Custer
    Aug 17, 2023 at 13:23

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