Independently, Kathryn Johnston (Columbia) and David Spergel (Flatiron) have pointed out to me that if you have a Hamiltonian dynamical system that is slightly out of steady-state, you can do a kind of expansion, in which the steady-state equation is just the zeroth order term in an expansion. The first-order term looks like the zeroth-order Hamiltonian acting on the first-order perturbation to the distribution function, plus the first-order perturbation to the Hamiltonian acting on the zeroth-order distribution function (equals a time derivative of the distribution function). That's cool!
Now couple that idea with the fact that a steady-state Hamiltonian system is a set of phase-mixed orbits nested in phase space (literally a 3-torus foliation of 6-space). Isn't this first-order equation the equation of a winding-up spiral mode? I think it is! If so, it might unite a bunch of phenomenology, from cold stellar streams to spiral structure in the disk to The Snail. I discussed all this with Adrian Price-Whelan (Flatiron).
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