Linear-scale view of a theoretical comet reservoir: a sparse spherical outer cloud surrounding a warped two-arm inner Oort structure.
Galactic tidal torque winds Neptune-scattered comets into a two-arm spiral — drag to rotate
The Milky Way's tidal gravity slowly rotates every comet orbit's orientation — and it does so faster for larger orbits. So at any snapshot, each radial shell has rotated by a different amount. Inner orbits have barely moved; outer orbits have wound much further around. Connect those positions and you trace an Archimedean spiral — like a stadium wave frozen mid-wave where the outer rows are further along.
The Milky Way's gravity acts like a slow spin on every comet orbit. Bigger orbits spin faster than smaller ones — that's the key. So at any moment, each ring of the cloud is at a different stage of turning. The inner ring has moved a little, the outer ring a lot. Connect those positions and you get a spiral — exactly like a stadium wave where the outer seats are further ahead.
Every comet orbit has a closest point to the Sun called its perihelion — its pointed end. The angle of that pointed end relative to the galactic plane is ω (omega). At the start, all comets scattered by Neptune share a similar orientation: ω ≈ 0°, meaning their pointed ends lie near the galactic equator. The galactic tide then rotates ω continuously; equilibria sit at 90° and 270° (the galactic poles).
Every comet orbit has a closest point to the Sun called its perihelion — like the sharp tip of an egg shape. The angle ω (say "omega") tells us which direction that tip is pointing. The Milky Way's gravity slowly spins ω around. It naturally settles at 90° or 270° — pointing straight toward a galactic pole.
The galactic tide acts like a potential-energy landscape for ω: two valleys at ω = 90° and ω = 270° (the galactic poles) and two hills at 0° and 180°. All comets start near the hilltop at ω = 0°. The tide then rolls each orbit downhill toward the nearest valley — this is the Kozai-Lidov mechanism. The ball in the diagram rolls through all four peaks and valleys; real comets settle into whichever valley they first encounter.
Think of ω as a ball rolling on a hilly landscape. The Milky Way's gravity creates two valleys (low-energy resting spots) at 90° and 270°, with hilltops at 0° and 180°. All comets start near a hilltop. The galaxy's gravity rolls each one downhill toward the nearest valley — this is the Kozai-Lidov effect. Once in a valley, a comet's orbit stays pointed toward that galactic pole.
This is a sky map — every point is a direction in the sky. Each dot marks where one comet's perihelion (closest approach to the Sun) currently points. At first they're scattered across the whole sky. As Kozai locking takes hold, each dot migrates toward the nearest galactic pole: half drain to the top edge (galactic north), half to the bottom edge (galactic south). The two bright bands that form are the two arms — not ribbons stretching outward, but two opposite concentrations of perihelion directions permanently pinned to the poles.
This map shows every direction in the sky. Each dot is one comet's "tip" direction — where its closest approach to the Sun is currently pointing. They start scattered everywhere. The Milky Way's gravity acts like a drain: half the comets get pulled toward the top of the map (galactic north), half toward the bottom (galactic south). When they all pile up at the top and bottom, you see two bright bands — those are the two arms.