On a mechanism that structures galaxies

By considering the interaction of a single stellar orbit with a weak cos 2ϕ potential it is shown that in the central regions of galaxies with slowly rising rotation curves, the elongations of the orbits will align along any potential valley and oscillate about it. This effect is more pronounced for elongated orbits. In such regions any pair of orbits will naturally align under their mutual gravity and so a bar will form. The gravity of this bar will drive a spiral structure in the outer parts of the galaxy where differential rotation is too strong to allow the orbits to be caught by the bar. The spiral structure carries a torque which slowly drains angular momentum from the bar, gradually making its outline more eccentric and slowing its pattern speed. In the outer parts of the bar only the more eccentric orbits align with the potential valley; the rounder ones form a ring or lens about the bar. As the pattern speed slows down, the corotation resonance and outer Lindblad resonance, which receive the angular momentum, move outwards. The evolution of the system is eventually slowed down by the weakness of these outer resonances where the material is rather sparse.