On the Origin of Galactic Rotation

Current theories on the origin of galactic rotation postulate widely different initial conditions. The assumed initial conditions consist of either density inhomogeneities or spin inhomogeneities, or more generally a combination of both. When the density contrast $$\mu \,=\,\delta \,\rho /\rho$$ increases the Universe is said to be gravitationally unstable; in a similar fashion, when the ‘spin contrast’ $$\xi \,=\,\omega^2/4\pi G\rho$$ increases (where ω is angular velocity) the Universe can be said to be spin unstable. In the tidal theory it is supposed that ξ is initially zero, and that density fluctuations grow because of gravitational instability and then interact to produce galactic spin. In the vortex theory it is supposed that μ is initially zero, and that spin fluctuations grow because of spin instability and form into galactic eddies characterized by a spin contrast of $$\xi \,\sim\,1$$ . These cosmogonies are discussed and it is shown that they both encounter difficulties. In particular, they are apparently unable to account for the basic difference between elliptical and spiral systems. A more general cosmogony is then discussed, which takes a less extreme view of the initial state, and starts from initial conditions consisting of both density and spin inhomogeneities. It is argued that when μ and ξ have initially comparable values, as in the case of the spinning-core theory, the main difficulties inherent in the previous theories are avoided. It is shown in an Appendix that the rotationally induced anisotropy in the expansion is of order ξ .