On the Galactic Law of Rotation

A uniformly rotating spherical cloud of nearly uniform density is supposed to contract into a thin disk, with each element of gas conserving its angular momentum. It is shown that if the cloud density is strictly uniform, there exists an axially symmetric disk-like state of centrifugal equilibrium with uniform angular velocity Ω; while if the cloud density decreases slightly (according to a specific law) from centre to surface, disk-like equilibrium is possible with a much more concentrated mass distribution, and with a uniform rotational velocity V . The difference between the two cloud density laws is slight, and it is probable that any nearly uniform sphere in uniform rotation can generate (with the same angular momentum constraint) two disks, with rotation laws that approximate respectively to Ω = constant and V = constant. The two models are regarded as smoothed-out, zero-order approximations to the barred and the normal spirals: which disk is formed from the collapsing primeval sphere depends on the relative strengths of the perturbations present.