On the rotation of elliptical galaxies

The tensor virial theorem is applied to elliptical galaxies having similar isophotes. In the absence of residual velocity anisotropy the shape of such a galaxy turns out to determine uniquely the ratio of the rotational and random kinetic energies independently of the galaxy's radial density-profile or the speed with which its form rotates. Curves are displayed of the expected projected ‘rotation’ velocities of elliptical galaxies under a variety of assumptions about their forms and degrees of residual anisotropy. In the absence of residual velocity anisotropy prolate spheroidal galaxies rotate only three-quarters as fast as equivalently aspherical oblate galaxies. The isotropic oblate models being almost certainly eliminated by Illingworth's rotation-velocity data, the possibility that all ellipticals are prolate is investigated. A distribution of true ellipticities of prolate galaxies is derived which will account for the apparent ellipticities reported by Sandage, Freeman & Stokes and the corresponding distribution of points in the (∊, υ/σ) plane determined. If ellipticals are all prolate there should be only a weak correlation between apparent ellipticity and rotation velocity. This possibility is consistent with Illingworth&s data. A better fit to the observations is provided by anisotropic oblate models. The limitations of these models as well as the implications of galactic rotation for cosmogony are discussed.