Although it has been anticipated a long time (1883) ago by
William Thomson (later Lord Kelvin) and
Peter Guthrie Tait in their book
Treatise on Natural Philosophy that a small presence of viscosity in a rotating, self-gravitating, otherwise ideal fluid mass would lose its stability, it is shown to be true only much later by
Paul H. Roberts and
Keith Stewartson in 1963. Similar to how an energy dissipation by viscosity will lead to loss of stability, Chandrasekhar showed that the dissipation by the gravitational radiation reaction would also lead to a loss of stability, although such an instability is unprecedented in a non-rotating star. The instability that arises only when there is a dissipation, but disappears in the absence of dissipation is referred to as the
secular instability. Both the Roberts–Stewartson instability and CFS instability are secular instability, although they do not both correspond to same modes in the following sense: In the absence of radiation reaction and viscosity, the
Maclaurin spheroid (a model for rotating, self-gravitating body) becomes marginally or neutrally stable when its
eccentricity reaches a critical value with two possible neutral modes, but it does not become unstable after this bifurcation. It is only in the presence of dissipation,
Maclaurin spheroid becomes unstable when eccentricity exceeds its bifurcation value. The Roberts–Stewartson instability stems from one of the neutral mode, whereas the CFS instability stems from the other neutral mode. ==References==