[1][2][3] Specifically, the instability arises when a non-axisymmetric perturbation mode that appears co-rotating in the inertial frame (from which gravitational waves are observed), is in fact is counter-rotating with respect to the rotating star.
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.
[4] 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.
[5] 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.