Chandrasekhar–Friedman–Schutz instability or shortly CFS instability refers to an instability that can occur in rapidly rotating

stars A star is a luminous spheroid of plasma held together by self-gravity. The nearest star to Earth is the Sun. Many other stars are visible to the naked eye at night; their immense distances from Earth make them appear as fixed points of ...

with which the instability arises for cases where the gravitational radiation reaction is unable to cope with the change in angular momentum associated with the perturbations. The instability was discovered by

Subrahmanyan Chandrasekhar Subrahmanyan Chandrasekhar (; 19 October 1910 – 21 August 1995) was an Indian Americans, Indian-American theoretical physicist who made significant contributions to the scientific knowledge about the structure of stars, stellar evolution and ...

in 1970 and later a simple intuitive explanation for the instability was provided by John L. Friedman and Bernard F. Schutz. Specifically, the instability arises when a non-axisymmetric perturbation mode that appears co-rotating in the inertial frame (from which

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are observed), is in fact is counter-rotating with respect to the rotating star.

Roberts–Stewartson instability and CFS instability

Although it has been anticipated a long time (1883) ago by William Thomson (later Lord Kelvin) and

Peter Guthrie Tait Peter Guthrie Tait (28 April 18314 July 1901) was a Scottish Mathematical physics, mathematical physicist and early pioneer in thermodynamics. He is best known for the mathematical physics textbook ''Treatise on Natural Philosophy'', which he ...

in their book

Treatise on Natural Philosophy ''Treatise on Natural Philosophy'' was an 1867 text book by William Thomson (later Lord Kelvin) and Peter Guthrie Tait, published by Oxford University Press. The ''Treatise'' was often referred to as T and ''T^1'', as explained by Alexander Ma ...

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''.Chandrasekhar, S. (1987). Ellipsoidal figures of equilibrium. New York: Dover. Page 95. 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

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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

{{reflist, 30em Astrophysics Fluid dynamics