On secular instabilities of rigidly rotating stars in general relativity - 11. Numerical results

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This is the second of two papers on secular instabilities in rigidly rotating, stationary, axisymmetric, incompressible stars. The time scales of the instabilities caused by gravitational radiation reaction and viscosity in these stars are calculated using the equations derived n the preceding paper (Comins). These instabilities cause the star's angular momentum to decrease and set upper limits to the angular frequency of stars with a given age. We find that all inviscid, incompressible stars are secularly unstable to gravitational radiation, and the consequent radiation reaction causes a loss of both energy and angular momentum in the star. When viscosity is introduced into the problem, it too causes secular instabilities, however in some cases these two dissipative effects counterbalance each other and actually increase the secular stability of the star. The e-folding times for solar density stars typically exceed the present lifetime of the Universe, but for white dwarfs and more especially neutron stars, these times are of astrophysical interest.

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