Applying the turning point theorem provided by Sorkin [95], Friedman Ipser and Sorkin [96] shows that, in the case of rotating stars, the secular axisymmetric instability sets in when the mass becomes maximum along a sequence of constant angular momentum. An equivalent criterion is provided by Cook et al. [38]: The secular axisymmetric instability sets in when the angular momentum becomes minimum along a sequence of constant rest mass.
The instability develops on a timescale that is limited by the time required for viscosity to redistribute the star's angular momentum. This timescale is long compared to the dynamical timescale and comparable to the spin-up time following a pulsar glitch. When it becomes secularly unstable, a star evolves in a quasi-stationary fashion until it encounters the dynamical instability and collapses to a black hole. Thus, the onset of the secular instability to axisymmetric perturbations separates stable neutron stars from neutron stars that will collapse to a black hole.
Goussard et al. [69] extend the stability criterion to hot protoneutron stars with nonzero total entropy. In this case, the loss of stability is marked by the configuration with minimum angular momentum along a sequence of both constant rest mass and total entropy.
In the nonrotating limit, Gondek et al. [73] compute frequencies and eigenfunctions of axisymmetric pulsations of hot proto-neutron stars and verify that the secular instability sets in at the maximum mass turning point, as is the case for cold neutron stars.
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Rotating Stars in Relativity
Nikolaos Stergioulas http://www.livingreviews.org/lrr-1998-8 © Max-Planck-Gesellschaft. ISSN 1433-8351 Problems/Comments to livrev@aei-potsdam.mpg.de |