A. I. Chugunov
Radiation-driven Chandrasekhar-Friedman-Schutz (CFS) instability (Chandrasekhar 1970; Friedman & Schutz 1978a,b) of rapidly rotating relativistic stars is considered using the multipolar expansion for gravitational radiation by Thorne (1980). It allows to derive the CFS instability criteria and obtain evolution equations for a star, affected by CFS instability, without appeal to the canonical energy formalism by Friedman & Schutz (1978a,b). In line with the arguments of Levin & Ushomirsky (2001), emission of gravitational waves directly affects the observed spin frequency [but not through dissipation of unstable mode as it follows from widely accepted equations by Lindblom, Owen, & Morsink (1998); Ho & Lai (2000)]. On a long timescale (when spin frequency changes significantly), the evolution equations can be reduced to one equation, which can be directly derived from energy conservation law. This equation, applicable in full general relativity at arbitrary spin rate, describes stellar evolution along the sequence of thermally equilibrium states and has no explicit dependence on the instability growing timescale. The special attention is devoted to the effects of differential rotation, which can be generated in a star on the course of CFS instability development [e.g., Levin & Ushomirsky 2001; Friedman et al. 2016]. It is argued that differential rotation, in principle, can affect theoretically predicted observational properties for certain initial conditions (e.g., if one considers evolution of strongly unstable star with very small initial amplitude of unstable mode), however it is unlikely that differential rotation can affect observations for realistic scenarios of neutron star evolution. In the latter case, equations by Lindblom, Owen, & Morsink (1998); Ho & Lai (2000) lead to almost the same evolution as equations, suggested here.
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