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I suggest a novel approach for deriving evolution equations for rapidlyrotating relativistic stars affected by radiation-drivenChandrasekhar-Friedman-Schutz (CFS) instability. This approach is based on themultipolar expansion of gravitational wave emission and appeals to the globalphysical properties of the star (energy, angular momentum, and thermal state),but not to canonical energy and angular momentum, which is traditional. Itleads to simple derivation of the CFS instability criterion for normal modesand the evolution equations for a star, affected by this instability. Theapproach also gives a precise form to simple explanation of the CFSinstability: it occurs when two conditions met: (a) gravitational wave emissionremoves angular momentum from the rotating star (thus releasing the rotationenergy) and (b) gravitational waves carry less energy, than the released amountof the rotation energy. Results are illustrated by r-mode instability in slowlyrotating Newtonian stars. In resulting evolution equations emission ofgravitational waves directly affects the spin frequency, being in line with thearguments by Levin & Ushomirsky (2001), but in contrast to widely acceptedequations by Lindblom et al. (1998); Ho & Lai (2000), there effective spinfrequency decrease is coupled with dissipation of unstable mode. This problem,initially stressed by Levin & Ushomirsky (2001), is shown to be superficial,and arises as a result of definition of the effective spin frequency byLindblom et al. (1998); Ho & Lai (2000). Namely, it is shown, that if thisdefinition is taken into account properly, the evolution equations coincidewith obtained here in the leading order in mode amplitude. I also argue thatthe next-to-leading order terms in evolution equations (which differ for Owenet al. 1998 and Ho & Lai 2000) require clarification and thus it would be moreself-consistent to omit them.

publications of the astronomical society of australia/publications astronomical society of australia

Radiation driven instability of rapidly rotating relativistic stars:  criterion and evolution equations via multipolar expansion of gravitational  waves