On the Relevance of ther‐Mode Instability for Accreting Neutron Stars and White Dwarfs

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Abstract
We present a case study for the relevance of the r-mode instability for accreting compact stars. Our estimates are based on approximations that facilitate "back of the envelope" calculations. We discuss two different cases. (1) For recycled millisecond pulsars, we argue that the r-mode instability may be active at rotation periods longer than the Kepler period (which provides the dynamical limit on rotation) as long as the core temperature is larger than about 2 × 105 K. Our estimates suggest that the instability may have played a role in the evolution of the fastest spinning pulsars and that it may be presently active in the recently discovered 2.49 ms X-ray pulsar, SAX J1808.4-3658, as well as the rapidly spinning neutron stars observed in low-mass X-ray binaries (LMXBs). This provides a new explanation for the remarkably similar rotation periods inferred from kilohertz, quasi-periodic oscillations in the LMXBs. The possibility that the rotation of recycled pulsars may be gravitational-radiation-limited is interesting, because the gravitational waves from a neutron star rotating at the instability limit may well be detectable with the new generation of interferometric detectors. (2) We also consider white dwarfs and find that the r-mode instability may possibly be active in short-period white dwarfs. Our order-of-magnitude estimates (for a white dwarf of M=M☉ and R=0.01 R☉ composed of C12) show that the instability could be operating for rotational periods shorter than P≈27-33 s. This number is in interesting agreement with the observed periods (greater than 28 s) of the rapidly spinning DQ Herculis stars. However, we find that the instability grows too slowly to affect the rotation of these stars significantly.