Runaway Heating By R-Modes of Neutron Stars in Low Mass X-ray Binaries

Recently Andersson et. al., and Bildsten have independently suggested that an r-mode instability might be responsible for stalling the neutron-star spin-up in strongly accreting, Low Mass X-ray Binaries (LMXBs). We show that if this does occur, then there are two possibilities for the resulting neutron-star evolution: If the r-mode damping is a decreasing function of temperature, then the star undergoes a cyclic evolution: (i) accretional spin-up triggers the instability near the observed maximum spin rate; (ii) the r-modes become highly excited through gravitational-radiation-reaction, and in a fraction of a year (0.13yrs in a particular model that we have considered) they viscously heat the star up to T ∼ 2.5× 10K; (iii) r-mode gravitational-radiation-reaction then spins the star down in tspindown ≃ 0.08(ffinal/130Hz) yrs to a limiting rotational frequency ffinal, whose exact value depends on the not fully understood mechanisms of r-mode damping; (iv) the r-mode instability shuts off; (v) the neutron star slowly cools and is spun up by accretion for ∼ 5 × 10yrs, until it once again reaches the instability point, closing the cycle. The shortness of the epoch of r-mode activity makes it unlikely that r-modes are currently excited in the neutron star of any galactic LMXBs, and unlikely that advanced LIGO interferometers will see gravitational waves from extragalactic LMXBs. Nevertheless, this cyclic evolution could be responsible for keeping the rotational frequencies within the observed LMXB frequency range. If, on the other hand, the r-mode damping is temperature independent, then a steady state with constant angular velocity and Tcore ≃ 4 × 10 K is reached, in which r-mode viscous heating is balanced by neutrino cooling and accretional spin-up torque is balanced by gravitational-radiation-reaction spin-down torque.