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, 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: (1) accretional spin-up triggers the instability near the observed maximum spin rate; (2) the r-modes become highly excited through gravitational radiation reaction, and in a fraction of a year (0.13 yr in a particular model that we have considered) they viscously heat the star up to T similar to 2.5 x 10(9) K; (3) r-mode gravitational radiation reaction then spins the star down in t(spindown) similar or equal to 0.08(f(final)/130 Hz)(-6) yr to a limiting rotational frequency f(final), whose exact value depends on the not fully understood mechanisms of r-mode damping; (4) the r-mode instability shuts off; and (5) the neutron star slowly cools and is spun up by accretion for similar to 5 x 10(6) yr, 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 T-core similar or equal to 4 x 10(8) 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. In this case (as Bildsten and Andersson et. al. have shown) the neutron stars in LMXBs could be potential sources of periodic gravitational waves, detectable by enhanced LIGO interferometers.