  Andersson et al. and Bildsten proposed that the spin of accreting neutron
stars is limited by removal of angular momentum by gravitational radiation
which increases dramatically with the spin frequency of the star. Both Bildsten
and Andersson et al. argued that the r-modes of the neutron star for
sufficiently quickly rotating and hot neutron stars will grow due to the
emission of gravitational radiation, thereby accounting for a time varying
quadrupole component to the neutron star's mass distribution. However, Levin
later argued that the equilibrium between spin-up due to accretion and
spin-down due to gravitational radiation is unstable, because the growth rate
of the r-modes and consequently the rate of gravitational wave emission is an
increasing function of the core temperature of the star. The system executes a
limit cycle, spinning up for several million years and spinning down in less
than a year. However, the duration of the spin-down portion of the limit cycle
depends sensitively on the amplitude at which the nonlinear coupling between
different r-modes becomes important. As the duration of the spin-down portion
increases the fraction of accreting neutron stars which may be emitting
gravitational radiation increases while the peak flux in gravitational
radiation decreases. Depending on the distribution of quickly rotating neutron
stars in the Galaxy and beyond, the number of gravitational emitters detectable
with LIGO may be large.
