  Neutron stars undergoing r-mode oscillation emit gravitational radiation that
might be detected on earth. For known millisecond pulsars the observed spindown
rate imposes an upper limit on the possible gravitational wave signal of these
sources. Taking into account the physics of r-mode evolution, we show that only
sources spinning at frequencies above a few hundred Hertz can be unstable to
r-modes, and we derive a more stringent universal r-mode spindown limit on
their gravitational wave signal, exploiting the fact that the r-mode saturation
amplitude is insensitive to the structural properties of individual sources. We
find that this refined bound limits the gravitational wave strain from
millisecond pulsars to values below the detection sensitivity of
next-generation detectors. Young sources are therefore a more promising option
for the detection of gravitational waves emitted by r-modes and to probe the
interior composition of compact stars in the near future.
