  We study the resonant tidal excitation of g modes in coalescing superfluid
neutron star (NS) binaries and investigate how such tidal driving impacts the
gravitational-wave (GW) signal of the inspiral. Previous studies of this type
treated the NS core as a normal fluid and thus did not account for its expected
superfluidity. The source of buoyancy that supports the g modes is
fundamentally different in the two cases: in a normal fluid core the buoyancy
is due to gradients in the proton-to-neutron fraction whereas in a superfluid
core it is due to gradients in the muon-to-electron fraction. The latter yields
a stronger stratification and a superfluid NS therefore has a denser spectrum
of g modes with frequencies above 10 Hz. As a result, many more g modes undergo
resonant tidal excitation as the binary sweeps through the bandwidth of GW
detectors such as LIGO. We find that roughly 10 times more orbital energy is
transferred into g mode oscillations if the NS has a superfluid core rather
than a normal fluid core. However, because this energy is transferred later in
the inspiral when the orbital decay is faster, the accumulated phase error in
the gravitational waveform is comparable for a superfluid and a normal fluid NS
(about 0.001-0.01 rad). A phase error of this magnitude is too small to be
measured from a single event with the current generation of GW detectors.
