  The recent LIGO-Virgo detection of gravitational waves from a binary neutron
star inspiral event GW170817 and the discovery of its accompanying
electromagnetic signals mark a new era for multimessenger astronomy. In the
coming years, advanced gravitational-wave detectors are likely to detect tens
to hundreds of similar events. Neutron stars in binaries can possess
significant spin, which is imprinted on the gravitational waveform via the
effective spin parameter $\chi_\text{eff}$. We explore the astrophysical
inferences made possible by gravitational-wave measurements of
$\chi_\text{eff}$. First, using a fiducial model informed by radio
observations, we estimate that $\approx15-30\%$ of binary neutron stars should
have spins measurable at $\gtrsim 90\%$ confidence level by advanced detectors
assuming the spin axis of the recycled neutron star aligns with the total
orbital angular momentum of the binary. Second, using Bayesian inference, we
show that it is possible to tell whether or not the spin axis of the recycled
neutron star tends to be aligned with the binary orbit using $\gtrsim 30$
detections. Finally, interesting constraints can be placed on neutron star
magnetic field decay after $\gtrsim 300$ detections, if the spin periods and
magnetic field strengths of Galactic binary neutron stars are representative of
the merging population.
