Inferring the population properties of binary neutron stars with gravitational-wave measurements of spin

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.