Comparing two models for measuring the neutron star equation of state from gravitational-wave signals

Observations of gravitational-wave signals from binary neutron-star mergers, like GW170817, can be used to constrain the neutron-star equation of state (EoS). One method involves modeling the EoS and measuring the model parameters through Bayesian inference. A previous study [B. D. Lackey and L. Wade, Phys. Rev. D 91, 043002 (2015)] has demonstrated the effectiveness of using a phenomenologically parameterized piecewise polytrope to extract constraining information from a simulated population of binary neutron-star mergers. Despite its advantages compared to more traditional methods of measuring the tidal deformability of neutron stars, notable deficiencies arise when using this EoS model. In this work, we describe in detail the implementation of a model built from a spectral decomposition of the adiabatic index that was used by the LIGO-Virgo Collaboration [arXiv:1805.11581] to constrain the neutron-star EoS from GW170817. We demonstrate its overall consistency in recovering the neutron-star EoS from a simulated signal to the piecewise-polytropic implementation used by Lackey and Wade and explain any differences that arise. We find that both models recover consistent tidal information from the simulate signals with tightest constraints on the EoS around twice nuclear saturation density. As expected, the statistical error that arises in the piecewise-polytmpic representation near the fixed joining densities is greatly reduced by using the spectral model. In addition, we find that our choice of prior can have a dominant effect on EoS constraints.