Degeneracy in the inference of phase transitions in the neutron star equation of state from gravitational wave data

Gravitational wave (GW) detections of binary neutron star inspirals will be crucial for constraining the dense matter equation of state (EoS). We demonstrate a new degeneracy in the mapping from tidal deformability data to the EoS, which occurs for models with strong phase transitions. We find that there exists a new family of EoS with phase transitions that set in at different densities and that predict neutron star radii that differ by up to ~500m, but that produce nearly identical tidal deformabilities for all neutron star masses. Next generation GW detectors and advances in nuclear theory may be needed to resolve this degeneracy.