Impact on Inferred Neutron Star Equation of State due to Nonlinear Hydrodynamics, Background Spin, and Relativity

Tidal interaction is a unique, detectable signature in gravitational wave signals from inspiraling binary neutron stars (BNSs), which can be used to constrain the neutron star (NS) equation of state (EoS). The tidal interaction is resonantly amplified as the orbital frequency approaches the NS fundamental mode (f-mode) frequency. It has been shown that the exclusion of tidal resonance in parameter estimation leads to a significant bias in the inferred NS tidal deformability and hence the NS EoS [Pratten et al. PRL 129, 081102 (2022)]. The strength and location of tidal resonance depend sensitively on the f-mode frequency, which is typically modeled using its universal relation with the tidal deformability that is derived for an isolated, non-spinning NS assuming only linear fluid perturbations. In a BNS inspiral, the f-mode frequency can be corrected by at least three known effects: nonlinear hydrodynamics, background spin, and relativity. We use Hamiltonian Monte Carlo simulations to estimate the systematic bias on tidal deformability when each frequency correction is ignored. Our study considers both loud, individual events and the stacking of a population of detections. Both scenarios are expected when the next-generation detectors are available with a sensitivity level increased by about an order of magnitude.