Impact of Dynamical Tides on the Reconstruction of the Neutron Star Equation of State

Gravitational waves (GWs) from inspiraling neutron stars afford us a unique opportunity to infer the as-of-yet unknown equation of state of cold hadronic matter at supranuclear densities. During the inspiral, the dominant matter effects arise due to the star’s response to their companion’s tidal field, leaving a characteristic imprint in the emitted GW signal. This unique signature allows us to constrain the cold neutron star equation of state. At GW frequencies above $\gtrsim 800\mathrm{Hz}$, however, subdominant tidal effects known as dynamical tides become important. In this Letter, we demonstrate that neglecting dynamical tidal effects associated with the fundamental ($f$) mode leads to large systematic biases in the measured tidal deformability of the stars and hence in the inferred neutron star equation of state. Importantly, we find that $f$-mode dynamical tides will already be relevant for Advanced LIGO’s and Virgo’s fifth observing run ($\sim 2025$)—neglecting dynamical tides can lead to errors on the neutron radius of $\mathcal{O}(1\mathrm{km})$, with dramatic implications for the measurement of the equation of state. Our results demonstrate that the accurate modeling of subdominant tidal effects beyond the adiabatic limit will be crucial to perform accurate measurements of the neutron star equation of state in upcoming GW observations.

Figure 1

One-dimensional posterior probability distributions of $\tilde{\mathrm{\Lambda }}$ for BNSs with mass ratio $q=0.855$ and varying source-frame chirp mass ${\mathcal{M}}_c$ with the APR4 EOS as measured in $A+$ (top) and ET (bottom). For lighter binaries, which have larger tidal deformabilities, we see significant biases between adiabatic (solid) and dynamical tidal (dashed) posteriors. Vertical dashed lines indicate the injected values. As ${\mathcal{M}}_c$ increases, the effects of dynamical tides become negligible.

Figure 2

Stacked likelihood of the tidal deformability for 12 BNS events in $A+$ (left) and ET (right) with adiabatic and dynamical tides (teal) and adiabatic tides only (red). The vertical dashed lines indicate the true value ${\mathrm{\Lambda }}_{1.33}^{\mathrm{true}}=341$ assuming APR4 as the common EOS of our population.

Figure 3

Mass-radius relation for 12 BNS observed in an $A+$ network. The population consists of binaries drawn from a Gaussian distribution consistent with the low-mass peak of galactic BNS, $m\sim \mathcal{N}({\mu }_i,{\sigma }_i)$, where ${\mu }_i=1.33M_{\odot }$. We use APR4 as the underlying equation of state, denoted by the black curve (black solid). Neglecting dynamical tidal effects induces biases $\sim \mathcal{O}(1\mathrm{km})$ in the inferred the mass-radius relation, excluding the true EOS at 90% credible interval for almost all NS masses.