Investigating the impact of quasi-universal relations on neutron star constraints in third-generation detectors

TL;DR

The paper analyzes how quasi-universal relations (qURs) linking neutron star properties—specifically the spin-induced quadrupole moment, f-mode frequency, and binary Love relations—affect EOS constraints in the era of third-generation gravitational-wave detectors. Using two extreme meta-model EOSs (MM− and MM+), a Bayesian framework with a detailed waveform model, and both zero-noise and noisy population realizations, the study quantifies biases in single-event and hierarchical EOS inferences. It finds that SIQM biases emerge at moderate-to-high spins but are mitigated when C_Q is allowed to vary; f-mode qUR biases are small relative to waveform systematics, while binary Love biases mainly affect next-to-leading tidal parameters and can propagate into Λ1, Λ2, with modest population-level impact. The results underscore the continued utility of qURs for GW analyses but emphasize the need for careful treatment and potential recalibration of qURs to avoid biases in next-generation EOS measurements, along with improvements to dynamical-tide modeling and higher-order tidal effects.

Abstract

Gravitational-wave observations of binary neutron star systems can shed light on the currently unknown dense matter equation of state. The equation of state determines a large number of neutron star properties, such as tidal deformability, radius, and quadrupole moment, several of which directly affect the emitted gravitational-wave signals. To reduce the dimensionality when computing gravitational-waves and when interpreting observational data, quasi-universal relations are commonly employed to connect different neutron star properties. However, quasi-universal relations are not exact and their use may introduce uncertainty and bias. We explore the potential biases arising from different quasi-universal relations in the third generation era: (i) the Love-Q relation connecting the spin-induced quadrupole moment and the tidal deformability, (ii) the relation between the fundamental mode frequency and the tidal deformability, and (iii) the binary Love relation. We find that for the quadrupole relation biases are only present for rapidly rotating systems, for the binary-Love relation induces moderate biases only in the next-to-leading-order tidal parameters, which can however propagate into the inferred equation of state at low masses. Regarding fundamental mode frequencies, we find that the employed relation introduces only negligible biases, while waveform systematic effects can become comparatively large. Our results highlight that while quasi-universal relations remain a useful tool within gravitational-wave analyses, careful treatment is needed to avoid biases in equation of state measurements with next-generation detectors.

Figures (14)

• Figure 1: Mass-radius curves for MM$^{-}$ (pink) and MM$^{+}$ (blue) with nuclear parameters listed in App. \ref{['Appdx:mm']}. The observed masses to 2$\sigma$ of the millisecond pulsar PSR J0740+6620 Fonseca:2021wxt (turquoise) and PSR J1614-2230 NANOGrav:2023hde (green) are shown alongside 90% confidence constraints from the analysis of GW170817 LIGOScientific:2017vwqLIGOScientific:2018ckiLIGOScientific:2018hze (yellow) and observations reported by the NICER mission for PSR J0030+0451 Miller:2019cac (light pink).
• Figure 2: Spin-induced quadrupole moment: Comparison of the qUR for the SIQM (black dashed lines) for MM$^{-}$ (pink) and MM$^{+}$ (blue). Points show a population of 1000 sources, with the 20 highest-SNR sources highlighted. The top panel displays the qUR for $C_Q$, while bottom panel shows deviations from the qUR, i.e., $\delta C_Q\equiv C_Q^{\rm EOS}-C_Q^{\rm qUR}$.
• Figure 3: Spin-induced quadrupole moment: Posterior density distributions when simulating signals with EOSs MM$^-$ (pink) and MM$^+$ (blue) for the Baseline (solid), Universal Relation (dashed), and $C_Q$ sampling (dotted) analyses as described in the text. True injected values are indicated (black solid lines). The posteriors shown are First column: Effective spin $\chi_{\rm eff}$. Second column: Detector frame chirp mass $\mathcal{M}_c$. Third column: Joint tidal deformability $\tilde{\Lambda}$. Fourth column: SIQM $C_Q$ in the case of the $C_Q$ sampling analysis, for the components $m_1$ (shaded) and $m_2$ (unshaded). Injected values for each component mass overlap as these are equal-mass, equal-spin systems.
• Figure 4: Spin-induced quadrupole moment: Posterior probability distributions of $\chi_{\mathrm{eff}} - \chi_{\mathrm{eff,true}}$, where $\chi_{\mathrm{eff,true}}$ is the true injected effective spin, for MM$^{-}$ (left) and MM$^{+}$ (right) EOS. An unbiased measurement corresponds to zero (black line). Results are shown for the ten highest-SNR events, ordered by the magnitude of the injected $\chi_{\mathrm{eff, true}}$, with the SNRs listed on the right. Two analyses are compared as described in the text: Baseline (solid) and Universal Relation (dashed). We choose to omit the $C_Q$ sampling analysis for clarity.
• Figure 5: Fundamental mode frequency:$f$-mode frequency $f_2$ obtained from MM$^{-}$ (pink) and MM$^{+}$ (blue) between masses of $1M_\odot$ and $2.2M_\odot$. Highlighted points show the components from the $20$ loudest binary sources of the population. Top panel: absolute $f$-mode frequencies compared with the qUR reference (black dashed line). Bottom panel: Deviations of the frequencies from the qUR, i.e., $\delta f_2\equiv f_2^{\rm qUR}-f_2^{\rm EOS}$.