Tidal effects in binary neutron star coalescence

We compare dynamics and waveforms from binary neutron star coalescence as computed by new long-term ($\sim 10 $ orbits) numerical relativity simulations and by the tidal effective-one-body (EOB) model including analytical tidal corrections up to second post-Newtonian order (2PN). The current analytical knowledge encoded in the tidal EOB model is found to be sufficient to reproduce the numerical data up to contact and within their uncertainties. Remarkably, no calibration of any tidal EOB free parameters is required, beside those already fitted to binary black holes data. The inclusion of 2PN tidal corrections minimizes the differences with the numerical data, but it is not possible to significantly distinguish them from the leading-order tidal contribution. The presence of a relevant amplification of tidal effects is likely to be excluded, although it can appear as a consequence of numerical inaccuracies. We conclude that the tidally-completed effective-one-body model provides nowadays the most advanced and accurate tool for modelling gravitational waveforms from binary neutron star inspiral up to contact. This work also points out the importance of extensive tests to assess the uncertainties of the numerical data, and the potential need of new numerical strategies to perform accurate simulations.

💡 Research Summary

This paper presents a comprehensive comparison between long‑duration numerical‑relativity (NR) simulations of binary neutron‑star (BNS) coalescence and the tidal effective‑one‑body (EOB) model that incorporates analytical tidal corrections up to second post‑Newtonian (2PN) order. The authors generate new NR data covering roughly ten orbital cycles before merger, using two high‑resolution shock‑capturing (HRSC) schemes: a third‑order CENO reconstruction and a fifth‑order WENO‑Z reconstruction, both coupled with adaptive‑mesh‑refinement (AMR) and Runge‑Kutta time integrators. The initial configuration consists of equal‑mass, irrotational neutron stars with a Γ=2 polytropic equation of state, compactness C≈0.14, radius R≈10.8 km, and a dimensionless Love number k₂≈0.079. Gravitational‑wave strain h₂₂ is extracted from the Newman‑Penrose scalar ψ₄ at a large radius (r≈750 M) and processed with a frequency‑domain integration method.

On the analytical side, the tidal EOB model is built upon the standard point‑mass EOB potential A₀(u) resummed through a (1,5) Padé approximant, with calibrated parameters a₅=−6.37 and a₆=+5.0 taken from binary‑black‑hole fits. The tidal contribution A_tidal(u) is expressed as A_tidal(u)=4X_ℓ κ_T^ℓ u^{2ℓ+2}