Tidal effects in binary neutron star coalescence

TL;DR

The paper tests whether the tidal effective-one-body (EOB) model, incorporating next-to-next-to-leading-order (NNLO) tidal corrections, can reproduce long-term numerical relativity (NR) simulations of binary neutron star coalescence up to contact. Using high-accuracy NR data and a careful error analysis, the authors show that the NNLO tidal EOB framework aligns with NR dynamics and waveform phasing up to contact without introducing new tidal calibration beyond those fitted to binary black holes. The results indicate that 2PN tidal corrections minimize residuals relative to NR data, but current NR uncertainties do not decisively distinguish next-order tidal terms from leading-order effects; evidence for strong tidal amplification is not required, placing conservative bounds on possible amplification and guiding future template construction. The study underscores the importance of extensive NR error assessments and suggests that NNLO tidal EOB is currently the most reliable analytical tool for modeling GW signals from binary neutron stars up to contact.

Abstract

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.

Figures (8)

• Figure 1: (color online) Numerical quadrupolar gravitational waveform extracted at the outermost radius $r_{\rm obs}=750=247.55M$ for the CENO and WENO data (run H). Top: real part and amplitude (dashed lines). Bottom: frequency. The vertical lines mark the contact of the WENO data.
• Figure 2: (color online) Numerical dynamics: $E(j)$ curves for two series of simulation (CENO and WENO data), and for two point-mass analytical models (EOB resummed and "canonical" Taylor-expanded 3PN). The vertical dashed line marks the angular momentum at contact.
• Figure 3: (color online) Binary dynamics from WENO NR simulations. Contour plot of the rest-mass density on the equatorial plane. The snapshots indicate the contact happens around dynamical time $t_{\rm c}\approx 2382M$. This dynamical time, corresponding to observer's retarded time $u_c=t-r_*^{\rm obs}$, locates the contact at GW frequency $M\omega^{\rm c}_{22}\approx 0.078$. Run H.
• Figure 4: Comparison between EOB and NR dynamics. Left panel: reduced binding energy ($E$) versus reduced angular momentum ($j$) curves. Right panel: differences with the tidal EOB model. The shaded region represents the estimated uncertainties on the "best" numerical curve. Numerical data are consistent with the tidal EOB model.
• Figure 5: Comparing numerical and analytical $\ell=m=2$ waveform: frequency (left panels) and modulus (right panels). The vertical line locates the NR contact. The shaded regions in the bottom panels are error estimates on the NR frequency and modulus.