High-order effective-one-body tidal interactions and gravitational scattering

Abstract

Using state-of-the-art scattering results in post-Minkowskian (PM) gravity, we improve the tidal sector of four different flavors of the effective-one-body (EOB) formalism. We notably explore both adiabatic and post-adiabatic gravitoelectric and gravitomagnetic quadrupolar tidal effects at the next-to-next-to-leading PM-order. When comparing the predictions of the so-constructed Lagrange-PM-tidal version of EOB to recent numerical-relativity data on the scattering of neutron stars, we find improved agreement with respect to existing EOB models and PM expansions. Our work lays the foundation for the development of an accurate tidal sector of the PM EOB models, and points out the need to explore improved resummation schemes in PN EOB for bound and circularized orbits.

Figures (3)

• Figure 1: Comparison of the tidal scattering angle as a function of $J_\text{in}/M^2$, where $J_\text{in}$ is the initial ADM momentum of the binary. Top: For the two exemplary binaries discussed in the main text with EOS Sly and MS1b respectively, we compare the NR tidal scattering angle from Fontbute:2025vdv with the (conservative) scattering angles for LEOB in the LJBL/$w$-EOB gauge (LEOB cons./$w$-EOB cons.), the non-resummed NNLO PM scattering angle from Kalin:2020lmzJakobsen:2023pvx and the TEOBResumS scattering angle with a tidal sector to NNLO Bernuzzi:2012ciAlbanesi:2025txj. For details about the different models see the main text. Note that for the LEOB and $w$-EOB models the post-adiabatic tidal coefficients $\kappa^A_{{\dot X}^2}(R_0)$ are set to zero. Bottom: Difference to NR tidal scattering angle for same set of models, with NR errors.
• Figure 2: The $w$-EOB tidal scattering angle computed for the SLy (Top) and MS1b (Bottom) binaries (see Table \ref{['tab:ns:params']} for their properties) with the tidal part of the $w$-potential (see main text for discussion) truncated at successive PM orders. Unless specified, the post-adiabatic tidal coefficient $\kappa_{\dot{E}^2}$ is set to zero. The tidal scattering angle including radiative effects is only plotted at 4PM for visual clarity but shows a similar convergent behaviour as the conservative tidal scattering angle, with a hierarchy $\chi_\text{cons.}^\text{nPM} < \chi_\text{rad.}^\text{nPM}$. We also show the scattering angle computed with two nonzero values of $\kappa_{\dot{E}^2}$: the (positive) numerical estimate discussed in the main text, and the (negative) value obtained from least-squares fits of the NR data in Fontbute:2025vdv. In these fits we only considered the datapoints that didn't show considerable hydrodynamics effects (i.e.$J_\text{in}/M^2 \gtrsim 1.39$ (1.52) for SLy (MS1b)).
• Figure 3: Comparison of $w$-EOB potentials, Eq. \ref{['eq:V']}, for the SLy binaries. We set the energy and angular momentum corresponding to the first point not containing significant hydrodynamic effects, $J_\text{in}/M^2 \simeq 1.39$. We contrast the NR potential obtained by inverting numerical scattering angles to $w$-EOB analytical potentials for different values of $\kappa_{\dot{E}^2}$. The value of $\kappa_{\dot{E}^2} \approx - 45$ is able to reproduce most of the missing PM information in the PM results and accurately reproduces the NR shape.