Gravitoelectric dynamical tides at second post-Newtonian order

Abstract

We present a gravitoelectric quadrupolar dynamical tidal-interaction Hamiltonian for a compact binary system, that is valid to second order in the post-Newtonian expansion. Our derivation uses the diagrammatic effective field theory approach, and involves Feynman integrals up to two loops, evaluated with the dimensional regularization scheme. We also derive the effective Hamiltonian for adiabatic tides, obtained by taking the appropriate limit of the dynamical effective Hamiltonian, and we check its validity by verifying the complete Poincaré algebra. In the adiabatic limit, we also calculate two gauge-invariant observables, namely, the binding energy for a circular orbit and the scattering angle in a hyperbolic scattering. Our results are important for developing accurate gravitational waveform models for neutron-star binaries for present and future gravitational-wave observatories.

Cost of Inferred Nuclear Parameters toward the f-mode Dynamical Tide in Binary Neutron Stars

“…The dominant contribution arises from the electric-type quadrupolar adiabatic tidal deformation appearing first at five post-Newtonian (PN) order (Hinderer et al 2010), and this has been used to infer the NS properties from the detected BNS candidates. A significant amount of effort has been made to develop an accurate waveform model, including different corrections such as the inclusion of higherorder electric and magnetic multipolar tidal corrections (Damour & Nagar 2010;Hinderer et al 2010;Bini et al 2012;Landry & Poisson 2015;Banihashemi & Vines 2020;Henry et al 2020;Poisson 2020;Mandal et al 2024) and the dynamical tidal correction due to resonant/nonresonant excitation of NS oscillation modes (Hinderer et al 2016;Steinhoff et al 2016;Schmidt & Hinderer 2019;Gupta et al 2021Gupta et al , 2023Kuan & Kokkotas 2022;Gamba & Bernuzzi 2023;Mandal et al 2023;Abac et al 2024;Pnigouras et al 2024). Although, for the detected events GW170817 and/or GW190425, there is a minor impact on the inferred NS properties due to the additional corrections of multipolar tidal effects (Godzieba et al 2021;Narikawa 2023;Pradhan et al 2023c) or due to the consideration of the dynamical corrections (Pratten et al 2020;Gamba & Bernuzzi 2023;Pradhan et al 2023c;Abac et al 2024); their importance will be significant for future events, accessible with increasing sensitivity of the current GW detectors or even with the next-generation detectors.…”