Dynamical Tides in General Relativity: Effective Action and Effective-One-Body Hamiltonian

TL;DR

This work develops a covariant effective action for fully dynamical quadrupolar tides in general relativity, focused on the quadrupolar f-mode of neutron stars, and embeds it into the effective-one-body (EOB) formalism to model inspirals with dynamical tides. It derives the covariant action, equations of motion, and both post-Newtonian and test-particle limits, then constructs a 1PN dynamical-tide EOB Hamiltonian and explores several gauge and resummation schemes, including a computationally efficient effective Love-number approach. The results show that dynamical tides can significantly enhance matter effects near resonance, especially for stars with large radii and low mass ratios, affecting the gravitational-wave phase and ISCO location. The TEOB framework developed here provides ready-to-use waveform infrastructure for LIGO/Virgo data analysis and EOS inference, with plans to extend to higher multipoles and dissipative sectors in future work.

Abstract

Tidal effects have an important impact on the late inspiral of compact binary systems containing neutron stars. Most current models of tidal deformations of neutron stars assume that the tidal bulge is directly related to the tidal field generated by the companion, with a constant response coefficient. However, if the orbital motion approaches a resonance with one of the internal modes of the neutron star, this adiabatic description of tidal effects starts to break down, and the tides become dynamical. In this paper, we consider dynamical tides in general relativity due to the quadrupolar fundamental oscillation mode of a neutron star. We devise a description of the effects of the neutron star's finite size on the orbital dynamics based on an effective point-particle action augmented by dynamical quadrupolar degrees of freedom. We analyze the post-Newtonian and test-particle approximations of this model and incorporate the results into an effective-one-body Hamiltonian. This enables us to extend the description of dynamical tides over the entire inspiral. We demonstrate that dynamical tides give a significant enhancement of matter effects compared to adiabatic tides, at least for neutron stars with large radii and for low mass-ratio systems, and should therefore be included in accurate models for gravitational-wave data analysis.

Figures (5)

• Figure 1: Dimensionless effective tidal deformability from a two timescale approximation under leading-order radiation reaction [see Sec. \ref{['keff']} with the replacement $r= (GM) (GM \Omega)^{-2/3}$, in units with $c=1$ and for an H4 equation of state and mass $1.35M_\odot$]. The index $l$ refers to the multipolar order, such that $k_2$ is the quadrupolar dimensionless tidal deformability and $k_3$ is the octupolar one.
• Figure 2: The frame of the tidally deformed neutron star is dragged in the direction of the orbital motion.
• Figure 3: Innermost stable circular orbit (ISCO) as a function of the mass ratio for a neutron-star--black-hole binary. As soon as the adiabatic tidal effects deviate from the point-mass case, the dynamical tidal effects are relevant, too. Here we used the 2PN accurate TEOB-$k_\text{eff}$ model with an effective Love number from Sec. \ref{['keff']}.
• Figure 4: Phase difference in radians between waveforms using the 2PN TEOB-$A_\text{AT}$ model Bini:2012gu as the baseline and the models summarized in Table \ref{['modtab']} for $m_1=1.350 M_\odot$ and a piecewise polytropic approximation of the H4 equation of state. While individual lines are shown for the 1PN truncation of the models, the shaded area encompasses the range of all dynamical models at 2PN order. The fact that the span with 2PN information lies within the 1PN span indicates that our conclusions about the importance of dynamical tides will likely remain valid when higher PN orders are included. Furthermore, the TEOB model (red curve) is always close to the upper part of the span.
• Figure 5: Same as Fig. \ref{['dphi']}, but for an equal-mass neutron-star binary.