Dynamical tides in general relativity: Effective action and effective-one-body Hamiltonian

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.

Comprehensive comparison of numerical relativity and effective-one-body results to inform improvements in waveform models for binary neutron star systems

“…The caveats with the choice of gauge for mapping GSF results to EOB potentials that contain explicit poles at the light ring r LR are discussed in [48]. In Eq.…”

“…The inclusion of the effects of dynamic tides from the NS's f −modes of oscillation is discussed in detail in Ref. [48]. Here, we consider only the most practical yet approximate of the models devised therein, where the potential from Eqs.…”

“…7. (iv) different resummation techniques for the EOB potentials, where we compare a Pade resummation with the calibration summarized in [46] with a logarithmic resummation of the EOB potentials as given explicitly in [48] with the calibration from [37] (shown black in Fig. 13).…”

“…(A1)-(A2h) of Ref. [48] with the calibration parameter K = 1.712 − 1.804ν − 39.77ν 2 + 103.166ν 3 determined in [37]. The potential D is taken from Eq.…”

“…The pure GSF-based model underestimates matter effects in the late inspiral, but was augmented by an additional term to develop a model that remains close to NR predictions [31,46]. Another line of recent work has focused on the enhancement of tidal effects due to the NS's finite fundamental (f −) mode frequency that also leads to an improved performance of the model in comparisons with NR results [47,48].…”