Relativistic effective action of dynamical gravitomagnetic tides for slowly rotating neutron stars

Abstract

Gravitomagnetic quasi-normal modes of neutron stars are resonantly excited by tidal effects during a binary inspiral, leading to a potentially measurable effect in the gravitational-wave signal. We take an important step towards incorporating these effects in waveform models by developing a relativistic effective action for the gravitomagnetic dynamics that clarifies a number of subtleties. Working in the slow-rotation limit, we first consider the post-Newtonian approximation and explicitly derive the effective action from the equations of motion. We demonstrate that this formulation opens a way to compute mode frequencies, yields insights into the relevant matter variables, and elucidates the role of a shift symmetry of the fluid properties under a displacement of the gravitomagnetic mode amplitudes. We then construct a fully relativistic action based on the symmetries and a power counting scheme. This action involves four coupling coefficients that depend on the internal structure of the neutron star and characterize the key matter parameters imprinted in the gravitational waves. We show that, after fixing one of the coefficients by normalization, the other three directly involve the two kinds of gravitomagnetic Love numbers (static and irrotational), and the mode frequencies. We discuss several interesting features and dynamical consequences of this action, and analyze the frequency-domain response function (the frequency-dependent ratio between the induced flux quadrupole and the external gravitomagnetic field), and a corresponding Love operator representing the time-domain response. Our results provide the foundation for deriving precision predictions of gravitomagnetic effects, and the nuclear physics they encode, for gravitational-wave astronomy.

20 pages; v2: added time domain response/Love operator and discussion of electric driving, minor typos corrected, submitted to journal; v3: extended discussion; v4: published

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Cited by in corpus (21)

• The Science of the Einstein Telescope
• Spin effects on neutron star fundamental-mode dynamical tides: phenomenology and comparison to numerical simulations
• New and Robust Gravitational-Waveform Model for High-Mass-Ratio Binary Neutron Star Systems with Dynamical Tidal Effects
• Modeling horizon absorption in spinning binary black holes using effective worldline theory
• Tidal response from scattering and the role of analytic continuation
• General relativistic dynamical tides in binary inspirals, without modes
• Renormalizing Love: tidal effects at the third post-Newtonian order
• Investigating tidal heating in neutron stars via gravitational Raman scattering
• Beyond the linear tide: impact of the non-linear tidal response of neutron stars on gravitational waveforms from binary inspirals
• Accurate and Efficient Waveform Model for Precessing Binary Black Holes
• Gravitoelectric dynamical tides at second post-Newtonian order
• Dynamical tides during the inspiral of rapidly spinning neutron stars: Solutions beyond mode resonance
• Effective-action model for dynamical scalarization beyond the adiabatic approximation
• Dipolar tidal effects in gravitational waves from scalarized black hole binary inspirals in quadratic gravity
• $f$-mode Imprints in Gravitational Waves from Coalescing Binaries involving Aligned Spinning Neutron Stars
• Geodesic structure and quasinormal modes of a tidally perturbed spacetime
• Radiating Love: adiabatic tidal fluxes and modes up to next-to-next-to-leading post-Newtonian order
• Cost of inferred nuclear parameters towards the f-mode dynamical tide in binary neutron stars
• Hidden symmetry between rotational tidal Love numbers of spinning neutron stars
• Modeling matter(s) in SEOBNRv5THM: Generating fast and accurate effective-one-body waveforms for spin-aligned binary neutron stars
• Observables and Unconstrained Spin Tensor Dynamics in General Relativity from Scattering Amplitudes