Tidal effects in the equations of motion of compact binary systems to next-to-next-to-leading post-Newtonian order

Abstract

As a first step in the computation of the orbital phase evolution of spinless compact binaries including tidal effects up to the next-to-next-to-leading (NNL) order, we obtain the equations of motion of those systems and the associated conserved integrals in harmonic coordinates. The internal structure and finite size effects of the compact objects are described by means of an effective Fokker-type action. Our results, complete to the NNL order, correspond to the second-post-Newtonian (2PN) approximation beyond the leading tidal effect itself, already occurring at the 5PN order. They are parametrized by three polarizability (or deformability) coefficients describing the mass quadrupolar, mass octupolar and current quadrupolar deformations of the objects through tidal interactions. Up to the next-to-leading (NL) order, we recover previous results in the literature; up to the NNL order for quasi-circular orbits, we confirm the known tidal effects in the (PN re-expansion of the) effective-one-body (EOB) Hamiltonian. In a future work, we shall derive the tidal contributions to the gravitational-wave flux up to the NNL order, which is the second step required to find the orbital phase evolution. * quentin.henry@iap.fr †

Tidal effects in quantum field theory

“…By focusing on operators quadratic in the Weyl tensor, they computed tidal contributions to spinless amplitudes arising from the electric and magnetic quadrupoles, up to the next-to-leading-PM order (O(G 3 )). 1 Converting their amplitudes to classical observables, they found agreement with results derived from conventional general relativistic methods [42,[44][45][46][47].…”

“…This factor is small in the PN limit, thus we can see already from the PM amplitude level that the corresponding operators must be subleading in the PN limit, in agreement with the constructions in refs. [44,45,47]. In fact, this squares perfectly with principles from classical gravitational effective field theories (EFTs).…”

“…Increasing n or decreasing k at fixed n increases the number of derivatives acting on the photon field, thereby increasing powers of in the resulting contributions to amplitudes [17]. However, the derivative structure of the subleading tidal terms in the worldline action [44,45,47] suggests that we are right to keep these terms. Therefore, much like in the case of spin effects where the spin vector absorbs a power of [18], we propose JHEP12(2020)024 that the tidal coefficients must scale with to absorb the factors from the operators.…”

“…Ref. [47] found an explicit field redefinition of the graviton field that removes traces of the Riemann curvature from the tidal worldline action, including in the presence of matter.…”

Interpreting binary neutron star mergers: describing the binary neutron star dynamics, modelling gravitational waveforms, and analyzing detections

“…In this framework, Newtonian quadrupolar tidal effects in the dynamics first appear at O(α 5 ). Relativistic corrections have been computed up to O(α 5 2 ) for the quadrupole and O(α 7 2 ) for the octupole [78,263]. The knowledge of effects in the GW signals will be described in more detail below.…”