Tidal effects in the gravitational-wave phase evolution of compact binary systems to next-to-next-to-leading post-Newtonian order

TL;DR

This paper calculates the tidal effects on gravitational-wave phase evolution in compact binary systems up to next-to-next-to-leading order, enhancing the precision of waveform models for gravitational-wave astronomy.

Contribution

It provides the first complete derivation of tidal contributions to GW energy flux and phase evolution at NNL order, including tail effects, using an effective matter action and multipolar-post-Minkowskian formalism.

Findings

Derived the tidal contributions to GW energy flux up to NNL order.

Included tail effects at leading and NL orders in the tidal flux.

Extended previous models to achieve a more accurate GW phase evolution.

Abstract

We compute the gravitational-wave (GW) energy flux up to the next-to-next-to-leading (NNL) order of tidal effects in a spinless compact binary system on quasi-circular orbits. Starting from an effective matter action, we obtain the stress-energy tensor of the system, which we use in a GW generation formalism based on multipolar-post-Minkowskian (MPM) and post-Newtonian (PN) approximations. The tidal contributions to the multipole moments of the system are first obtained, from which we deduce the instantaneous GW energy flux to NNL order (formally 7PN order). We also include the remaining tidal contributions of GW tails to the leading (formally 6.5PN) and NL (7.5PN) orders. Combining it with our previous work on the conservative equations of motion (EoM) and associated energy, we get the GW phase and frequency evolution through the flux-balance equation to the same NNL order. These results extend and complete several preceding results in the literature.