Radiating Love: adiabatic tidal fluxes and modes up to next-to-next-to-leading post-Newtonian order

Abstract

We present the analytical evaluation of the gravitational energy and angular momentum flux with tidal effects for inspiraling compact binaries, at the next-to-next-to-leading post-Newtonian (2PN) order, within the diagrammatic Effective Field Theory approach. We first compute the stress-energy tensor for a binary system, which requires the evaluation of two-point Feynman integrals, up to two loops. Then we extract the multipole moments of the system, which we present for generic orbits in center-of-mass coordinates, and which are needed to evaluate the total gravitational energy and the angular momentum flux for generic orbits. Finally, we provide the expressions for gauge invariant quantities for circular orbits, such as the fluxes, mode amplitudes, and phase of the emitted gravitational wave. Our results are useful for updating previous theoretical studies, as well as related phenomenological analyses and waveform models.