Spin induced multipole moments for the gravitational wave flux from binary inspirals to third Post-Newtonian order

TL;DR

The paper addresses the need for spin-dependent gravitational-wave flux expressions at 3PN for inspiraling binaries. It applies Non-Relativistic General Relativity (NRGR), an effective field theory, to perform a scale-separated multipole matching that yields spin-dependent source moments I^{ij}, J^{ij}, I^{ijk}, and J^{ijk} up to O(S) and O(S^2) and the cross-term O(S_A S_B), including finite-size corrections. These multipoles feed into the energy flux and GW phase, with the authors laying out all the spin-related ingredients and outlining that the full 3PN energy flux will be presented in a companion paper, powerloss. The results complete the last missing ingredients for the spin sector at 3PN and lay the groundwork for precise waveform templates for spinning binaries, matching existing spinless PN results and previous spin calculations.

Abstract

Using effective field theory techniques we calculate the source multipole moments needed to obtain the spin contributions to the power radiated in gravitational waves from inspiralling compact binaries to third Post-Newtonian order (3PN). The multipoles depend linearly and quadratically on the spins and include both spin(1)spin(2) and spin(1)spin(1) components. The results in this paper provide the last missing ingredient required to determine the phase evolution to 3PN including all spin effects which we will report in a separate paper.

Figures (7)

• Figure 1: Leading order contribution to the effective action after integrating out the radiation field. The double solid line denotes the binary system and the wiggly line denotes the radiation graviton.
• Figure 2: ${\cal O}({\bf S}_A)$ worldline coupling to: a) radiation and b) potential modes. A blob represents couplings linear in spin induced by the terms in $L_{\rm sg}$.
• Figure 3: ${\cal O}({\bf S}_A^2)$ worldline coupling to: a) radiation and b) potential modes. A box represents couplings quadratic in spin due to the finite size operator in $L_{ES^2}$.
• Figure 4: Nonlinear gravitational effects at ${\cal O}({\bf S}_1 {\bf S}_2)$.
• Figure 5: Nonlinear gravitational effects from finite size at ${\cal O}({\bf S}_A^2)$.