Spin induced multipole moments for the gravitational wave amplitude from binary inspirals to 2.5 Post-Newtonian order

TL;DR

This work advances gravitational-wave modeling for spinning binaries by computing spin-induced source multipole moments required for the waveform amplitude at $2.5$PN within the NRGR EFT framework. It derives the remaining spin-dependent multipoles, including the current octupole $J^{ijk}$ and the mass/current 16-, 32-poles, to leading orders in spin, and reproduces the tail contribution from the $J^{ij}M$ interaction. By combining worldline spin couplings with nonlinear gravitational effects and employing careful power counting, the authors provide the ingredients for spin-inclusive waveform templates and verify IR-divergent tail corrections through a time-redefinition. These results, together with prior work on the GW phase, enable more precise parameter estimation and cross-checks with numerical relativity for rapidly rotating binaries.

Abstract

Using the NRGR effective field theory formalism we calculate the remaining source multipole moments necessary to obtain the spin contributions to the gravitational wave amplitude to 2.5 Post-Newtonian (PN) order. We also reproduce the tail contribution to the waveform linear in spin at 2.5PN arising from the nonlinear interaction between the current quadrupole and the mass monopole.

Figures (3)

• Figure 1: ${\cal O}({\bf S}_A)$ worldline coupling to: a) radiation and b) potential modes. A blob represents couplings linear in spin.
• Figure 2: First nonlinear diagrams that contribute to $J^{ijk}$ at ${\cal O}({\bf S})$. As explained in the text, the diagram in Fig \ref{['nonlS9']}a represents a sub-leading effect.
• Figure 3: Tail diagram that describes the interaction between the source current quadrupole $J^{ij}$ and the monopole $M$. The dashed line here represents the background mode which builds up the geometry sourced by the binary.