Spin effects on gravitational waves from inspiraling compact binaries at second post-Newtonian order

TL;DR

This paper derives the gravitational-wave strain from spinning compact binaries through 2PN order, including spin-orbit, spin–spin, and self-induced spin-quadrupole effects. By combining the spin-influenced orbital dynamics with the radiative multipole moments, the authors provide explicit forms for the polarizations and, for nonprecessing, circular binaries, closed expressions for the spin-weighted spherical-harmonic modes. A key result is that quadratic-in-spin terms arise from the equations of motion, while spin-orbit terms receive contributions from both orbital dynamics and radiation-field corrections, yielding ready-to-use templates for data analysis and NR benchmarking. The work enables improved waveform modeling across analytical and numerical-relativity interfaces and confirms consistency with perturbative and test-particle limits.

Abstract

We calculate the gravitational waveform for spinning, precessing compact binary inspirals through second post-Newtonian order in the amplitude. When spins are collinear with the orbital angular momentum and the orbits are quasi-circular, we further provide explicit expressions for the gravitational-wave polarizations and the decomposition into spin-weighted spherical-harmonic modes. Knowledge of the second post-Newtonian spin terms in the waveform could be used to improve the physical content of analytical templates for data analysis of compact binary inspirals and for more accurate comparisons with numerical-relativity simulations.