Spin supplementary conditions for spinning compact binaries

TL;DR

This paper analyzes various spin supplementary conditions (SSC) in spinning compact binaries, examining their effects on dynamics, conserved quantities, and gravitational waveforms at leading-order spin-orbit interaction.

Contribution

It compares different SSCs within a Hamiltonian framework, deriving conserved quantities and gravitational waveforms, highlighting their impact on binary dynamics.

Findings

Conserved quantities depend on the chosen SSC.

Waveforms and energy loss rates vary with SSC.

Acceleration dependence appears in some SSC formulations.

Abstract

We consider different spin supplementary conditions (SSC) for a spinning compact binary with the leading-order spin-orbit (SO) interaction. The Lagrangian of the binary system can be constructed but it is acceleration-dependent in two cases of SSC. We rewrite the generalized Hamiltonian formalism proposed by Ostrogradsky and compute the conserved quantities and the dissipative part of relative motion during the gravitational radiation of each SSC. We give the orbital elements and observed quantities of the SO dynamics, for instance the energy and the orbital angular momentum losses and waveforms and discuss their SSC dependence.