Self-interaction spin effects in inspiralling compact binaries

TL;DR

This work extends the post-Newtonian description of spinning compact-binary inspirals by computing all contributions to the gravitational-wave frequency evolution $\frac{df}{dt}$ and the accumulated cycles $\mathcal{N}$ up to second order, explicitly including the first self-interaction spin (SS-self) terms. The authors derive the circular-orbit frequency evolution $\left\langle \dfrac{d\omega}{dt} \right\rangle^{\circ}$ with PN, SO, SS, QM, DD, and tail components, parameterized by $\beta$ and $\sigma$, and integrate to obtain $\omega(t)$ and $\phi(t)$, hence $\mathcal{N}$. They demonstrate that SS-self contributions can be commensurate with proper spin-spin terms in systems like the double pulsar J0737-3039 and discuss the implications for LIGO/VIRGO and LISA phasing, representing the first correction to radiation reaction in the Lense-Thirring regime. Overall, the results refine GW phasing models and underscore the need to include SS-self effects in high-precision waveform templates.

Abstract

Gravitational radiation drives compact binaries through an inspiral phase towards a final coalescence. For binaries with\textit{spin, mass quadrupole and magnetic dipole moments}, various contributions add to this process, which is characterized by the rate of increase $df/dt$ of the gravitational wave frequency and the accumulated number $\mathcal{N}$ of gravitational wave cycles. We present here all contributions to $df/dt$ and $% \mathcal{N}$ up to the second post-Newtonian order. Among them we give for the first time the contributions due to the \textit{self-interaction of individual spins}. These are shown to be commensurable with the proper spin-spin contributions for the recently discovered J0737-3039 double pulsar, and argued to represent the first corrections to the radiation reaction in the Lense-Thirring approach.