Radiation reaction for spinning bodies in effective field theory II: Spin-spin effects

TL;DR

This work advances the modeling of spinning binary inspirals by computing radiation-reaction effects at $4.5$PN order that are quadratic in the spins, using an effective field theory approach for spinning bodies and including finite-size corrections. The authors derive the leading spin-spin radiation-reaction acceleration and spin evolution from first principles via a nonconservative Routhian and the in-in formalism, employing source multipoles and ensuring energy balance with the far-zone power, up to Schott terms. A key finding is that spin-spin radiation reaction induces spin precession at this order and that finite-size effects contribute to the RR force, differing from the spin-orbit sector. These results refine waveform modeling for spinning binaries and enhance the extraction of physical information from gravitational-wave observations.

Abstract

We compute the leading Post-Newtonian (PN) contributions at quadratic order in the spins to the radiation-reaction acceleration and spin evolution for binary systems, entering at four-and-a-half PN order. Our calculation includes the back-reaction from finite-size spin effects, which is presented for the first time. The computation is carried out, from first principles, using the effective field theory framework for spinning extended objects. At this order, nonconservative effects in the spin-spin sector are independent of the spin supplementary conditions. A non-trivial consistency check is performed by showing that the energy loss induced by the resulting radiation-reaction force is equivalent to the total emitted power in the far zone. We find that, in contrast to the spin-orbit contributions (reported in a companion paper), the radiation reaction affects the evolution of the spin vectors once spin-spin effects are incorporated.