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Using the gravitational potential and source multipole moments bilinear inthe spins, first computed to next-to-leading order (NLO) in the post-Newtonian(PN) expansion within the effective field theory (EFT) framework, we completehere the derivation of the dynamical invariants and flux-balance equations,including energy and angular momentum. We use these results to calculatespin-spin effects in the orbital frequency and accumulated phase to NLO forcircular orbits. We also derive the linear momentum and center-of-mass fluxesand associated kick-velocity, to the highest relevant PN order. We explicitlydemonstrate the equivalence between the quadratic-in-spin source multipolesobtained using the EFT formalism and those rederived later with moretraditional tools, leading to perfect agreement for spin-spin radiativeobservables to NLO among both approaches.

Gravitational radiation from inspiralling compact objects: Spin-spin effects completed at the next-to-leading post-Newtonian order