Séminaire Amplitudes et Gravitation sur l'Yvette (IHES/IPhT)
The hierarchical limit of the three-body problem is relevant to many systems in astrophysics and provides a regime where solutions to the notorious three-body problem can be obtained using techniques from scattering amplitudes and effective field theory. In this talk, I will describe how to model the dynamics of hierarchical triples, which are three-body systems composed of two bodies separated by a distance $r$ and a third body a distance $\rho$ away, with $r \ll \rho$. I will show the application of the method of regions for evaluating Fourier transform integrals by systematically expanding in the small ratio $r/\rho$. With this technique, I will present our results for the conservative three-body potential at $\mathcal{O}(G2)$ at leading and next-to-leading order in $r/\rho$. Our results are exact in velocity, and can be used in analyses involving both bound and unbound hierarchical triples in astrophysical systems.
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Julio Parra-Martinez & Alessandro Podo
