Binarybinary scattering in the secular limit
Abstract
Binarybinary interactions are important in a number of astrophysical contexts including dense stellar systems such as globular clusters. Although less frequent than binarysingle encounters, binarybinary interactions lead to a much richer range of possibilities such as the formation of stable triple systems. Here, we focus on the regime of distant binarybinary encounters, I.e. two binaries approaching each other on an unbound orbit with a periapsis distance Q much larger than the internal binary separations. This 'secular' regime gives rise to changes in the orbital eccentricities and orientations, which we study using analytic considerations and numerical integrations. We show that 'direct' interactions between the three orbits only occur starting at a high expansion order of the Hamiltonian (hexadecupole order), and that the backreaction of the outer orbit on the inner two orbits at lower expansion orders is weak. Therefore, to good approximation, one can obtain the changes of each orbit by using previously known analytic results for binarysingle interactions, and replacing the mass of the third body with the total mass of the companion binary. Nevertheless, we find some dependence of the 'binarity' of the companion binary, and derive explicit analytic expressions for the secular changes that are consistent with numerical integrations. In particular, the eccentricity and inclination changes of orbit 1 due to orbit 2 scale as ∊_{SA, 1}(a_{2}/Q)^{2}[m_{3}m_{4}/(m_{3} + m_{4})^{2}], where ∊_{SA, 1} is the approximate quadrupoleorder change, and a_{2} and (m_{3}, m_{4}) are the companion binary orbital semimajor axis and component masses, respectively. Our results are implemented in several python scripts that are freely available.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 March 2020
 DOI:
 10.1093/mnras/staa691
 arXiv:
 arXiv:2002.04950
 Bibcode:
 2020MNRAS.494..850H
 Keywords:

 gravitation;
 celestial mechanics;
 stars: kinematics and dynamics;
 globular clusters: general;
 Astrophysics  High Energy Astrophysical Phenomena;
 Astrophysics  Instrumentation and Methods for Astrophysics
 EPrint:
 Accepted for publication in MNRAS. 19 pages, 9 figures. Code can be found at https://github.com/hamers/flybys_bin