We recently derived, using the density-of-states approximation, analytic distribution functions for the outcomes of direct single-binary scatterings. Using these outcome distribution functions, we present in this paper a self-consistent statistical mechanics-based analytic model obtained using the Fokker-Planck limit of the Boltzmann equation. Our model quantifies the dominant gravitational physics, combining both strong and weak single-binary interactions, which drives the time evolution of binary orbital parameter distributions in dense stellar environments. We focus in particular the distributions of binary orbital energies and eccentricities. We find a novel steady-state distribution of binary eccentricities, featuring strong depletions of both the highest and the lowest eccentricity binaries. In energy space, we compare the predictions of our analytic model to the results of numerical N-body simulations, and find that the agreement is good for the initial conditions considered here. This work is a first step towards the development of a fully self-consistent semi-analytic model for dynamically evolving binary star populations in dense stellar environments due to direct few-body interactions.
Bibliographical noteFunding Information:
NWCL gratefully acknowledges the generous support of a Fondecyt Iniciación grant 11180005, as well as support from Millenium Nucleus NCN19-058 (TITANs) and funding via the BASAL Centro de Excelencia en Astrofisica y Tecnologias Afines (CATA) grant PFB-06/2007. NWCL also thanks support from ANID BASAL project ACE210002 and ANID BASAL projects ACE210002 and FB210003. NCS received financial support from the Israel Science Foundation (Individual Research grant 2565/19), and the BSF portion of a NSF-BSF joint research grant (NSF grant No. AST-2009255/BSF grant No. 2019772). WL acknowledges support from NASA via grant 20-TCAN20-001 and NSF via grant AST-2007422.
© 2022 The Author(s).
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