Relating binary-star planetary systems to central configurations

TL;DR

This paper explores how central configurations in the N-body problem can model coplanar binary-star exoplanetary systems, providing insights into their stability and potential observational signatures.

Contribution

It demonstrates that restricting masses to planetary ranges significantly limits central configurations, linking them to known planetary architectures and guiding future stability and observational studies.

Findings

Over 90% reduction in phase space for central configurations with planetary masses

Both equal and unequal binary stars can form central configurations

Configurations resemble Sun-Jupiter-Trojan-like architectures with deviations under ten degrees

Abstract

Binary-star exoplanetary systems are now known to be common, for both wide and close binaries. However, their orbital evolution is generally unsolvable. Special cases of the N-body problem which are in fact completely solvable include dynamical architectures known as central configurations. Here, I utilize recent advances in our knowledge of central configurations to assess the plausibility of linking them to coplanar exoplanetary binary systems. By simply restricting constituent masses to be within stellar or substellar ranges characteristic of planetary systems, I find that (i) this constraint reduces by over 90 per cent the phase space in which central configurations may occur, (ii) both equal-mass and unequal-mass binary stars admit central configurations, (iii) these configurations effectively represent different geometrical extensions of the Sun-Jupiter-Trojan-like architecture, (iv) deviations from these geometries are no greater than ten degrees, and (v) the deviation increases as the substellar masses increase. This study may help restrict future stability analyses to architectures which resemble exoplanetary systems, and might hint at where observers may discover dust, asteroids and/or planets in binary star systems.