Relating binary-star planetary systems to central configurations

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 SunJupiter-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.

Terrestrial Planet Formation at Home and Abroad

“…It is well-known that giant planets' orbits can migrate long distances, inward or outward, driven by exchanges with the gaseous protoplanetary disk (e.g. Lin and Papaloizou 1986;Veras and Armitage 2004) or a disk of planetesimals (e.g. Fernandez and Ip 1984;Murray et al 1998).…”

The Long-Term Dynamical Evolution of Planetary Systems

“…Ejection proceeds via scattering on to highly eccentric orbits, and hence a prediction of planet-planet scattering models is the existence of a population of planets around young stars with very large orbital separation Scharf and Menou 2009;Malmberg et al 2011). The frequency of ejections from scattering is probably too small to explain the large abundance of apparently unbound Jupiter-mass objects discovered by microlensing (Sumi et al 2011), if those are to be free-floating rather than simply on wide but bound orbits (Veras and Raymond 2012).…”

“…Characterizing the relationship between small planets orbiting close to the host star and more massive planets at larger separations could provide insights into the effects of planet scattering on the formation of inner, rocky planets. Similarly, the abundance and mass distribution of planets with large orbital separations (Malmberg et al 2011;Boley et al 2012) or free-floating planets may provide insights into the planets that are scattered to the outskirts of planetary systems or into the galaxy as freefloating planets Veras et al 2011;Veras and Raymond 2012;. In addition, the fact that planet-planet scattering perturbs both the inner and outer parts of planetary systems may introduce a natural correlation between the presence of debris disks and close-in low-mass planets, as well as an anticorrelation between debris disks and eccentric giant planets (Raymond et al 2011Raymond and Armitage 2013).…”

“…As a result, large numbers of free-floating planets in young clusters point to other mechanisms for ejection, most likely planet-planet interactions in young planetary systems (Moorhead and Adams 2005;Chatterjee et al 2008). One should also note that dynamical mechanisms are unlikely to be able to explain the population of free-floating planets as inferred by micro-lensing observations (Veras and Raymond 2012).…”

Binary star influence on post-main-sequence multi-planet stability

“…Georgakarakos 2008), similar concise expressions for four-body problems are rarer (e.g. Loks & Sergysels 1985;Sergysels & Loks 1987), even despite major recent progress with central configuration theory (Érdi & Czirják 2016;Hamilton 2016;Veras 2016c). Further, when one of the bodies loses mass -as is the case for a main-sequence star which becomes a white dwarf -then not even the two-body problem is solvable (see Chapter 4 of Veras 2016a).…”