Long-Term Stability of Planets in Binary Systems

Abstract

A simple question of celestial mechanics is investigated: in what regions of phase space near a binary system can planets persist for long times? The planets are taken to be test particles moving in the field of an eccentric binary system. A range of values of the binary eccentricity and mass ratio is studied, and both the case of planets orbiting close to one of the stars, and that of planets outside the binary orbiting the system's center of mass, are examined. From the results, empirical expressions are developed for both 1) the largest orbit around each of the stars, and 2) the smallest orbit around the binary system as a whole, in which test particles survive the length of the integration (10^4 binary periods). The empirical expressions developed, which are roughly linear in both the mass ratio mu and the binary eccentricity e, are determined for the range 0.0 <= e <= 0.7-0.8 and 0.1 <= mu <= 0.9 in both regions, and can be used to guide searches for planets in binary systems. After considering the case of a single low-mass planet in binary systems, the stability of a mutually-interacting system of planets orbiting one star of a binary system is examined, though in less detail.Comment: 19 pages, 5 figures, 7 tables, accepted by the Astronomical Journa

Dynamical Stability and Habitability of Extra-Solar Planets

“…Numerical studies by Rabl & Dvorak (1988;hereafter, RD) and Holman & Wiegert (1999; hereafter, HW) determined the stable region as a function of the binary's mass-ratio and eccentricity, and the motion of the planet was circular The numerical investigation by Pilat-Lohinger & Dvorak (2002;hereafter, PLD) also analyzed the influence of the planet's eccentricity. In these three investigations, the stable regions of planetary motion have been determined in a similar way.…”

“…The discovery of planets in such systems convinced many research groups to examine the planetary formation and evolution in binary star systems, either in general or for selected ones (see e.g. Holman et al 1997;Holman & Wiegert 1999;Ford et al 2000;Pilat-Lohinger & Dvorak 2002;Pilat-Lohinger et al 2003;Dvorak et al 2003a,b;Thébault et al 2010;Musielak et al 2005;Haghighipour 2006;Raghavan et al 2006;Cuntz et al 2007;Kley & Nelson 2008;Paardekooper et al 2008;Takeda et al 2008;Saleh & Rasio 2009;Marzari et al 2010;Haghighipour et al 2010;and many others).…”

“…Although, planets moving in 540 E. Pilat-Lohinger P-type (or circumbinary) orbits have been detected during the last few months, we learned during this symposium that the existence of these planets is still quite questionable. Dynamical studies of P-type motion by Dvorak et al (1989), Holman & Wiegert (1999), Pilat-Lohinger et al (2003) have shown that a planetary orbit surrounding both stars is only stable for distances (from the mass-center) larger than twice the separation of the two stars. In the case of eccentric motion of the binary, the planet's distance to the mass-center has to be increased in order to be stable.…”

Formation, migration, and stability of extrasolar planetary systems

“…To estimate the fraction of binaries that allow for stable Earth-like orbits, we must combine our exploration of planetary stability with the observed distributions of binary parameters (DM91). Our initial survey of parameter space (David et al 2003) indicates that the ejection time of an Earth-like planet is a steeply increasing function of the binary periastron p (see also Chambers et al 1996, Holman & Wiegart 1999. To a good working approximation, the ejection time varies with periastron according to the exponential law τ ej = τ 0 exp[(p − 1)/ 0 ], where the length scale 0 and time scale available at https://www.cambridge.org/core/terms.…”

Planetary Survival and Ejection in Transient Multiple Star Systems

“…Given the orbit of the host binary (semimajor axis a B =21 AU and eccentricity e B =0.42), the planet is located very close to the boundary of stability (Holman & Wiegert 1999), where is highly perturbed and therefore strongly hostile to planet formation (Thébault 2011. One of the solutions, as suggested by Thébault 2011, is that the binary had a initially wider orbit, but later shrunk to the present one via close stellar encounter.…”