Stability of planetary orbits in binary systems

Abstract

Abstract. Stability of S-type and P-type planetary orbits in binary systems of different mass and separation ratios is investigated. Criteria for stable, marginally stable and unstable planetary orbits are specified. These criteria are used to determine regions of stability of planetary orbits in different binary systems with Jupiter-type planets. The obtained results show that the regions of stability for S-type orbits depend on the distance ratio between the star and planet, and the stellar companions, in the range of 0.22 and 0.46, depending on the mass ratio. For P-type orbits, the regions of stability also depend on that distance ratio, in the range of 1.75 and 2.45, again depending on the the mass ratio. Applications of these results to three observed binary systems with giant planets, namely, τ Boo, HD 195019 and GJ 86, show that the orbits of the giant planets in those systems can be classified as stable, as expected.

Stringent Criteria for Stable and Unstable Planetary Orbits in Stellar Binary Systems

“…They determined the planet's ejection time for systems with a variety of orbital eccentricities and semimajor axes. For fixed companion masses, the ejection time was found to be a steep function of the periastron distance (or orbital radius for circular orbits) to the primary star, a prediction that is consistent with subsequent results by Musielak et al (2005).…”

“…In our previous work (Stuit 1995;Musielak et al 2005), we studied the stability of S-type orbits in stellar binary systems and deduced the orbital stability limits for planets; these limits were found to depend on the stellar mass ratios, a result that will be further explored in this Letter. We considered initially circular planetary orbits and classified them by using the following criteria: 0% ≤ truly stable ≤ 5%, 5% !…”

“…Therefore, there is an urgent need for defining stringent mathematical criteria that can be used to precisely determine whether a planetary orbit in a binary system is stable or unstable and, furthermore, to verify the stability criteria previously used by Musielak et al (2005) and others (e.g., Holman & Wiegert 1999;David et al 2003). The main purpose of this Letter is to pose such criteria by using the concept of Jacobi's integral and Jacobi's constant (Szebehely 1967;Roy 2005).…”

Dynamical Stability and Habitability of the γ Cephei Binary‐Planetary System

“…Extensive studies have been done on the dynamical stability of S-type binary-planetary systems (Rabl & Dvorak 1988;Benest 1988Benest , 1989Benest , 1993Benest , 1996Wiegert & Holman 1997;Holman & Wiegert 1999;Pilat-Lohinger & Dvorak 2002;Dvorak et al 2003Dvorak et al , 2004Pilat-Lohinger et al 2004;Musielak et al 2005). Although in these articles the stability of S-type systems has been studied for different values of the binary's mass ratio and orbital parameters, simulations have been limited to restricted cases such as coplanar orbits, similar-mass binary components, and circular planetary orbits, and /or the durations of simulations have been no more than tens of thousands of the binary's orbital period.…”

Dynamical Stability and Habitability of Extra-Solar Planets

“…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).…”