Secular dynamics of planetesimals in tight binary systems: application toγ-Cephei

Abstract

Context. The secular dynamics of small planetesimals in tight binary systems play a fundamental role in establishing the possibility of accretional collisions in such extreme cases. The most important secular parameters are the forced eccentricity and secular frequency, which depend on the initial conditions of the particles, as well as on the mass and orbital parameters of the secondary star. Aims. We construct a second-order theory (with respect to the masses) for the planar secular motion of small planetasimals and deduce new expressions for the forced eccentricity and secular frequency. We also reanalyze the radial velocity data available for γ-Cephei and present a series of orbital solutions leading to residuals compatible with the best fits. Finally, we discuss how different orbital configurations for γ-Cephei may affect the dynamics of small bodies in circumstellar motion. Methods. The secular theory is constructed using a Lie series perturbation scheme restricted to second order in the small parameter. The orbital fits were analyzed with a minimization code that employs a genetic algorithm for a preliminary solution plus a simulated annealing for the fine tuning. Results. For γ-Cephei, we find that the classical first-order expressions for the secular frequency and forced eccentricity lead to large inaccuracies ∼50% for semimajor axes larger than one tenth the orbital separation between the stellar components. Low eccentricities and/or masses reduce the importance of the second-order terms. The dynamics of small planetesimals only show a weak dependence with the orbital fits of the stellar components, and the same result is found including the effects of a nonlinear gas drag. Thus, the possibility of planetary formation in this binary system largely appears insensitive to the orbital fits adopted for the stellar components, and any future alterations in the system parameters (due to new observations) should not change this picture. Finally, we show that planetesimals migrating because of gas drag may be trapped in mean-motion resonances with the binary, even though the migration is divergent.

Dynamical analysis and constraints for the HD 196885 system

“…Thebault 2011; Beaugé et al 2010). However, Giuppone et al (2011) pointed out that for these types of compact systems, the frequencies are sometimes not satisfactorily determined from first-order approximations (second-order on mass are needed), and therefore, some works on formation based on these approximations should probably be reviewed.…”

“…It is therefore advisable to keep this wide range of possible configurations in mind, and to combine radial velocity fits with possible formation scenarios (e.g. γ-Cephei, Giuppone et al 2011).…”

Stellar scattering and the origin of the planet aroundγ-Cephei-A

“…A second-order expression was calculated recently by Giuppone et al (2011), which depends explicitly on the stellar masses. However, the difference between both values is only relevant for high values of e f , which is beside the purpose of the present study.…”

Planetary Survival and Ejection in Transient Multiple Star Systems

“…Although most of these planet-bearing stars are wide binaries with separations >100 AU, there are five of them with binary separation only ∼ 20 AU, including Gl86 Ab (Queloz et al 2000), γ Cephei Ab (Hatzes et al 2003), HD41004 Ab (Zucker et al 2004), HD196885 Ab (Chauvin et al 2011), and most recently α Centauri Bb (Dumusque et al 2012). Planets in such binary systems challenge the current planetary formation theory, because stars in such close separation induce strong perturbations and thus inhibit planet formation around them (Thébault et al 2006;Thébault et al 2008;Paardekooper et al 2008;Xie & Zhou 2008, 2009Haghighipour 2010;Fragner et al 2011;Giuppone et al 2011).…”