Secular Dynamics of Planetesimals in Tight Binary Systems: Application to $\gamma$-Cephei

C.A. GIUPPONE, A.M. LEIVA, J. CORREA OTTO, C. BEAUGÉ

ASTRONOMY AND ASTROPHYSICS

EDP SCIENCES S A

Año: 2011 p. 1 - 10

0004-6361

The secular dynamics of massless particles in tight binary systems play a fundamental role in establishing the possibility of accretional collisions in such extreme systems. The most important secular parameters are the forced eccentricity and the secular frequency, which depend on the initial conditions of the particle as well as on the mass and orbital parameters of the secondary star.We construct a second-order theory (with respect to the masses) for the secular motion and deduce new expressions for the forced eccentricity and secular frequency. We also reanalyze the radial velocity data available for $gamma$-Cephei and present a series of orbital solutions leading to residuals compatible with the best fits. Finally, we discuss how different orbital configurations for $gamma$-Cephei may affect the dynamics of small planetesimals in circumstellar motion.The secular theory is constructed using a Lie series perturbation scheme, while the analysis of the orbital fits is done with a minimization code based on a genetic algorithm. For $gamma$-Cephei, we find that the classical first-order expressions for the secular quantities lead to large inaccuracies for semimajor axis larger than $sim 0.1$ the orbital separation between the stellar components. Small eccentricities and/or masses reduce these discrepancies. The dynamics of small planetesimals only show a weak dependence with the orbital fits of the stellar components. The same result is also found including the effects of a nonlinear gas drag. Thus, it appears that the possibility of planetary formation in this binary system should not be significantly modified by any future modifications in the system parameters.