On the Dynamical Stability of γ Cephei, an S-Type Binary Planetary System

Precision radial velocity measurements of the γ Cephei (HR8974) binary system suggest the existence of a planetary companion with a minimum mass of 1.7 Jupiter-mass on an elliptical orbit with a ∼2.14 AU semimajor axis and 0.12 eccentricity [1]. I present in this paper a summary of the results of an extensive numerical study of the orbital stability of this three-body system for different values of the semimajor axis and orbital eccentricity of the binary, and also the orbital inclination of the planet. Numerical integrations indicate that the system is stable for the planet’s orbital inclination ranging from 0 to 60 degrees, and for the binary’s orbital eccentricity less than 0.5. The results also indicate that for large values of the inclination, the system may be locked in a Kozai resonance. INTRODUCTION The existence of planets in binary star systems is no longer a mere idea. Approximately 35% of extrasolar planets discovered till 2002 exist in multiple star systems [2]. These systems are mostly wide binaries with separations between 500 and 750 AU, and with planets revolving around one of the stars. At such large distances, the perturbative effect of one star on the formation and dynamical evolution of planets around the other star is entirely negligible. A recently discovered Jupiter-like planet around the primary of the γ Cephei binary system is, however, an exception to this rule. Gamma Cephei is a close spectroscopic binary composed of a 1.59 solar-mass K1 IV subgiant and a 0.4 solar-mass red M dwarf [3]. The semimajor axis of this system has been reported to have a lower value of 18.5 AU [1] and an upper value of 21 AU [4]. Precision radial velocity measurements suggest that a planet with a minimum mass of 1.7 Jupiter-mass revolves around the primary of this system on an elliptical orbit with an eccentricity of 0.12 ± 0.05 and a semimajor axis of approximately 2.14 AU. Being the first discovered S-type binary-planetary system1, it is quite valuable to investigate whether this system is dynamically stable, and for what values of its orbital parameters its stability will remain. In this paper I present a summary of the results of an extensive numerical study of the dynamical stability of this system for different values of the orbital parameters of the binary and also the orbital inclination of the planet. A more comprehensive study of the dynamics of this system are to be published elsewhere. 1 As classified by Rabl & Dvorak (1988), a binary-planetary system is called S-type when the planet revolves around one of the stars, and P-type when the planet revolves around the entire binary. On the Dynamical Stability of γ Cephei, an S-Type Binary Planetary SystemFebruary 2, 20081