Planet formation in binary stars: the case of γ Cephei

A&A 486, 617-628 (2008)
DOI: 10.1051/0004-6361:20079324

Planet formation in binary stars: the case of $\gamma$ Cephei

W. Kley¹ and R. P. Nelson²

¹ Institut für Astronomie und Astrophysik & Kepler Center for Astro and Particle Physics, Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany
e-mail: wilhelm.kley@uni-tuebingen.de
² Astronomy Unit, School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London, E1 4NS, UK
e-mail: R.P.Nelson@qmw.ac.uk

Received 23 December 2007 / Accepted 7 May 2008

Abstract
Context. Over 30 planetary systems have been discovered to reside in binary stars. As some of the binary separations are smaller than 20 astronomical units (AU) the gravitational perturbation of the secondary star has a very strong influence on the planet formation process, as it truncates the protoplanetary disc, possibly shortens its lifetime, and stirs up the embedded planetesimals. Due to its small semi-major axis (18.5 AU) and relatively large eccentricity e = 0.35 the binary star $\gamma$ Cephei represents a particularly challenging example worthy of study in greater detail.
Aims. In the present study we model the orbital evolution and growth of embedded protoplanetary cores of about 30 earth masses in the putative protoplanetary disc surrounding the primary star in the $\gamma$ Cep system.
Methods. We assume coplanarity of the disc, binary, and planet and perform two-dimensional hydrodynamic simulations of embedded cores in a protoplanetary disc perturbed by a secondary companion. Before embedding the planet, the equilibrium structure of the disc for the observed binary parameters of $\gamma$ Cep is determined. We initiate the embedded planets in the disc on circular orbits with different initial distances from the primary.
Results. The presence of the eccentric secondary star perturbs the disc periodically and generates strong spiral arms at periapse that propagate toward the disc centre. The disc perturbations then weaken as the secondary approaches apoapse. The disc also becomes slightly eccentric ( $e_{\rm disc}$ $\approx$ 0.1-0.15), and displays a slow retrograde precession in the inertial frame. Embedded cores interact with the eccentric disc, and are periodically disturbed both by the strong spiral shocks and the eccentric binary. For all initial separations considered (from 2.5 to 3.5 AU) the cores migrate inward. In contrast, their eccentricity evolution depends primarily on the starting position in the disc. For initial semi-major axes $a_{\rm p}$ $\gtrsim$ 2.7 we find a strong increase in the planetary eccentricity despite the presence of inward migration. Only cores that are initially far from the disc outer edge ( $a_{\rm p}$ $\lesssim$ 2.7 AU) have a bounded orbital eccentricity that converges, after mass accretion, roughly to the value of the planet observed in the $\gamma$ Cep system.
Conclusions. Even though a close binary system such as $\gamma$ Cep still presents a challenge to planet formation theory, we have shown that under the condition that protoplanetary cores can form at around 2.5 AU, it is possible to evolve and grow such a core to form a planet with a final configuration similar to what is observed.

Key words: methods: numerical -- hydrodynamics -- planets and satellites: formation -- stars: binaries: general

Planet formation in binary stars: the case of Cephei

Planet formation in binary stars: the case of $\gamma$ Cephei