How did the planet in the Gamma-Cephei binary system form ?

Among the more than 100 extra-solar planets today discovered, 15 have been found within binary systems. One of the more interesting of these systems is Gamma-Cephei, since it is the one with the closest companion star (Figure1). The detected planet is slightly more massive than Jupiter and orbits at 2.1 AU from the central star.

Gamma-f1.gif Previous studies have shown that this planet is on a stable orbit, but the question is how it could form within such a binary system : the companion star is indeed so close to the primary that its perturbing effect could prevent planetary accretion. Indeed, the "standard" scenario of planetary formation requires a dynamically "quiet" environment. Only in this quiet environment can impacts between planetesimals — planetesimals being the primordial km- sized "bricks" whose accretion will lead to 1000km-sized planetary embryos — be soft enough in order to lead to mutual accretion rather than erosion. Figure 1 The Gamma Cephei system To study the dynamical conditions allowing accretion in such a system, the crucial parameter is thus the impact velocity among planetesimals during the accretion phase. This velocity distribution can be studied using numerical simulations. Such simulations show that the secondary star induces strong perturbations of planetesimal orbits in the 1-4 AU region (orbits beyond 4 AU are unstable), with important eccentricity oscillations. These oscillations yield relative velocities higher than 1 km/s, thus preventing accretion (Figure 2). Figure 2 Effect of the companion star perturbations on a population of test planetesimals. Particles orbits are initially circular (e = 0) between 1 and 5 AU and are gradually excited, with large eccentricity oscillations which get narrower and narrower as time proceeds. At some point, these eccentricity oscillations become so narrow that they lead to orbital crossing between neighbouring planetesimals at very high encounter velocities, 1km/s, thus preventing any accretion. Gamma-f2.gif The situation becomes more favourable to planetary accretion when taking into account gas drag effect on planetesimals. It is indeed likely that a substantial amount of gas from the initial nebulae was still present as planetesimal accretion started. Should this gas be dense enough, then it would tend to align planetesimal orbits, hence lowering their impact velocities. Planetesimal sizes are here a crucial parameter : the smaller there are, the more sensitive to gaseous friction they get. Our simulations show that, for a gas nebulae slightly denser than the "standard" minimum mass solar nebulae and for planetesimals larger than 5 km, friction reduces encounter velocities to values allowing accretion (Figure 3). The (yet unanswered) question is : did such a high gas density stage really occur ?

Gamma-f3.gif Figure 3 Same as Fig.2, but with gas drag. The effect of the gas is to damp the orbital perturbations induced by the companion star but also to align neighbouring planetesimals orbits. This prevents the large eccentricity oscillations of Fig.2 to set in, and thus strongly reduces encounter velocities between particles. Another consequence of gaseous friction is the progressive orbital drift towards the central star it induces on planetesimals, with in particular the progressive emptying of the outer regions of the system. But even if planetary embryos of 1000 km could form, problems are not over yet. There is one important stage left before the completion of planetary formation, i.e. the final mutual perturbations and accreting encounters between those large embryos. Here again, perturbations by the companion star might hinder the process. However, new specific simulations show that this stage might successfully complete despite the perturbing star. There is nevertheless one important problem : the final planet is never at the right location ; it always ends up within 1.5 AU from the central star regardless of the initial conditions chosen (Figure 4). How can we reconcile this puzzling result with observational data ? Several hypothesis might be considered. It is for instance possible that the separation between the 2 stars was larger in the beginning and was reduced after the formation of the planet. This could be the case if the binary system was initially in a clustered stellar environment where neighbouring stars might have dynamically perturbed the system. It is also possible that one or several additional yet-undetected giant planet(s) orbit around Gamma Cephei and that mutual perturbations among planets might have affected their initial locations. Figure 4 Mutual evolution of planetary embryos of initial size 1000 km. As time goes on, embryos progressively accrete each other to form fewer but increasingly larger objects. At the end of the run, a 10 Earth-masses body, i.e. with a mass sufficient to trigger the final gas infall leading to a Jupiter-sized planet, have formed. However, it’s final position is around 1,5 AU, well within the actual location of the observed planet. Gamma-f4.gif

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References Thébault, P., Marzari, F., Scholl, H., Turrini, D., Barbieri, M., "Planetary formation in the Gamma Cephei system", 2004, accepted in Astronomy & Astrophysics Contact Philippe Thébault (Observatoire de Paris, LESIA)

Dernière modification le 4 mars 2013