Planetesimal accretion in binary star systems

Planetesimal accretion in close binary systems is a complex process for the gravitational perturbations of the companion star on the planetesimal orbits. These perturbations excite high eccentricities that can halt the accumulation process of planetesimals into planets also in those regions around the star where stable planetary orbits would eventually be possible. However, the evolution of a planetesimal swarm is also affected by collisions and gas drag. In particular, gas drag combined with the secular perturbations of the secondary star forces a strong alignment of all the planetesimal periastra. Since periastra are also coupled to eccentricities via the secular perturbations of the companion, the orbits of the planetesimals, besides all being aligned, also have very close values of eccentricity. This orbital "phasing" strongly reduces the contribution of the eccentricity to the relative velocities between planetesimals, and the impact speeds are dominated by the Keplerian shear: accretion becomes possible. This behavior is not limited to small planetesimals but also affects bodies as large as 100 km in diameter. The effects of gas drag are in fact enhanced by the presence of the constant forced component in the orbital eccentricity of the planetesimals. We describe analytically the periastron alignment by using the secular equations developed by Heppenheimer, and we test the prediction of the theory with a numerical code that integrates the orbits of a swarm of planetesimals perturbed by gas drag and collisions. The gas density is assumed to decrease outward, and the collisions are modeled as inelastic. Our computations are focused on the alpha Centauri system, which is a good candidate for terrestrial planets as we will show. The impact velocities between planetesimals of different sizes are computed at progressively increasing distances from the primary star and are compared with estimates for the maximum velocity for accretion. According to our simulations in the a Centauri system, the formation of a planet within 2 AU of the primary star is possible because of the orbital phasing forced by gas drag.