Relative velocities among accreting planetesimals in binary systems: The circumprimary case

We investigate classical planetesimal accretion in a binary star system of separation a⩽50 AU by numerical simulations, with particular focus on the region at a distance of 1 AU from the primary. The planetesimals orbit the primary, are perturbed by the companion and are in addition subjected to a gas drag force. We concentrate on the problem of relative velocities Δv among planetesimals of different sizes. For various stellar mass ratios and binary orbital parameters we determine regions where Δv exceed planetesimal escape velocities v (thus preventing runaway accretion) or even the threshold velocity v for which erosion dominates accretion. Gaseous friction has two crucial effects on the velocity distribution: it damps secular perturbations by forcing periastron alignment of orbits, but at the same time the size-dependence of this orbital alignment induces a significant Δv increase between bodies of different sizes. This differential phasing effect proves very efficient and almost always increases Δv to values preventing runaway accretion, except in a narrow e≃0 domain. The erosion threshold Δv>v is reached in a wide (a,e) space for small <10-km planetesimals, but in a much more limited region for bigger ≃50-km objects. In the intermediate v<Δv<v domain, a possible growth mode would be the type II runaway growth identified by Kortenkamp et al. [Kortenkamp, S., Wetherill, G., Inaba, S., 2001. Science 293, 1127 1129].