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

We investigate classical planetesimal accretion in a binary star system of separation ab<50AU 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 dv among planetesimals of different sizes. For various stellar mass ratios and binary orbital parameters we determine regions where dv exceed planetesimal escape velocities v_esc (thus preventing runaway accretion) or even the threshold velocity v_ero 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 dv increase between bodies of different sizes. This differential phasing effect proves very efficient and almost always increases dv to values preventing runaway accretion, except in a narrow domain of almost circular companion orbits. The erosion threshold dv>v_ero is reached in a wide (ab,eb) space for small (<10km) planetesimals, but in a much more limited region for bigger ~50km objects. In the intermediate v_esc<dv < v_ero domain, a possible growth mode would be the type II runaway growth identified by Kortenkmap et al.(2001)