On gas drag in a circular binary system

Abstract

We investigate both analytically and numerically the motion of massless particles orbiting primary star in a close circular binary system with particular focus on the gas drag effects. These are the first calculations with particles ranging in size from 1m to 10km, which account for the presence of a tidally perturbed gaseous disk. We have found numerically that the radial mass transport by the tidal waves plays a crucial role in the orbital evolution of particles. Numerical results are confirmed analytical calculations that do not assume anything about origin of the radial flow in the disk. We demonstrate that the migration rate of a particle in a disk out of radial equilibrium is enhanced due to the enhanced mass flux of gas colliding with the particle and the migration is always directed inward regardless of the sign of the radial gas velocity. Within the framework of the perturbation theory we derive general, formulae for short-term variations of the particle semi-major axis, eccentricity and inclination in such disk. The formulae account for departures from axial symmetry by introducing effective components of the gas velocity. They agree with numerical results within several percent. We have also found in numerical simulations that the tidal waves introduce coherence in periastron longitude and eccentricity for particles on neighbouring orbits. The degree of the coherence depends on the particle size and on the distance from the primary star, being most prominent for particles with 10m radius. The results are important mainly in the context of planetesimal formation and, to a lesser degree, during the early planetesimal accretion stage.