Gas drag effects on planetesimals in the 2:1 resonance with proto-Jupiter

The combined effects are studied of gas drag and gravitational perturbations by a proto-Jupiter on the orbital evolution of a swarm of planetesimals in the primordial asteroid belt in the 2:1 mean motion resonance region. The gas drag in the primordial nebula causes planetesimals to spiral towards the Sun and, therefore, to cross mean motion resonances with proto-Jupiter. The dynamics of planetesimals are numerically investigated while passing through an inner resonance in a planar model. It is found that eccentricities are drastically increased and the maximum value reached by each planetesimal depends only on the resonance argument ψ at the resonance entry. The higher average eccentricity of the swarm within the resonance borders induces a faster spiralling rate of planetesimals and a consequent decrease of their number density, in particular at the 2:1, the most relevant resonance in the asteroid belt. This phenomenon causes the formation of a gap in the swarm at the resonance location. By intergrating a large number of planetesimal orbits, the gap formation process is analysed; it is found that the planetesimal number density near the resonance centre is reduced to 10–40% of its average value, depending on the free eccentricity assumed for the proto-Jupiter. Relative velocities between planetesimals are increased by a factor of four by resonant perturbations, favouring fragmentation at impacts; higher impact velocities and the reduced planetesimal density slow down the planetesimal accretion process and inhibit the formation of big bodies in the resonance region.