Eccentricity Evolution for Planets in Gaseous Disks

We investigate the hypothesis that interactions between a giant planet andthe disk from which it forms promote eccentricity growth. These interactionsare concentrated at discrete Lindblad and corotation resonances. Interactionsat principal Lindblad resonances cause the planet's orbit to migrate and open agap in the disk if the planet is sufficiently massive. Those at first orderLindblad and corotation resonances change the planet's orbital eccentricity.Eccentricity is excited by interactions at external Lindblad resonances whichare located on the opposite side of corotation from the planet, and damped byco-orbital Lindblad resonances which overlap the planet's orbit. If the planetclears a gap in the disk, the rate of eccentricity damping by co-orbitalLindblad resonances is reduced. Density gradients associated with the gapactivate eccentricity damping by corotation resonances at a rate whichinitially marginally exceeds that of eccentricity excitation by externalLindblad resonances. But the corotation torque drives a mass flux which reducesthe density gradient near the resonance. Sufficient partial saturation ofcorotation resonances can tip the balance in favor of eccentricity excitation.A minimal initial eccentricity of a few percent is required to overcome viscousdiffusion which acts to unsaturate corotation resonances by reestablishing thelarge scale density gradient. Thus eccentricity growth is a finite amplitudeinstability. Formally, interactions at the apsidal resonance, which is aspecial kind of co-orbital Lindblad resonance, appears to damp eccentricityfaster than external Lindblad resonances can excite it. However, apsidal waveshave such long wavelengths that they do not propagate in protoplanetary disks.This reduces eccentricity damping by the apsidal resonance to a modest level.Comment: Submitted to Ap