How Consumption and Repulsion Set Planetary Gap Depths and the Final Masses of Gas Giants

Abstract: Planets open gaps in discs. Gap opening is typically modeled by considering the planetary Lindblad torque which repels disc gas away from the planet's orbit. But gaps also clear because the planet consumes local material. We present a simple, easy-to-use, analytic framework for calculating how gaps deplete and how the disc's structure as a whole changes by the combined action of Lindblad repulsion and planetary consumption. The final mass to which a gap-embedded gas giant grows is derived in tandem. The analytics are tested against 1D numerical experiments and calibrated using published multi-dimensional simulations. In viscous alpha discs, the planet, while clearing a gap, initially accretes practically all of the gas that tries to diffuse past, rapidly achieving super-Jupiter if not brown dwarf status. By contrast, in inviscid discs---that may still accrete onto their central stars by, say, magnetized winds---planets open deep, repulsion-dominated gaps. Then only a small fraction of the disc accretion flow is diverted onto the planet, which grows to a fraction of a Jupiter mass. Transitional disc cavities might be cleared by families of such low-mass objects opening inviscid, repulsion-dominated, overlapping gaps which allow most of the outer disc gas to flow unimpeded onto host stars.