Disk Accretion onto High‐Mass Planets

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Abstract
We analyze the nonlinear, two-dimensional response of a gaseous, viscous protoplanetary disk to the presence of a planet of one Jupiter mass (1 MJ) and greater that orbits a 1 M☉ star by using the ZEUS hydrodynamics code with high resolution near the planet's Roche lobe. The planet is assumed to be in a circular orbit around the central star and is not allowed to migrate. A gap is formed about the orbit of the planet, but there is a nonaxisymmetric flow through the gap and onto the planet. The gap partitions the disk into an inner (outer) disk that extends inside (outside) the planet's orbit. For a 1 MJ planet and typical disk parameters, the accretion through the gap onto the planet is highly efficient. That is, the rate is comparable to the accretion rate toward the central star that would occur in the absence of the planet (at the location of the planet). For typical disk parameters, the mass-doubling timescale is less than 105 yr, considerably shorter than the disk lifetime. Following shocks near the L1 and L2 Lagrangian points, disk material enters the Roche lobe in the form of two gas streams. Shocks occur within the Roche lobe as the gas streams collide, and shocks lead to rapid inflow toward the planet within much of planet's Roche lobe. Shocks also propagate in the inner and outer disks that orbit the star. For higher mass planets (of order 6 MJ), the flow rate onto the planet is considerably reduced, which suggests an upper mass limit to planets in the range of 10 MJ. This rate reduction is related to the fact that the gap width increases relative to the Roche (Hill sphere) radius with increasing planetary mass. The flow in the gap affects planetary migration. For the 1 MJ planet case, mass can penetrate from the outer disk to the inner disk, so that the inner disk is not depleted. The results suggest that most of the mass in gas giant planets is acquired by flows through gaps.
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