Circum-planetary discs as bottlenecks for gas accretion onto giant planets

Abstract

Context. With hundreds of exoplanets detected, it is necessary to revisit giant planets accretion models to explain their mass distribution. In particular, formation of sub-jovian planets remains unclear, given the short timescale for the runaway accretion of massive atmospheres. However, gas needs to pass through a circum-planetary disc. If the latter has a low viscosity (as expected if planets form in "dead zones"), it might act as a bottleneck for gas accretion. Aims. We investigate what the minimum accretion rate is for a planet under the limit assumption that the circum-planetary disc is totally inviscid, and the transport of angular momentum occurs solely because of the gravitational perturbations from the star. Methods. To estimate the accretion rate, we present a steady-state model of an inviscid circum-planetary disc, with vertical gas inflow and external torque from the star. Hydrodynamical simulations of a circum-planetary disc were conducted in 2D, in a planetocentric frame, with the star as an external perturber in order to measure the torque exerted by the star on the disc. Results. The disc shows a two-armed spiral wave caused by stellar tides, propagating all the way in from the outer edge of the disc towards the planet. The stellar torque is small and corresponds to a doubling time for a Jupiter mass planet of the order of 5 Myr. Given the limit assumptions, this is clearly a lower bound of the real accretion rate. Conclusions. This result shows that gas accretion onto a giant planet can be regulated by circum-planetary discs. This suggests that the diversity of masses of extra-solar planets may be the result of different viscosities in these discs.

Accretion of Jupiter-Mass Planets in the Limit of Vanishing Viscosity

“…This torque was already considered in Rivier et al (2012) in their 2D simulations. The authors there assumed that in the inviscid case the torque is deposited only in the very inner part of the CPD.…”

“…However, we cannot provide a reliable estimate of the mass of the CPD with our isothermal simulations, particularly in the limit of vanishing viscosity, which could lead to a significant pileup of material in the CPD. An order of magnitude analytic estimate in Rivier et al (2012) reported a CPD mass of ∼10 −3 M J . Even assuming a CPD mass of 0.01 M J , the stellar torque would lead to an accretion rate of only 2.5 × 10 −6 M J yr −1 .…”

“…How massive the disk can become cannot be studied using isothermal simulations and will be the object of a future study. In Rivier et al (2012), it was estimated analytically that the maximum mass of the CPD is ∼10 −3 M J ; at this mass, its vertical pressure gradient becomes large enough to stop the vertical inflow, so that the mass of the CPD cannot grow further. This estimate is probably valid only at the order of magnitude level.…”

Accreting Circumplanetary Disks: Observational Signatures

“…This tidal force can drive global spiral arms and shocks in circumplanetary disks, leading to accretion. 2D and 3D simulations (Rivier et al 2012;Szulágyi et al 2014) have shown that the accretion induced by tidal forces is 2 × 10 −10 M yr −1 assuming that dissipation in the circumplanetary disk leads to a steady accretion. However, shock dissipation is unlikely to be uniform throughout the circumplanetary disk and mass may pile up in the disk by shock dissipation.…”

Giant Planet Formation and Migration

“…Another possibility is that accretion is regulated by the circumplanetary disc that forms around high-mass planets (Ayliffe and Bate 2009a,b;Ward and Canup 2010). These subdiscs are discussed in detail elsewhere in this volume; here we just mention that recent simulations show that the circumplanetary disc may indeed be a bottleneck (Rivier et al 2012;Szulágyi et al 2014). …”