Gas accretion on to planetary cores: three-dimensional self-gravitating radiation hydrodynamical calculations

Abstract

We present results from three‐dimensional, self‐gravitating radiation hydrodynamical models of gas accretion by planetary cores. In some cases, the accretion flow is resolved down to the surface of the solid core – the first time such simulations have been performed. We investigate the dependence of the gas accretion rate upon the planetary core mass, and the surface density and opacity of the encompassing protoplanetary disc. Accretion of planetesimals is neglected. We find that high‐mass protoplanets are surrounded by thick circumplanetary discs during their gas accretion phase but, contrary to locally isothermal calculations, discs do not form around accreting protoplanets with masses ≲ when radiation hydrodynamical simulations are performed, even if the grain opacity is reduced from interstellar values by a factor of 100. We find that the opacity of the gas plays a large role in determining the accretion rates for low‐mass planetary cores. For example, reducing the opacities from interstellar values by a factor of 100 leads to roughly an order of magnitude increase in the accretion rates for protoplanets. The dependence on opacity becomes less important in determining the accretion rate for more massive cores where gravity dominates the effects of thermal support and the protoplanet is essentially accreting at the runaway rate. Increasing the core mass from 10 to 100 M increases the accretion rate by a factor of ≈50 for interstellar opacities. Beyond , the ability of the protoplanetary disc to supply material to the accreting protoplanet limits the accretion rate, independent of the opacity. Finally, for low‐mass planetary cores (≲), we obtain accretion rates that are in agreement with previous one‐dimensional quasi‐static models. This indicates that three‐dimensional hydrodynamical effects may not significantly alter the gas accretion time‐scales that have been obtained from quasi‐static models.

Slowly-growing gap-opening planets trigger weaker vortices

“…At the resolution of our fiducial simulations, the circumplanetary discs are not sufficiently well resolved to generate realistic growth rates (Zhu 2015). Moreover, accretion on to the planet is a function of a more complex set of disc parameters dependent on thermodynamics and feedback (Ayliffe & Bate 2009), which we neglect in this study.…”

“…Again, for planet properties akin to Jupiter, studies findṀ p ≈ 10 −5 M J yr −1 (e.g. Papaloizou & Nelson 2005;Ayliffe & Bate 2009;Rivier et al 2012). If circumplanetary disc accretion rates were only weakly dependent on planet semimajor axis, this would favour vortex formation at larger disc radii.…”

Revisiting the “radial-drift barrier” of planet formation and its relevance in observed protoplanetary discs

“…For the remainder of the disc population, the outcome of pre-planetesimals will likely depend on their ability to reach the high Reynolds number Stokes regime. However, the case of a steep radial temperature profile can be encountered in at least one particular situation: circumplanetary discs which typically have temperature profiles with q = 1 (Ayliffe & Bate 2009). In this environment, we predict from our Stokes criterion that planetesimals will be accreted onto the planet.…”

Effects of stellar flybys on planetary systems: 3D modeling of the circumstellar disk’s damping effects

“…Variable smoothing and softening lengths have been introduced as in Price & Monaghan (2004), Springel & Hernquist (2002), and Price & Monaghan (2007). To realistically model the gas accretion onto the planet, we implemented the algorithm described in Ayliffe & Bate (2009). The planet potential is modified adding a surface potential term,…”