Pebble Accretion in Turbulent Protoplanetary Disks

Abstract

It has been realized in recent years that the accretion of pebble-sized dust particles onto planetary cores is an important mode of core growth, which enables the formation of giant planets at large distances and assists planet formation in general. The pebble accretion theory is built upon the orbit theory of dust particles in a laminar protoplanetary disk (PPD). For sufficiently large core mass (in the "Hill regime"), essentially all particles of appropriate sizes entering the Hill sphere can be captured. However, the outer regions of PPDs are expected to be weakly turbulent due to the magnetorotational instability (MRI), where turbulent stirring of particle orbits may affect the efficiency of pebble accretion. We conduct shearing-box simulations of pebble accretion with different levels of MRI turbulence (strongly turbulent assuming ideal magnetohydrodynamics, weakly turbulent in the presence of ambipolar diffusion, and laminar) and different core masses to test the efficiency of pebble accretion at a microphysical level. We find that accretion remains efficient for marginally coupled particles (dimensionless stopping time τ s ∼ 0.1 − 1) even in the presence of strong MRI turbulence. Though more dust particles are brought toward the core by the turbulence, this effect is largely canceled by a reduction in accretion probability. As a result, the overall effect of turbulence on the accretion rate is mainly reflected in the changes in the thickness of the dust layer. On the other hand, we find that the efficiency of pebble accretion for strongly coupled particles (down to τ s ∼ 0.01) can be modestly reduced by strong turbulence for low-mass cores.

Diffusion and Concentration of Solids in the Dead Zone of a Protoplanetary Disk

“…The result is a layer of particles significantly thicker than expected from the accretion shear stress (see also Riols & Lesur 2018, however). Xu et al (2017) confirmed this result by showing significantly more depressed accretion stress than vertical diffusion of particles in ambipolar diffusion dominated flow, as compared to ideal-MHD models. Therefore, the solid particle distribution appears to be regulated by anisotropic velocity fluctuations, whether the disk is controlled by Ohmic resistance or ambipolar diffusion.…”

“…Our measured mean center and scale height of the particle disk is listed in Table 2 along with their standard deviation over time. For comparison, the layer of particles in numerical simulations of ambipolar diffusion regulated flow seems to be thinner compared with what we find in an Ohmic dead zone. In simulations with a net vertical magnetic flux of β 0 10 4 and an ambipolar diffusion number of Am 1 in the mid-plane, where Am is the number of times a neutral particle collides with ions during Ω −1 K (Hawley & Stone 1998;Chiang & Murray-Clay 2007), the measured scale height of the particles of τ s = 0.1 covers a range of values from ∼0.04 to ∼0.1H g (Zhu et al 2015;Xu et al 2017;Riols & Lesur 2018). This is smaller than our measured value of ∼0.2H g , but remains noticeably larger than what streaming turbulence alone supports at ∼0.02H g (Carrera et al 2015).…”

A balanced budget view on forming giant planets by pebble accretion

“…But cores perturb gas streamlines onto horseshoe orbits in 2D (e.g., Ormel 2013, their Figure 12) and "transient horseshoes" in 3D (e.g., Fung et al 2015), either of which can deflect particles, particularly those with small τ , away from the core, and conceivably radically altering accretion probabilities. Xu et al (2017) have tested some of the scaling relations of Ormel & Klahr (2010) using 3D simulations, but only under restrictive conditions and with mixed results. A more comprehensive study, starting with re-deriving accretion cross sections and velocities for 2D laminar flow patterns, would be welcome (see also Popovas et al 2018).…”

Gas-assisted Growth of Protoplanets in a Turbulent Medium

“…While these processes can produce architectures similar to the solar system, they are not sufficient to explain the diverse system architectures that are observed around other stars. In particular, recent theoretical work has pointed to the possibility that accretion of "pebble" sized bodies may be important in both determining the growth timescale of cores and providing a reservoir of solid material through radial drift (Ormel & Klahr 2010, Perets & Murray-Clay 2011, Ormel & Kobayashi 2012, Lambrechts & Johansen 2012, Levison et al 2015, Morbidelli et al 2015, Visser & Ormel 2016, Ida et al 2016, Xu et al 2017. In this paper we will introduce an order of magnitude model of protoplanetary growth by pebble accretion, focusing on the regime in which the core is sufficiently massive that the gravity of the core is non-negligible.…”