On the filtering and processing of dust by planetesimals

Abstract

Context. Circumstellar disks are known to contain a significant mass in dust ranging from micron to centimeter size. Meteorites are evidence that individual grains of those sizes were collected and assembled into planetesimals in the young solar system. Aims. We assess the efficiency of dust collection of a swarm of non-drifting planetesimals with radii ranging from 1 to 10 3 km and beyond. Methods. We calculate the collision probability of dust drifting in the disk due to gas drag by planetesimal accounting for several regimes depending on the size of the planetesimal, dust, and orbital distance: the geometric, Safronov, settling, and three-body regimes. We also include a hydrodynamical regime to account for the fact that small grains tend to be carried by the gas flow around planetesimals. Results. We provide expressions for the collision probability of dust by planetesimals and for the filtering efficiency by a swarm of planetesimals. For standard turbulence conditions (i.e., a turbulence parameter α = 10 −2 ), filtering is found to be inefficient, meaning that when crossing a minimum-mass solar nebula (MMSN) belt of planetesimals extending between 0.1 AU and 35 AU most dust particles are eventually accreted by the central star rather than colliding with planetesimals. However, if the disk is weakly turbulent (α = 10 −4 ) filtering becomes efficient in two regimes: (i) when planetesimals are all smaller than about 10 km in size, in which case collisions mostly take place in the geometric regime; and (ii) when planetary embryos larger than about 1000 km in size dominate the distribution, have a scale height smaller than one tenth of the gas scale height, and dust is of millimeter size or larger in which case most collisions take place in the settling regime. These two regimes have very different properties: we find that the local filtering efficiency x filter,MMSN scales with r −7/4 (where r is the orbital distance) in the geometric regime, but with r −1/4 to r 1/4 in the settling regime. This implies that the filtering of dust by small planetesimals should occur close to the central star and with a short spread in orbital distances. On the other hand, the filtering by embryos in the settling regime is expected to be more gradual and determined by the extent of the disk of embryos. Dust particles much smaller than millimeter size tend only to be captured by the smallest planetesimals because they otherwise move on gas streamlines and their collisions take place in the hydrodynamical regime. Conclusions. Our results hint at an inside-out formation of planetesimals in the infant solar system because small planetesimals in the geometrical limit can filter dust much more efficiently close to the central star. However, even a fully-formed belt of planetesimals such as the MMSN only marginally captures inward-drifting dust and this seems to imply that dust in the protosolar disk has been filtered by planetesimals even smaller than 1 km (not included in this study) or that it has been assembled into planetesi...

The Emerging Paradigm of Pebble Accretion

“…These expressions are, within orders of unity, consistent with recent works (Ormel and Klahr 2010;Ormel and Kobayashi 2012;Johansen 2012, 2014;Guillot et al 2014;Ida et al 2016). …”

“…To obtain the actual growth timescale, M P;grw should be divided by the pebble flux P M P;disk . Guillot et al (2014) already introduced Eq. (7.26) as the filtering mass: M P;grw is also the mass in planetesimals needed to ensure accretion of a single pebble.…”

On the water delivery to terrestrial embryos by ice pebble accretion

“…As already shown by previous studies Guillot et al 2014;Morbidelli & Nesvorny 2012), a swarm of planetesimals or embryos filters only a minor fraction of the pebble flow (typically <50%) unless the size distribution of the bodies is narrowly peaked at 10 3 -10 4 km in radius (see Guillot et al 2014). By contrast, if massive planets already exist at t ∼ t start , they can efficiently halt the flow of the pebbles by opening a gap in the gas disk (e.g., Paardekooper & Mellema 2006;Rice et al 2006;Zhu et al 2012;Pinilla et al 2012;Morbidelli & Nesvorny 2012;.…”

“…Our model takes the effects of disk turbulence on the growth and vertical diffusion of dust particles into account. Turbulent diffusion is particularly important in our model because it determines the efficiency of pebble accretion by an embryo lying at the midplane (Guillot et al 2014;Johansen et al 2015;Morbidelli et al 2015;Moriarty & Fischer 2015). We parametrize the turbulent diffusion coefficient as D = αc s h g , where α is a dimensionless free parameter.…”

“…2, we place an rocky embryo at 1 AU in a protoplanetary disk and allow it to accrete icy pebbles at times t > t start . Following Guillot et al (2014), we evaluate the rate of pebble accretion by an embryo,Ṁ e , aṡ (14)) at 100 AU as a function of particle radius a for Σ d = 10 −2 Σ g with different values of the turbulence parameter α. The dotted line shows the simple estimate…”