We show that condensation is an efficient particle growth mechanism that leads to growth beyond decimetre-sized pebbles close to an ice line in protoplanetary discs. As coagulation of dust particles is frustrated by bouncing and fragmentation, condensation could be a complementary, or even dominant, growth mode in the early stages of planet formation. Ice particles diffuse across the ice line and sublimate, and vapour diffusing inwards across the ice line recondenses onto already existing particles, causing them to grow. We develop a numerical model of the dynamical behaviour of ice particles close to the water ice line, approximately 3 AU from the host star. Particles move with the turbulent gas, modelled as a random walk. They also sediment towards the midplane and drift radially towards the central star. Condensation and sublimation are calculated using a Monte Carlo approach. Our results indicate that, with a turbulent α-value of 0.01, growth from millimetre to at least decimetre-sized pebbles is possible on a time scale of 1000 years. We find that particle growth is dominated by ice and vapour transport across the radial ice line, with negligible growth caused by transport across the atmospheric ice line. Ice particles mix outwards by turbulent diffusion, leading to net growth across the entire cold region. The resulting particles are large enough to be sensitive to concentration by streaming instabilities, pressure bumps and vortices, which can cause further growth into planetesimals. In our model, particles are considered to be homogeneous ice particles. Considering the more realistic composition of ice condensed onto rocky ice nuclei might affect the growth time scales, by release of refractory ice nuclei after sublimation. We also ignore sticking and fragmentation in particle collisions. These effects will be the subject of future investigations.
Solid particles in protoplanetary discs can grow by direct vapour deposition outside of ice lines. The presence of microscopic silicate particles may nevertheless hinder growth into large pebbles, since the available vapour is deposited predominantly on the small grains that dominate the total surface area. Experiments on heterogeneous ice nucleation, performed to understand ice clouds in the Martian atmosphere, show that the formation of a new ice layer on a silicate surface requires a substantially higher water vapour pressure than the deposition of water vapour on an existing ice surface. In this paper, we investigate how the difference in partial vapour pressure needed for deposition of vapour on water ice versus heterogeneous ice nucleation on silicate grains influences particle growth close to the water ice line. We developed and tested a dynamical 1D deposition and sublimation model, where we include radial drift, sedimentation, and diffusion in a turbulent protoplanetary disc. We find that vapour is deposited predominantly on already ice-covered particles, since the vapour pressure exterior of the ice line is too low for heterogeneous nucleation on bare silicate grains. Icy particles can thus grow to centimetre-sized pebbles in a narrow region around the ice line, whereas silicate particles stay dust-sized and diffuse out over the disc. The inhibition of heterogeneous ice nucleation results in a preferential region for growth into planetesimals close to the ice line where we find large icy pebbles. The suppression of heterogeneous ice nucleation on silicate grains may also be the mechanism behind some of the observed dark rings around ice lines in protoplanetary discs, as the presence of large ice pebbles outside ice lines leads to a decrease in the opacity there.
We show that condensation is an efficient particle growth mechanism, leading to growth beyond decimeter-sized pebbles close to an ice line in protoplanetary discs. As coagulation of dust particles is frustrated by bouncing and fragmentation, condensation could be a complementary, or even dominant, growth mode in the early stages of planet formation. Ice particles diffuse across the ice line and sublimate, and vapour diffusing back across the ice line recondenses onto already existing particles, causing them to grow. We develop a numerical model of the dynamical behaviour of ice particles close to the water ice line, approximately 3 AU from the host star. Particles move with the turbulent gas, modelled as a random walk. They also sediment towards the midplane and drift radially towards the central star. Condensation and sublimation are calculated using a Monte Carlo approach. Our results indicate that, with a turbulent α-value of 0.01, growth from millimeter to at least decimeter-sized pebbles is possible on a time scale of 1000 years. We find that particle growth is dominated by ice and vapour transport across the radial ice line, with growth due to transport across the atmospheric ice line being negligible. Ice particles mix outwards by turbulent diffusion, leading to net growth across the entire cold region. The resulting particles are large enough to be sensitive to concentration by streaming instabilities, and in pressure bumps and vortices, which can cause further growth into planetesimals. In our model, particles are considered to be homogeneous ice particles. Taking into account the more realistic composition of ice condensed onto rocky ice nuclei might affect the growth time scales, by release of refractory ice nuclei after sublimation. We also ignore sticking and fragmentation in particle collisions. These effects will be the subject of future investigations.
Icy pebbles may play an important role in planet formation close to the water ice line of protoplanetary discs. There, dust coagulation is more efficient and re-condensation of vapor on pebbles may enhance their growth outside the ice line. Previous theoretical studies showed that disruption of icy pebbles due to sublimation increases the growth rate of pebbles inside and outside the ice line, by freeing small silicate particles back in the dust reservoir of the disc. However, since planet accretion is dependent on the Stokes number of the accreting pebbles, the growth of planetesimals could be enhanced downstream of the ice line if pebbles are not disrupting upon sublimation. We developed two experimental models of icy pebbles using different silicate dusts, and we exposed them to low-temperature and low-pressure conditions in a vacuum chamber. Increasing the temperature inside the chamber, we studied the conditions for which pebbles are preserved through sublimation without disrupting. We find that small silicate particles (<50 μm) and a small quantity of ice (around 15 per cent pebble mass) are optimal conditions for preserving pebbles through sublimation. Furthermore, pebbles with coarse dust distribution (100–300 μm) do not disrupt if a small percentage (10–20 per cent mass) of dust grains are smaller than 50 μm. Our findings highlight how sublimation is not necessarily causing disruption, and that pebbles seem to survive fast sublimation processes effectively.
Abstract. Pebbles with sizes of centimeters to decimeters are needed in order to form kilometer-sized planetesimals, which in turn are needed for planet formation to proceed. The well-studied mechanism of coagulation is efficient only up to millimeter-sized dust grains. In this proceeding a numerical model of ice condensation as a complementary growth mechanism in turbulent protoplanetary discs is discussed. Close to an ice line, particles grow efficiently by ice condensation, which, combined with radial mixing, can supply a large extent of the disc with icy pebbles. Growth from millimeter-sized dust grains to at least decimeter-sized pebbles is possible on a time scale of only 10 000 years. The resulting particles are large enough to enable further growth into planetesimals via a variety of particle concentration mechanisms and subsequent gravitational collapse.
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