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Register a new userPlanetesimal formation around the snow line: I. Monte Carlo simulations of silicate dust pile-up in a turbulent disk
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Context: The formation of rocky planetesimals is a long-standing problem in planet formation theory. One of the possibilities is that it results from gravitational instability as a result of pile-up of small silicate dust particles released from sublimating icy pebbles that pass the snow line. Aims: We want to understand and quantify the role of the water snow line for the formation of rock-rich and ice-rich planetesimals. In this paper, we focus on the formation of rock-rich planetesimals. A companion paper examines the combined formation of both rock-rich and ice-rich planetesimals. Methods: We develop a new Monte Carlo code to calculate the radial evolution of silicate particles in a turbulent accretion disk, accounting for the back-reaction (i.e., inertia) of the particles on their radial drift velocity and diffusion. Results depend in particular on the particle injection width (determined from the radial sublimation width of icy pebbles), the pebble scale height and the pebble mass flux through the disk. The scale height evolution of the silicate particles, which is the most important factor for the runaway pile-up, is automatically calculated in this Lagrange method. Results: From the numerical results, we derive semi-analytical relations for the scale height of the silicate dust particles and the particles-to-gas density ratio at the midplane, as functions of a pebble-to-gas mass flux ratio and the $alpha$ parameters for disk gas accretion and vertical/radial diffusion. We find that the runaway pile-up of the silicate particles (formation of rocky planetesimals) occurs if the pebble-to-gas mass flux ratio is $> [(alpha_{Dz}/alpha_{acc})/3 times 10^{-2}]^{1/2}$ where $alpha_{Dz}$ and $alpha_{acc}$ are the $alpha$ parameters for vertical turbulent diffusion and disk gas accretion.
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We develop a simple model to predict the radial distribution of planetesimal formation. The model is based on the observed growth of dust to mm-sized particles, which drift radially, pile-up, and form planetesimals where the stopping time and dust-to-gas ratio intersect the allowed region for streaming instability-induced gravitational collapse. Using an approximate analytic treatment, we first show that drifting particles define a track in metallicity--stopping time space whose only substantial dependence is on the disks angular momentum transport efficiency. Prompt planetesimal formation is feasible for high particle accretion rates (relative to the gas, $dot{M}_p / dot{M} > 3 times 10^{-2}$ for $alpha = 10^{-2}$), that could only be sustained for a limited period of time. If it is possible, it would lead to the deposition of a broad and massive belt of planetesimals with a sharp outer edge. Including turbulent diffusion and vapor condensation processes numerically, we find that a modest enhancement of solids near the snow line occurs for cm-sized particles, but that this is largely immaterial for planetesimal formation. We note that radial drift couples planetesimal formation across radii in the disk, and suggest that considerations of planetesimal formation favor a model in which the initial deposition of material for giant planet cores occurs well beyond the snow line.
We present high-resolution computer simulations of dust dynamics and planetesimal formation in turbulence generated by the magnetorotational instability. We show that the turbulent viscosity associated with magnetorotational turbulence in a non-stratified shearing box increases when going from 256^3 to 512^3 grid points in the presence of a weak imposed magnetic field, yielding a turbulent viscosity of $alphaapprox0.003$ at high resolution. Particles representing approximately meter-sized boulders concentrate in large-scale high-pressure regions in the simulation box. The appearance of zonal flows and particle concentration in pressure bumps is relatively similar at moderate (256^3) and high (512^3) resolution. In the moderate-resolution simulation we activate particle self-gravity at a time when there is little particle concentration, in contrast with previous simulations where particle self-gravity was activated during a concentration event. We observe that bound clumps form over the next ten orbits, with initial birth masses of a few times the dwarf planet Ceres. At high resolution we activate self-gravity during a particle concentration event, leading to a burst of planetesimal formation, with clump masses ranging from a significant fraction of to several times the mass of Ceres. We present a new domain decomposition algorithm for particle-mesh schemes. Particles are spread evenly among the processors and the local gas velocity field and assigned drag forces are exchanged between a domain-decomposed mesh and discrete blocks of particles. We obtain good load balancing on up to 4096 cores even in simulations where particles sediment to the mid-plane and concentrate in pressure bumps.
Planet formation models begin with proto-embryos and planetesimals already fully formed, missing out a crucial step, the formation of planetesimals/proto-embryos. In this work, we include prescriptions for planetesimal and proto-embryo formation arising from pebbles becoming trapped in short-lived pressure bumps, in thermally evolving viscous discs to examine the sizes and distributions of proto-embryos and planetesimals throughout the disc. We find that planetesimal sizes increase with orbital distance, from ~10 km close to the star to hundreds of kilometres further away. Proto-embryo masses are also found to increase with orbital radius, ranging from $10^{-6} M_{rm oplus}$ around the iceline, to $10^{-3} M_{rm oplus}$ near the orbit of Pluto. We include prescriptions for pebble and planetesimal accretion to examine the masses that proto-embryos can attain. Close to the star, planetesimal accretion is efficient due to small planetesimals, whilst pebble accretion is efficient where pebble sizes are fragmentation limited, but inefficient when drift dominated due to low accretion rates before the pebble supply diminishes. Exterior to the iceline, planetesimal accretion becomes inefficient due to increasing planetesimal eccentricities, whilst pebble accretion becomes more efficient as the initial proto-embryo masses increase, allowing them to significantly grow before the pebble supply is depleted. Combining both scenarios allows for more massive proto-embryos at larger distances, since the accretion of planetesimals allows pebble accretion to become more efficient, allowing giant planet cores to form at distances upto 10 au. By including more realistic initial proto-embryo and planetesimal sizes, as well as combined accretion scenarios, should allow for a more complete understanding in the beginning to end process of how planets and planetary systems form.
Content: For up to a few millions of years, pebbles must provide a quasi-steady inflow of solids from the outer parts of protoplanetary disks to their inner regions. Aims: We wish to understand how a significant fraction of the pebbles grows into planetesimals instead of being lost to the host star. Methods:We examined analytically how the inward flow of pebbles is affected by the snow line and under which conditions dust-rich (rocky) planetesimals form. When calculating the inward drift of solids that is due to gas drag, we included the back-reaction of the gas to the motion of the solids. Results: We show that in low-viscosity protoplanetary disks (with a monotonous surface density similar to that of the minimum-mass solar nebula), the flow of pebbles does not usually reach the required surface density to form planetesimals by streaming instability. We show, however, that if the pebble-to-gas-mass flux exceeds a critical value, no steady solution can be found for the solid-to-gas ratio. This is particularly important for low-viscosity disks (alpha < 10^(-3)) where we show that inside of the snow line, silicate-dust grains ejected from sublimating pebbles can accumulate, eventually leading to the formation of dust-rich planetesimals directly by gravitational instability. Conclusions: This formation of dust-rich planetesimals may occur for extended periods of time, while the snow line sweeps from several au to inside of 1 au. The rock-to-ice ratio may thus be globally significantly higher in planetesimals and planets than in the central star.
One of the most important questions in the field of planet formation is how mm-cm sized dust particles overcome the radial drift and fragmentation barriers to form kilometer-sized planetesimals. ALMA observations of protoplanetary disks, in particular transition disks or disks with clear signs of substructures, can provide new constraints on theories of grain growth and planetesimal formation and therefore represent one possibility to progress on this issue. We here present ALMA band 4 (2.1 mm) observations of the transition disk system Sz 91 and combine them with previously obtained band 6 (1.3 mm) and 7 (0.9 mm) observations. Sz 91 with its well defined mm-ring, more extended gas disk, and evidence of smaller dust particles close to the star, is a clear case of dust filtering and the accumulation of mm sized particles in a gas pressure bump. We computed the spectral index (nearly constant at $sim$3.34), optical depth (marginally optically thick), and maximum grain size ($sim,0.61$ mm) in the dust ring from the multi-wavelength ALMA observations and compared the results with recently published simulations of grain growth in disk substructures. Our observational results are in very good agreement with the predictions of models for grain growth in dust rings that include fragmentation and planetesimal formation through the streaming instability.
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