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Formation of dust-rich planetesimals from sublimated pebbles inside of the snow line

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 Added by Shigeru Ida
 Publication date 2016
  fields Physics
and research's language is English




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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.



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We present a study on the formation of planetary systems around low mass stars similar to Trappist-1, through the accretion of either planetesimals or pebbles. The aim is to determine if the currently observed systems around low mass stars favour one scenario over the other. We ran numerous N-body simulations, coupled to a thermally evolving viscous disc model, including prescriptions for planet migration and photoevaporation. We examine the differences between the pebble and planetesimal accretion scenarios, but also look at the influences of disc mass, planetesimal size, and the percentage of solids locked up within pebbles. When comparing the resulting planetary systems to Trappist-1, we find that a wide range of initial conditions for both accretion scenarios can form planetary systems similar to Trappist-1, in terms of planet mass, periods, and resonant configurations. Typically these planets formed exterior to the water iceline and migrated in resonant convoys to close to the central star. When comparing the planetary systems formed from pebbles to those formed from planetesimals, we find a large number of similarities, including average planet masses, eccentricities, inclinations and period ratios. One major difference was that of the water content of the planets. When including the effects of ablation and full recycling of the planets envelope with the disc, planets formed from pebbles were extremely dry, whilst those formed from planetesimals were extremely wet. If the water content is not fully recycled and instead falls to the planets core, or if ablation of the water is neglected, then the planets formed from pebbles are extremely wet, similar to those formed from planetesimals. Should the water content of the Trappist-1 planets be determined accurately, this could point to a preferred formation pathway for planetary systems, or to specific physics that may be at play.
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.
Context. The water snowline divides dry and icy solid material in protoplanetary disks, and has been thought to significantly affect planet formation at all stages. If dry particles break up more easily than icy ones, then the snowline causes a traffic jam, because small grains drift inward at lower speeds than larger pebbles. Aims. We aim to evaluate the effect of high dust concentrations around the snowline onto the gas dynamics. Methods. Using numerical simulations, we model the global radial evolution of an axisymmetric protoplanetary disk. Our model includes particle growth, evaporation and recondensation of water, and the back-reaction of dust onto the gas, taking into account the vertical distribution of dust particles. Results. We find that the dust back-reaction can stop and even reverse the net flux of gas outside the snowline, decreasing the gas accretion rate onto the star to under $50%$ of its initial value. At the same time the dust accumulates at the snowline, reaching dust-to-gas ratios of $epsilon gtrsim 0.8$, and delivers large amounts of water vapor towards the inner disk, as the icy particles cross the snowline. However, the accumulation of dust at the snowline and the decrease in the gas accretion rate only take place if the global dust-to-gas ratio is high ($varepsilon_0 gtrsim 0.03$), if the viscous turbulence is low ($alpha_ u lesssim 10^{-3} $), if the disk is large enough ($r_c gtrsim 100, textrm{au}$), and only during the early phases of the disk evolution ($t lesssim 1, textrm{Myr}$). Otherwise the dust back-reaction fails to perturb the gas motion.
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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