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Register a new userGravitational instability of a dust layer composed of porous silicate dust aggregates in a protoplanetary disk
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Planetesimal formation is one of the most important unsolved problems in planet formation theory. In particular, rocky planetesimal formation is difficult because silicate dust grains are easily broken when they collide. Recently, it has been proposed that they can grow as porous aggregates when their monomer radius is smaller than $sim$ 10 nm, which can also avoid the radial drift toward the central star. However, the stability of a layer composed of such porous silicate dust aggregates has not been investigated. Therefore, we investigate the gravitational instability of this dust layer. To evaluate the disk stability, we calculate Toomres stability parameter $Q$, for which we need to evaluate the equilibrium random velocity of dust aggregates. We calculate the equilibrium random velocity considering gravitational scattering and collisions between dust aggregates, drag by mean flow of gas, stirring by gas turbulence, and gravitational scattering by gas density fluctuation due to turbulence. We derive the condition of the gravitational instability using the disk mass, dust-to-gas ratio, turbulent strength, orbital radius, and dust monomer radius. We find that, for the minimum mass solar nebula model at 1 au, the dust layer becomes gravitationally unstable when the turbulent strength $alphalesssim10^{-5}$. If the dust-to-gas ratio is increased twice, the gravitational instability occurs for $alphalesssim10^{-4}$. We also find that the dust layer is more unstable in disks with larger mass, higher dust-to-gas ratio, and weaker turbulent strength, at larger orbital radius, and with a larger monomer radius.
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Comets are thought to have information about the formation process of our solar system. Recently, detailed information about comet 67P/Churyumov-Gerasimenko has been found by a spacecraft mission Rosetta. It is remarkable that its tensile strength was estimated. In this paper, we measure and formulate the tensile strength of porous dust aggregates using numerical simulations, motivated by porous dust aggregation model of planetesimal formation. We perform three-dimensional numerical simulations using a monomer interaction model with periodic boundary condition. We stretch out a dust aggregate with a various initial volume filling factor between $10^{-2}$ and 0.5. We find that the tensile stress takes the maximum value at the time when the volume filling factor decreases to about a half of the initial value. The maximum stress is defined to be the tensile strength. We take an average of the results with 10 different initial shapes to smooth out the effects of initial shapes of aggregates. Finally, we numerically obtain the relation between the tensile strength and the initial volume filling factor of dust aggregates. We also use a simple semi-analytical model and successfully reproduce the numerical results, which enables us to apply to a wide parameter range and different materials. The obtained relation is consistent with previous experiments and numerical simulations about silicate dust aggregates. We estimate that the monomer radius of comet 67P has to be about 3.3--220 $mathrm{mu m}$ to reproduce its tensile strength using our model.
We introduce a possible disruption mechanism of dust grains in planet formation by their spinning motion. This mechanism has been discussed as rotational disruption for the interstellar dust grains. We theoretically calculate whether porous dust aggregates can be disrupted by their spinning motion and if it prohibits dust growth in protoplanetary disks. We assume radiative torque and gas-flow torque as driving sources of the spinning motion, assume that dust aggregates reach a steady-state rigid rotation, and compare the obtained tensile stress due to the centrifugal force with their tensile strength. We model the irregularly-shaped dust aggregates by introducing a parameter, $gamma_mathrm{ft}$, that mimics the conversion efficiency from force to torque. As a result, we find that porous dust aggregates are rotationally disrupted by their spinning motion induced by gas flow when their mass is larger than $sim10^8$ g and their volume filling factor is smaller than $sim 0.01$ in our fiducial model, while relatively compact dust aggregates with volume filling factor more than 0.01 do not face this problem. If we assume the dust porosity evolution, we find that dust aggregates whose Stokes number is $sim0.1$ can be rotationally disrupted in their growth and compression process. Our results suggest that the growth of dust aggregates may be halted due to rotational disruption or that other compression mechanisms are needed to avoid it. We also note that dust aggregates are not rotationally disrupted when $gamma_mathrm{ft}leq0.02$ in our fiducial model and the modeling of irregularly-shaped dust aggregates is essential in future work.
Coagulation of dust aggregates plays an important role in the formation of planets and is of key importance to the evolution of protoplanetary disks (PPDs). Characteristics of dust, such as the diversity of particle size, porosity, charge, and the manner in which dust couples to turbulent gas, affect the collision outcome and the rate of dust growth. Here we present a numerical model of the evolution of the dust population within a PPD which incorporates all of these effects. The probability that any two particles collide depends on the particle charge, cross-sectional area and their relative velocity. The actual collision outcome is determined by a detailed collision model which takes into account the aggregate morphology, trajectory, orientation, and electrostatic forces acting between charged grains. The data obtained in this research reveal the characteristics of dust populations in different environments at the end of the hit-and-stick growth, which establishes the foundation for the onset of the next growth stage where bouncing, mass transfer and fragmentation become important. For a given level of turbulence, neutral and weakly charged particles collide more frequently and grow faster than highly charged particles. However, highly charged particles grow to a larger size before reaching the bouncing barrier, and exhibit a Runaway growth, in which a few large particles grow quickly by accreting smaller particles while the rest of the population grows very slowly. In general, highly charged aggregates have a more compact structure and are comprised of larger monomers than neutral/weakly charged aggregates. The differences in the particle structure/composition not only affect the threshold velocities for bouncing and fragmentation, but also change the scattering and absorption opacity of dust, influencing the appearance of PPDs.
The streaming instability (SI) has been extensively studied in the linear and non-linear regimes as a mechanism to concentrate solids and trigger planetesimal formation in the midplane of protoplanetary discs. A related dust settling instability (DSI) applies to particles while settling towards the midplane. The DSI has previously been studied in the linear regime, with predictions that it could trigger particle clumping away from the midplane. This work presents a range of linear calculations and non-linear simulations, performed with FARGO3D, to assess conditions for DSI growth. We expand on previous linear analyses by including particle size distributions and performing a detailed study of the amount of background turbulence needed to stabilize the DSI. When including binned size distributions, the DSI often produces converged growth rates with fewer bins than the standard SI. With background turbulence, we find that the most favorable conditions for DSI growth are weak turbulence, characterized by $alpha lesssim 10^{-6}$ with intermediate-sized grains that settle from one gas scale-height. These conditions could arise during a sudden decrease in disc turbulence following an accretion outburst. Ignoring background turbulence, we performed a parameter survey of local 2D DSI simulations. Particle clumping was either weak or occurred slower than particles settle. Clumping was reduced by a factor of two in a comparison 3D simulation. Overall, our results strongly disfavor the hypothesis that the DSI significantly promotes planetesimal formation. Non-linear simulations of the DSI with different numerical methods could support or challenge these findings.
The experiments presented aim to measure the outcome of collisions between sub-mm sized protoplanetary dust aggregate analogues. We also observed the clusters formed from these aggregates and their collision behaviour. The experiments were performed at the drop tower in Bremen. The protoplanetary dust analogue materials were micrometre-sized monodisperse and polydisperse SiO$_2$ particles prepared into aggregates with sizes between 120~$mu$m and 250~$mu$m. One of the dust samples contained aggregates that were previously compacted through repeated bouncing. During three flights of 9~s of microgravity each, individual collisions between aggregates and the formation of clusters of up to a few millimetres in size were observed. In addition, the collisions of clusters with the experiment cell walls leading to compaction or fragmentation were recorded. We observed collisions amongst dust aggregates and collisions between dust clusters and the cell aluminium walls at speeds ranging from about 0.1 cm/s to 20 cm/s. The velocities at which sticking occurred ranged from 0.18 to 5.0 cm/s for aggregates composed of monodisperse dust, with an average value of 2.1 cm/s for reduced masses ranging from 1.2x10-6 to 1.8x10-3 g with an average value of 2.2x10-4 g. From the restructuring and fragmentation of clusters composed of dust aggregates colliding with the aluminium cell walls, we derived a collision recipe for dust aggregates ($sim$100 $mu$m) following the model of Dominik & Thielens (1997) developed for microscopic particles. We measured a critical rolling energy of 1.8x10-13 J and a critical breaking energy of 3.5x10-13 J for 100 $mu$m-sized non-compacted aggregates.
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