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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.
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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.
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.
We directly measure twenty overhanging cliffs on the surface of comet 67P/Churyumov-Gerasimenko extracted from the latest shape model and estimate the minimum tensile strengths needed to support them against collapse under the comets gravity. We find extremely low strengths of around one Pa or less (one to five Pa, when scaled to a metre length). The presence of eroded material at the base of most overhangs, as well as the observed collapse of two features and implied previous collapse of another, suggests that they are prone to failure and that true material strengths are close to these lower limits (although we only consider static stresses and not dynamic stress from, for example, cometary activity). Thus, a tensile strength of a few pascals is a good approximation for the tensile strength of 67Ps nucleus material, which is in agreement with previous work. We find no particular trends in overhang properties with size, over the $sim10-100$ m range studied here, or location on the nucleus. There are no obvious differences, in terms of strength, height or evidence of collapse, between the populations of overhangs on the two cometary lobes, suggesting that 67P is relatively homogenous in terms of tensile strength. Low material strengths are supportive of cometary formation as a primordial rubble pile or by collisional fragmentation of a small (tens of km) body.
The structure of cometary dust is a tracer of growth processes in the formation of planetesimals. Instrumentation on board the Rosetta mission to comet 67P/Churyumov- Gerasimenko captured dust particles and analysed them in situ. However, these deposits are a product of a collision within the instrument. We conducted laboratory experiments with cometary dust analogues, simulating the collection process by Rosetta instruments (specifically COSIMA, MIDAS). In Paper I we reported that velocity is a key driver in determining the appearance of deposits. Here in Paper II we use materials with different monomer sizes, and study the effect of tensile strength on the appearance of deposits. We find that mass transfer efficiency increases from $sim$1 up to $sim$10% with increasing monomer diameter from 0.3 $mu$m to 1.5 $mu$m (i.e. tensile strength decreasing from $sim$12 to $sim$3 kPa), and velocities increasing from 0.5 to 6 m/s. Also, the relative abundance of small fragments after impact is higher for material with higher tensile strength. The degeneracy between the effects of velocity and material strength may be lifted by performing a closer study of the deposits. This experimental method makes it possible to estimate the mass transfer efficiency in the COSIMA instrument. Extrapolating these results implies that more than half of the dust collected during the Rosetta mission has not been imaged. We analysed two COSIMA targets containing deposits from single collisions. The collision that occurred closest to perihelion passage led to more small fragments on the target.
Understanding the heat transfer mechanism within dust aggregates is of great importance for many subjects in planetary science. We calculated the coordination number and the thermal conductivity through the solid network of compressed dust aggregates. We found a simple relationship between the coordination number and the filling factor and revealed that the thermal conductivity through the solid network of aggregates is represented by a power-law function of the filling factor and the coordination number.
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