ИСТИНА

Introduction: Fragmentation of dust aggregates in the protoplanetary disk through evaporation of ice at the snowline is important to define location of the planetesimals formation in the disk. The process involves the ratio of sizes and/or densities of aggregates before and after evaporation of ice and allows us to determine whether they would accumulate nearby the snowline or move to smaller radial distances of inner planets formation [1, 2]. The effect of icy dust aggregates structure near the snowline was evaluated in the earlier studies [3] but how the structure of icy aggregate affects the parameters of fragments and planetesimals formation was not clarified. The problem is addressed in this study. The structure, composition, size, and density of ice-containing dust aggregates was constrained using the cometary nucleus data available including those of 67P/Churyumov-Gerasimenko comet revealed by the Rosetta mission [4], as well from several Kuiper Belt objects (see [5] and references therein). In particular, a high refractory-to-ice mass ratio inside the nucleus (δ> 3) was derived [5]. The cometary nucleus is composed of fairly dense pebbles consisting mainly (~ 90%) of silicates, sulphides and a large fraction of organic matter, and only ~ 10% of water ice [4]. The mass ratio of pebbles is up to ~99% and only ~1% amounts to fluffy dust particles. Experiments with collisions of small particles of fractal structure showed that initially fractal dimension growths resulting in sticking fractal clusters and then it is replaced by bouncing when aggregate sizes reach ~ 1 cm for stony aggregates and at least tenfold larger for icy aggregates (see [4] and references therein). This is confirmed by the results of modeling [8]. Input parameters and method: With regard to these data, we consider a pebble-sized icy aggregate near the snowline having various fractal dimension meaning its variable porosity. It was suggested that a spherical aggregate consists of two smaller sets of spherical particles (pebbles) of different size and density due to their different composition/origin. One type of particles is assumed to consist mostly of ice evaporating completely at the snowline, a minor fraction of refractory grains inside being neglected. The other type of particles are refractories, which consist mainly of silicates, sulphides and organics while a minor fraction of water ice inside is ignored. The latter particles are assumed to fully preserve when crossing the snowline. In our model we vary size and density of both types of particles thus simulating the porosity and composition variations of the medium. The fractal icy assembly approach and the modified permeable particle method [6-8] were used. For the both types of particles a selected size range and the inversed power-law size distribution with variable exponent was accepted. Following the data available on the pebble sizes achievable in the protoplanetary disc, the aggregate diameter varied in the range from 1 to 10 cm. The smallest diameter of each type particles inside the aggregate was at least one two-hundredth of the aggregate’s diameter. The possible even smaller diameters of particles were not included due to computational limits. Results and discussion: The results of our modeling were obtained for the following set of parameters: Diameter of the aggregate is 10 cm; fractal dimension is 2.75; diameters of refractory particles are varied from 0.05 to 0.1 cm; diameters of ice particles are varied from 0.5 cm to 1 cm, i.e. ten times larger; exponent in the inverse power-law size distribution is equal to 3.5 (similar to interstellar dust particles and crater sizes), which yields the average diameters ~0.06 cm and 0.6 cm for refractory and ice particles respectively; density of refractory particles is taken equal to 1.2 g cm3; density of ice particles is assumed to be 0.1 g cm3 corresponding to rather high porosity ~0.9. The total mass of the aggregate was obtained to be 60.1 g, the masses of refractory and ice components are 54.2 and 5.9 g, respectively; their ratio is similar to that in the 67P nucleus. Fig. 1. Left: The dust aggregate with diameter of 10 cm and total number of particles N=306336 before evaporation of ice at the snowline. Blue balls are ice particles, yellow are the chains of refractory particles. Right: The largest refractory fragment resulting from evaporation of ice; number of particles N1=107487, that is 35% of the total number; the maximum size L=7.7 cm. Mass of the largest fragment (shown in Fig. 1) is ~ 32% of the total mass of aggregate before the ice evaporation; size of this fragment is ~77% of the aggregate diameter. Mass of the second large fragment is 7.5 times less. In the option with greater ice mass fraction and higher density of ice particles, similar result of massive large fragments was derived. Such large fragments drift from the snowline with rather high velocity into the inner planet formation zone [2]. However, in the case of smaller ice particles than refractory ones our modeling yields very small fragments of only several particles left. In such a case they will be slow down by the gas drag and accumulate in the asteroid formation zone. It is aware that the results of modeling are to be analyzed in the whole range of the input parameters possible variations, which would allow us to estimate characteristics of the resulting fragments at the inner side of the snowline. Another goal is to assess the rate of sticking and aggregation of fragments at the snowline, jointly with their radial drift and influence of turbulent diffusion in the disk gas. Providing the aggregation of fragments was efficient, it would drastically affect the radial motion and distribution of dust aggregates implying significant impact on the formation of planetesimals. This work was supported by the Russian Foundation for Basic Research (Project 17-02-00507). References: [1] Ida S., Guillot T. Formation of dust-rich planetesimals from sublimated pebbles inside of the snow line // Astron. and Astrophys. 2016. V. 596. Article id. L3. 5 р id. L3. 5 р. 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