Context. Comets are remnants of the icy planetesimals that formed beyond the ice line in the solar nebula. Growing from μm-sized dust and ice particles to km-sized objects is, however, difficult because of growth barriers and time scale constraints. The gravitational collapse of pebble clouds that formed through the streaming instability may provide a suitable mechanism for comet formation. Aims. We study the collisional compression of silica, ice, and silica/ice-mixed pebbles during gravitational collapse of pebble clouds. Using the initial volume-filling factor and the dust-to-ice ratio of the pebbles as free parameters, we constrain the dust-to-ice mass ratio of the formed comet and the resulting volume-filling factor of the pebbles, depending on the cloud mass. Methods. We use the representative particle approach, which is a Monte Carlo method, to follow cloud collapse and collisional evolution of an ensemble of ice, silica, and silica/ice-mixed pebbles. Therefore, we developed a collision model which takes the various collision properties of dust and ice into account. We study pebbles with a compact size of 1 cm and vary the initial volume-filling factors, φ 0 , ranging from 0.001 to 0.4. We consider mixed pebbles as having dust-to-ice ratios between 0.5 and 10. We investigate four typical cloud masses, M, between 2.6 × 10 14 (very low) and 2.6 × 10 23 g (high). Results. Except for the very low-mass cloud (M = 2.6 × 10 14 g), silica pebbles are always compressed during the collapse and attain volume-filling factors in the range from φ V ≈ 0.22 to 0.43, regardless of φ 0 . Ice pebbles experience no significant compression in very low-mass clouds. They are compressed to values in the range φ V ≈ 0.11 to 0.17 in low-and intermediate-mass clouds (M = 2.6 × 10 17 −2.6 × 10 20 g); in high-mass clouds (M = 2.6 × 10 23 g), ice pebbles end up with φ V ≈ 0.23. Mixed pebbles obtain filling factors in between the values for pure ice and pure silica. We find that the observed cometary density of ∼0.5 g cm −3 can only be explained by either intermediate-or high-mass clouds, regardless of φ 0 , and also by either very low-or low-mass clouds for initially compact pebbles. In any case, the dust-to-ice ratio must be in the range of between 3 ξ 9 to match the observed bulk properties of comet nuclei.

Context. Comet formation by gravitational instability requires aggregates that trigger the streaming instability and cluster in pebble-clouds. These aggregates form as mixtures of dust and ice from (sub-)micrometre-sized dust and ice grains via coagulation in the solar nebula. Aim. We investigate the growth of aggregates from (sub-)micrometre-sized dust and ice monomer grains. We are interested in the properties of these aggregates: whether they might trigger the streaming instability, how they compare to pebbles found on comets, and what the implications are for comet formation in collapsing pebble-clouds. Methods. We used Monte Carlo simulations to study the growth of aggregates through coagulation locally in the comet-forming region at 30 au. We used a collision model that can accommodate sticking, bouncing, fragmentation, and porosity of dust- and ice-mixed aggregates. We compared our results to measurements of pebbles on comet 67P/Churyumov-Gerasimenko. Results. We find that aggregate growth becomes limited by radial drift towards the Sun for 1 μm sized monomers and by bouncing collisions for 0.1 μm sized monomers before the aggregates reach a Stokes number that would trigger the streaming instability (Stmin). We argue that in a bouncing-dominated system, aggregates can reach Stmin through compression in bouncing collisions if compression is faster than radial drift. In the comet-forming region (~30 au), aggregates with Stmin have volume-filling factors of ~10−2 and radii of a few millimetres. These sizes are comparable to the sizes of pebbles found on comet 67P/Churyumov-Gerasimenko. The porosity of the aggregates formed in the solar nebula would imply that comets formed in pebble-clouds with masses equivalent to planetesimals of the order of 100 km in diameter.

We explore the growth of planetary embryos by planetesimal accretion up to and beyond the point where pebble accretion becomes efficient at the so-called Hill-transition mass. Both the transition mass and the characteristic mass of planetesimals formed by the streaming instability increase with increasing distance from the star. We developed a model for the growth of a large planetesimal (embryo) embedded in a population of smaller planetesimals formed in a filament by the streaming instability. The model includes in a self-consistent way the collisional mass growth of the embryo, the fragmentation of the planetesimals, the velocity evolution of all involved bodies, as well as the viscous spreading of the filament. We find that the embryo accretes all available material in the filament during the lifetime of the protoplanetary disc only in the inner regions of the disc. In contrast, we find little or no growth in the outer parts of the disc beyond 5-10 AU. Overall, our results demonstrate very long timescales for collisional growth of planetesimals in the regions of the protoplanetary disc where giant planets form. As such, in order to form giant planets in cold orbits, pebble accretion must act directly on the largest bodies present in the initial mass-function of planetesimals with little or no help from mutual collisions.

The dynamics of planetesimals plays an important role in planet formation because their velocity distribution sets the growth rate to larger bodies. When planetesimals form in the gaseous environment of protoplanetary discs, their orbits are nearly circular and planar due to the effect of gas drag. However, mutual close encounters of the planetesimals increase eccentricities and inclinations until an equilibrium between stirring and damping is reached. After disc dissipation there is no more gas that damps the motion and mutual close encounters as well as encounters with planets stir the orbits again. After disc dissipation there is no gas that can damp the motion, and mutual close encounters and encounters with planets can stir the orbits. The large number of planetesimals in protoplanetary discs makes it difficult to simulate their dynamics by means of direct N-body simulations of planet formation. Therefore, we developed a novel method for the dynamical evolution of planetesimals that is based on following close encounters between planetesimal-mass bodies and gravitational stirring by planet-mass bodies. To separate the orbital motion from the close encounters we employ a Hamiltonian splitting scheme, as used in symplectic N-body integrators. Close encounters are identified using a cell algorithm with linear scaling in the number of bodies. A grouping algorithm is used to create small groups of interacting bodies which are integrated separately. Our method can simulate a large number of planetesimals interacting through gravity and collisions at low computational cost. The typical computational time is of the order of minutes or hours, up to a few days for more complex simulations, compared to several hours or even weeks for the same setup with full N-body. The dynamical evolution of the bodies is sufficiently well reproduced. This will make it possible to study the growth of planetesimals through collisions and pebble accretion coupled to their dynamics for a much larger number of bodies than previously accessible with full N-body simulations.