2.2 Assembling the planetesimals

Thanks to the coupling with the disc, small (sub-micron-sized) particles will collide with each other gently enough that they will always stick together. Therefore, they will efficiently form millimetre-sized aggregates, in a process referred to as coagulation, that tend to settle on the midplane of the disc.

The simplest assumption for the formation of a planetesimal is that this process continues up to the kilometre-sized scale. As the particles grow, however, so does their speed, and the outcome of a collision no longer necessarily leads to bigger objects, as energetic impacts can be neutral (so the particles will bounce off each other) or even destructive (so the particles fragment and are broken apart once more).

However, there is also another problem that occurs around the metre-sized scale, as illustrated by the following activity. Metre-sized particles, referred to as ‘rocks’ will have τ_S ~ 1, and so move with the maximum radial drift speed.

Activity 3 showed that the radial drift for metre-sized particles can be very rapid. Radial drift therefore reduces the abundance of rocks in the outer regions of the disc, while potentially increasing it in the regions closer to the star. The fact that rocks move through the disc very rapidly gives rise to the ‘metre-sized barrier problem’ in explaining how planetesimals form: the growth to kilometre-sized planetesimals must happen fast enough to be complete before the medium-sized particles drift toward the centre, but also occur via a mechanism that avoids fragmentation.

Figure 5 shows a schematic view of the current picture of planetesimal formation. Once smaller fragments have formed, they settle vertically into the disc: see Figure 5(a). Next, the fragments drift radially towards the centre, leading to a possible build-up of solids in the inner disc: see Figure 5(b). Over-densities of solid material form through streaming instabilities and then lead to the formation of planetesimals through gravitational collapse: see Figure 5(c).

Figure 5 Schematic illustration of the formation of planetesimals.

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The figure has three parts: In part (a), a cross-section of a protoplanetary disc is shown. The cross-section resembles a triangle, which is broader on the right and tapers towards the left. The leftward arrow at the left end is labelled ‘to star’. A thin green layer is shown bounding the top and bottom surfaces of the disc. The interior of the disc is a blue region having two groups of black dots of varying sizes. From each of the black dots near the top surface, a downward arrow is shown. From each of the black dots near the bottom surface, an upward arrow is shown. This diagram is labelled ‘coagulation and vertical settling’. Part (b) shows the same cross-section of a protoplanetary disc. Now, the blue region is empty. A series of short leftward arrows is shown in a horizontal line passing through the middle of the disc. These arrows are labelled ‘radial drift’. The middle portion of the disc is labelled ‘possible pile-up of solids in inner disc’. A rectangular section of the middle portion of the blue region is magnified. In the magnified image, two thin green bands are shown between thick blue bands. These thin bands are labelled ‘gravitational collapse of streaming instability over-densities’. In part (c), the same cross-section is shown. Now the blue region is filled with black dots. The dots nearer to the green bands at the top and at the bottom are smaller in size, while the dots lying in the middle portion of the blue region are larger in size. The smaller dots are labelled ‘remaining solids’. This diagram is labelled ‘formation of planetesimals with a range of initial masses’.

Figure 5 Schematic illustration of the formation of planetesimals.