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# 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 τS ~ 1, and so move with the maximum radial drift speed.

## Activity 3

1. Consider a thin protoplanetary disc with aspect ratio H/r = 0.05 and dimensionless pressure constant n = 3. Calculate the radial drift speed for a particle with τS = 1 at 1 au from a star of mass 1 M☉. Hint: the Keplerian speed at 1 au from a 1 M☉ star as calculated in Activity 1 is vK = 29.8 × 103 m s-1.

2. Moving at the constant speed from part (a), how long would the particle take to travel a distance of 1 au? Express your answer in terms of the number of orbital periods at 1 au.

### Discussion

1. In this case,

   so with τS = 1, the radial drift speed is

   (Note that this is equal to Δv, calculated in Activity 1, which is as expected according to the expression for the maximum radial drift speed derived earlier for the case τS = 1.)

2. The time t to travel a distance of 1 au radially at the speed from part (a) is

   Since the orbital period at a distance of 1 au from a 1 M☉ star is 1 y = 3.16 × 107 s, this timescale is only about 40 orbital periods.

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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