Mtbf, Mttf, Mttr, y Mtbs

The typical lifetime of a protoplanetary disc is about 106-107yrs (Muzerolle et al., 2010). During this time the disc gradually clears the diffuse dust, incorporating it in larger objects and planets. The mechanism that leads from micron sized dust grains to the formation of planets differs for terrestrial rocky planets and gas giant planets. The former are supposed to form through sticking and coagulation of dust grains, in a process described by the Core Accretion model (Mizuno, 1980; Pollack et al., 1996). For the latter there are currently two main theories: the just mentioned Core Accretion and the Gravitational Instability (Boss, 1997). Recently, a third one was proposed, the Tidal Downsizing Hypothesis (Nayakshin, 2010), with the advantage of solving some issues of the previous theories.

In the Core Accretion model dust grains stick together until they form planetesimals and then planets. The first phases are similar for all kinds of planets, but if planetesimals become big enough, they can eventually attract gas and give origin to giant planets. In this model, however, it is difficult to explain how the passage from micron-sized dust grains to km-sized planetesimals occurs, because above one meter diameter collisions would make objects bounce and shatter rather than sticking together (Blum & Wurm, 2008).

The Gravitational Instability model, on the other hand, starts from the collapse of the solar nebula in clumps of dust and gas. This model, first proposed by Kuiper (1951), was improved by Boss (1997) to include the presence of rocky cores in giant plantes. Starting from a mix of gas and dust, owing to gravitation, dust and heavier materials would sink toward the centre of the clump, while gas would surround the central core. This model

1.6. From dust to planets

mainly explains the formation of giant planets, but not of terrestrial planets.

The Tidal Downsizing tries to overcome issues from both theories. In this model, planet formation starts from the collapse of the protoplanetary disc into clumps as in the Gravitational Instability, but subsequently, during migration to the central star, planet- embryos may lose the external shell and be left with a rocky core, typical of terrestrial planets. This theory seems to solve the issues related to both the previous models, although it may not work in some circumstances, as the authors explained: the initial clumps need to be isolated or slowly accreted, otherwise they would become too hot and grain sedimentation would not occur. Further, the model depends on dust opacity, which in real protoplanetary discs is sometimes not well known. In any case, it offers a new perspective and provides new suggestions in the planet formation mechanism.

1.6.1 Mechanisms of dust grain growth

Despite the uncertainty on the process of dust growth, the formation of planetesimals through sticking of smaller particles is widely accepted. In order to address the issue as to how very large objects can from from tiny dust grains, many laboratory experiments have been performed in the literature. The following description is taken from the reviews by Blum & Wurm (2008) and Testi et al. (2014).

Four important mechanisms have emerged in case of collisions of dust grains: sticking, bouncing, fragmentation and erosion, which depend on dust size, relative velocities and grain morphology. Particles will stick together when their sizes are of the order of microns, while with increasing size and speed they will first compact, then bounce and fragment.

However, if on one hand fragmentation is a barrier to the formation of planetesimal, on the other one it accounts for the presence of the observed small grains: Dullemond & Dominik (2005) pointed out that the sticking process alone would deplete small particles within a thousand years, while observations confirm their existence in protoplanetary discs, which are millions of years old. In this context, fragmentation becomes a means to replenish the discs of the missing small grains.

Not only size but also morphology and composition play a role in the outcome of collisions: micron-sized spherical particles will stick only if their relative velocities are below 1 ms−1_{, but this threshold can increase to tens of meters per second if dust grains}

have an irregular shape or if they are made of water ice instead of silicate.

Particles can grow in size also through mass transfer, which happens when small grains impact larger agglomerates. However, if the colliding grain is below a certain mass thresh- old the outcome will be erosion instead. The formation of planetesimal is therefore a complex process which involves many mechanisms, responsible not only for their creation but also destruction. Hence, other secondary effects have been proposed to overcome the barriers which can hinder dust growth: the presence of organic material with particular high sticking efficiency, magnetised grains, or secondary agglomeration dependent on the surrounding environment. Charged particles can also favour coagulation of dust aggre- gates, according to Ivlev & Morfill (2002), although this result seems to be in contrast with the “charge barrier” highlighted by Okuzumi (2009), and which would prevent particles from sticking especially in the first stages.

Dust grain size can be also inferred from some properties of their emitted light. The measurement of dust growth from observational data and its analysis through models will be the topic of Chapter 5.