Stis

Solar System to Scale

Fig. 5.22 Coronographic images of the disk of P Pic obtained with the STIS instrument on the HST. Top : overall image; bottom: enlargement of the central portion, with a vertical exaggeration of 4 times, to reveal the warping of the disk. The intensity (and thus the quantity of dust) is a maximum near the equatorial plane (After Heap et al., 2000)

portion shows that the disk there is warped over a distance of about 100 AU. It appears to be devoid of material in the very centre out to a radius of about 20 AU.

The images of the disk obtained in the visible and infrared have enabled constraints to be set of the size distribution of the grains and their spatial distribution. The dimensions range form the sub-micron to the millimetre, with a maximum between 1 and 20 |m. The scattering properties of the grains (Artymowicz, 2000) have been obtained from visible-light coronographic images of the central region. They suggest a composition that is basically crystalline silicates (olivine and pyroxene). The high albedo (>0.4) differentiates the material from that in the rings or the small bodies in the Solar System, which is darker.

Spectroscopic observation of the disk in the visible and UV regions has revealed an unexpected phenomenon. Certain narrow lines of neutral atoms (Na, C) or ionized atoms (Ca+, Mn+, Fe+, Zn+) are observed repeatedly. They have allowed the abundance of the gas to be determined: the gas/dust ratio thus obtained is very low (< 3 x 10-3), whereas it is estimated to have been 100 in the early Solar System. So the disk of P Pic is therefore devoid of gas, which suggests that the low fraction that is observed to be present derives from evaporation or collisions between the small bodies.

This theory is reinforced by the discovery in visible and UV spectra of variable lines, that are strongly shifted towards the red (Vidal-Madjar et al., 1994; Lecavelier des Etangs et al., 2000; Fig. 5.23). These have been interpreted as the signature of

Fig. 5.23 The spectrum of P Pic in the Ca+ line. Top: The scale on the abscissa is the velocity in km/s. The stable component corresponds to a velocity of 20 km/s relative to the star. Two components shifted towards the red are also detected, one narrow one at 50 km/s and the other, wider one at 100 km/s. Centre: Geometrical model of the phenomenon. Bottom: Numerical simulation based on the model (After Lecavelier des Etangs et al., 2000)

Fig. 5.23 The spectrum of P Pic in the Ca+ line. Top: The scale on the abscissa is the velocity in km/s. The stable component corresponds to a velocity of 20 km/s relative to the star. Two components shifted towards the red are also detected, one narrow one at 50 km/s and the other, wider one at 100 km/s. Centre: Geometrical model of the phenomenon. Bottom: Numerical simulation based on the model (After Lecavelier des Etangs et al., 2000)

planetesimals, typically 1 km in diameter, that are evaporating and falling onto the central star with velocities that may reach 300 km/s. The frequency of these events, which varies from one year to the next, may be as many at 200 per year.

Could this mechanism explain the longevity of the disk around P Pic? Taking account of the thickness and size of the disk, the evaporation mechanism, which is perforce limited to the central region, is undoubtedly inadequate. We therefore need to imagine that multiple collisions occur at large distances from the star.

The frequency at which planetesimals decay onto P Pic is several orders of magnitude greater than the fall of comets into the Sun, which implies the existence of a different mechanism. Perturbations by planets could explain the phenomenon. Beust and Morbidelli (1996) have studied the effect of a massive planet with an eccentricity of 0.05; they have shown that its perturbations would lead to decay of particles in a 4:1 resonance after 10 000 revolutions.

Other factors also favour the theory that at least one planet exists within the disk around P Pic (Artymowicz, 2000): the dispersion in the orbital inclinations of the dust; certain photometric variations; the central gap at distances less than 40 AU; the asymmetries in the disk and the fact that it is warped. The last could be explained by the presence of a planet following an inclined orbit within the central gap, the existence of which it would also explain.

5.4 The Formation of Planetesimals and Planetary Embryos

How do planet form within the protoplanetary disk? They are the results of the accretion of dust particles, which have agglomerated into larger and larger bodies. For collisions between particles to lead to the formation of a larger body, and not simply result in their being dispersed in smaller fragments, there are specific limitations regarding the collision velocities, and the physical characteristics of the grains (internal cohesive force, porosity, etc. ...).

5.4.1 From Microscopic Particles to Centimetre-Sized Grains

The mechanism by which particles that are microscopic in size aggregate within a disk has been studied, particularly by Weidenschilling and Cuzzi (1993), and by Weidenschilling (1997). These particles stick together as a result of inelastic collisions and van der Waals forces acting on the surface of the grains. The rate and velocity of the collisions primarily depends on the properties of the gas, which is by far the largest component of the disk, in which the particles are suspended. The solid particles, being denser than the gas, tend to migrate towards the median plane, which has the effect of increasing the collision rate. The velocities of the small particles (which are less than 10 |m across) are linked to that of the gas surrounding them, and depend on its temperature, whereas the large bodies (with sizes greater than one kilometre) are subject to gravitational perturbations. At intermediate sizes, the particles are affected by the motion of the gas.

The first stage in accretion, caused by thermal motion, is possible thanks to the low relative velocities of the particles, which come to collide and then adhere to one another thanks to the van der Waals forces at their surface. The structures that result, which are both predicted by modelling and actually observed in the laboratory, are porous in nature, and fractal, up to sizes of about one centimetre (Weidenschilling, 2000).

5.4.2 From Centimetre-Sized Grains to Kilometre-Sized Bodies

The growth of the grains between sizes of a few centimetres to a few kilometres is not as well understood. The surface adhesion forces are inadequate, and gravity is still ineffective, with the drag force exerted by the gas still being far greater than the escape velocity from the surface of a small body. Safronov (1969) and Goldreich and Ward (1973) proposed a mechanism of gravitational instability causing a mass of material to collapse into a body about a kilometre across. This mechanism, however, cannot be involved, because of effects linked to turbulence, which keep the density below the critical value needed for collapse (Cuzzi et al., 1993). Although the clumping mechanism remains poorly understood, it may be noted that the drag exerted by the gas favours collisions between particles of different sizes, which have different velocities relative to one another.

Modelling the formation of planetesimals has been carried out for small icy bodies in the Solar System (Weidenschilling, 2000). The simulation takes as its starting point, grains 1 |m across uniformly mixed into a disk of given thickness. The results are shown in Fig. 5.24. After a time, t, equal to 1000 years, the peak of the distribution corresponds to grains that are centimetre-sized and which formed through thermal accretion, and which rapidly fall to the median plane and sweep up any small particles surrounding them. The mean plane becomes more and more dense, which favours the formation of a few larger bodies. As soon as the latter reach about a kilometre in size (at t = 2000 years), the escape velocities from their surface become greater than the radial velocities, and gravitational perturbations become significant.

Similar models have been constructed for other protoplanetary disks. The overall evolution of the size distributions is, on the whole, similar, and only the time scale changes. The time required to form planetesimals is proportional to the local orbital period. From 2000 years at 1 AU, it becomes 3 x 105 years at 30 AU, a time that is far less than the lifetime of protoplanetary disks. The presence of planets that have actually formed or are in the process of formation within these disks is therefore completely plausible.

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