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Astron. Astrophys. 356, 1089-1111 (2000)

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5. Conclusion

This article follows the numerical works of Barge & Sommeria (1995), Tanga et al. (1996), Bracco et al. (1999) and Godon & Livio (1999c) concerning the interaction between dust particles and large-scale vortices in the solar nebula. The originality of our study is to start from an exact and realistic solution of the fluid equations and to provide analytical results and relevant parameters for the trapping process. Moreover, we have considered for the first time the effect of small-scale turbulent fluctuations on the motion of the particles and determined an explicit expression for the escape time by solving a problem of quantum mechanics. These theoretical results have been formulated in the context of Keplerian disks and planet formation but they can clearly have applications in other fields of astrophysics and geophysics, for example the transport of polluants in the Earth's atmosphere.

The vortex scenario provides an attractive mechanism to form planetesimals on very short time scales. This does not contradict the overall picture of planet formation which has been developed over the last decades. On the contrary, it fills the gap between two domains which were difficult to connect: sticking processes are still necessary to produce centimetric particles and collisions between planetesimals is of course the main engine of planet's growth. In between, the vortex scenario could come at work to facilitate, at some preferred locations of the disk, the Safronov-Goldreich-Ward instability which was initially proposed for forming planetesimals.

The predictions of the vortex model are remarkably consistent with the structure of the solar system. The capture process is optimal at two preferred locations of the nebula which correspond, for relevant sizes of the particles (i.e. some centimeters), to the position of telluric and giant planets. The transition between the two groups of planets happens to coincide with the passage from the Stokes to the Epstein regime where the gas drag law changes. The asymmetry between the two optima may be ascribed to the size of the vortices which are bigger in the outer zone.

Of course, the results discussed here rely upon the existence of vortices in the disk. Their presence in the solar nebula is reasonable due to the ubiquitous appearance of vortices in rotating flows and two-dimensional turbulence. However, numerical simulations and even laboratory experiments are necessary to ascertain their existence in Keplerian flows. A first step was undertaken by Bracco et al. (1998,1999) and Godon & Livio (1999a,b,c) who observed the formation of anticyclones developing from an energetic random initial vorticity field in a Keplerian flow. More work remains to be done to understand the generation (and maintenance) of vorticity in such disks (convection, baroclinic instability...) and to determine the effect of three-dimensionality (Hodgson & Brandenburg 1998) on the stability of theses vortices.

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© European Southern Observatory (ESO) 2000

Online publication: April 17, 2000