Dynamics of self-gravitating dust clouds and the formation of planetesimals

Due to the gravitational force, clouds of dust and gas in the interstellar medium can contract and form stars and planet systems. Here we show that if the dust grains are electrically charged then the self-gravitation can be balanced by the “electrostatic pressure” and the collapse can be halted. In this case, the dust cloud may form soft dust planets, having the weight of a small moon or satellite, but a radius larger than of our Sun. There exist a critical mass beyond which the dust cloud collapses and forms a solid planet. We here present a simple model for the dynamics and equilibrium of self-gravitating dust clouds and apply the model to typical parameters for dust in molecular clouds and in the interstellar medium. © 2005 Elsevier B.V. All rights reserved. PACS: 52.35.Hr; 52.65.Kj; 52.40.Db It has become more and more clear that dust plays a central role in the formation of stars and planets [1–5] and that dust is abundant both in planetary rings in our Solar system [6–8] and in the Earth’s atmosphere [9], as well as in laboratory and processing plasmas [10,11]. The standard model for the formation of a solar system is that a cloud of gas and dust collapses to form a central star. Due to the angular momentum in the material, some of the material forms a protoplanetary disk of dust and gas which spins around the star. Dust and ice particles grow by agglomeration [12] or by colliding and sticking to each other. Eventually, larger objects are formed which starts attracting material by their gravitational forces. Observations of the young (20 Myr) star β Pictoris reveal that it is surrounded by a dust disk which shows features of ∼ 10 μm-sized crystalline silica and olivine grains near the star, as well as of sub-μm dust grains in bands at a distance of 6, 16 and 30 AU from the star [1]. It is believed that most of this material has been generated from comets and planetesimals after that the original proto-planetary disk * Corresponding author. E-mail addresses: [email protected] (K. Avinash), [email protected] (B. Eliasson), [email protected] (P.K. Shukla). 0375-9601/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.physleta.2005.12.061 was formed [13]. This might be an early stage of a Solar system. We here present a scenario which could lead to the formation of planets directly from interstellar dust without the initial formation of a central star. This could happen if the dust cloud has a mass of a satellite or of a small planet, i.e., much less than the mass of a star. If the dust particles are immersed in an ionized gas, they will be charged electrically—typically the electric charge is negative due to the attachment of electrons onto the grain surface [14]. Various turbulent processes in the dilute interstellar medium [15] can produce density fluctuations in the dust. The self-gravity in the dust then leads to an instability [16–18] where the dust contracts into separate dust clouds in space. When the negatively charged dust grains become densely enough packed in the dust cloud, a large part of the electrons are absorbed by the dust grains and there will be an overweight of free positively charged ions compared to free electrons. A negative potential is then set up in the cloud that balances the ion pressure and prevents the ions from escaping the dust cloud. The Coulomb force on the dust due to this potential behaves like an effective pressure force, i.e., it expels particles from the regions of high density. Hence it balances the gravitational force to halt the collapse of the dust cloud. In Fig. 1 we illustrate the geometry of a dust cloud where the gravitational force acting on 106 K. Avinash et al. / Physics Letters A 353 (2006) 105–108 Fig. 1. The geometry of a spherically symmetric dust cloud with radius R. At equilibrium, the attractive gravity force mdg acting on a dust grain is balanced by the repulsive electric force qdE. Here, md and qd are the mass and electric charge, respectively, of the dust grain, while g and E are the gravity and the electric field, respectively. the dust grains is balanced by the electric force. Based on this physics, dust cloud equilibria have recently been constructed [19]. Here we concentrate on the time dependent dynamics and the stability of the dust cloud. It should be noted that these equilibria are strictly quasi-neutral and hence are different from the earlier work where gravitation was balanced by the electric field arising due to charge separation [16–18]. In a fluid description, the dynamics of a spherically symmetric dust cloud can be described by the dimensionless continuity and momentum equations