Gravitation clumping

Within this new higher density medium, it is nonetheless possible for gravitational clumping to occur and for bodies of sizes of the order of 1 km to form. 

Myr through runaway accretion (Pollack et al., 1996). However, such a nebula is likely to be marginally gravitationally unstable, a situation that could result in the rapid formation of gas giant planets in a few thousand years by the formation of self-gravitating clumps of gas and dust (Boss, 1997, 2000, 2002b). 

A more promising model involves the concentration of millimeter-sized particles in stagnant regions between the smallest eddies, forming gravitationally bound clumps (Cuzzi et al. 2001). Calculations show that turbulence can increase the local solid/gas density up to 100 (i.e. 104 times that in the protoplanetary disk as a whole), at which point the high particle density tends to shut off the turbulence (Cuzzi et al. 2008). 

If a gravitationally bound clump forms, the relative velocities of the particles within the clump must be damped before the clump can collapse to form a solid planetesimal. Gas drag and particle-particle collisions will do this, with damping being more effective for small particles. The collapse rate is limited by the pressure of gas within the clump - as particles move inwards, the gas becomes compressed, opposing further collapse (Cuzzi Weidenschilling 2006). The rate of collapse is set by the time required for particles to settle to the center, which may be hundreds of orbital periods for millimeter-sized particles (Cuzzi Weidenschilling 2006). 

Low-density clumps orbit the star at roughly Keplerian speeds, while gas in the surrounding disk typically orbits at 50m s-1 more slowly. As a result, clumps are vulnerable to disruption by the ram pressure of the gas. However, numerical simulations suggest that the mutual gravitational attraction of solid particles within a clump is sufficient to keep them largely intact during collapse, provided the initial clump is > 103 km in diameter (Cuzzi et al. 2008 see Figure 10.3). 

In this model, large gravitationally bound clumps form only occasionally, which would explain why planetesimal formation in the Asteroid Belt continued for several million years. This mechanism also reproduces the narrow size distribution of chondrules seen in chondritic meteorites (Cuzzi et al. 2001). While the mean chon-drule size differs from one meteorite type to another, the size distributions closely... 

Figure 10.3 The effect of ram pressure acting on a clump of particles in a gas disk. The six panels show the positions of the particles after 1.75 orbital periods. Each point in the plots is a superparticle representing a large number of millimetersized objects. The clump is initially 10 model units in diameter, equivalent to 104 km. Upper panels (front, above, and side views) without any cohesion, the clump is soon shredded. Lower panels when gravitational forces between particles are included, the clump remains mostly intact and becomes more compact. From Cuzzi et al. (2007).

Clump Formation in a Marginally Gravitationally Unstable Disk... 

At present, it is unclear whether the protoplanetary nebula could have evolved to the point where it was marginally unstable, or whether disk instabilities would have redistributed mass in the disk prior to the formation of gravitationally bound clumps. If marginally unstable disks do develop, then giant-planet formation by disk instability seems unavoidable. It is worth noting that current simulations of disk instability tend to generate planets with masses greater than... 

Gases and grains in interstellar clouds probably experienced many shock events during the formation of planetesimals and meteorites. These events are as follows 1) coagulation of dust into clumps, which settle to the equatorial plane of the nebula 2) breakup of the gravitationally unstable dust disk into clusters of dust clumps 3) coalescence of the clusters into 1 km planetesimals ... 

A suspension is a dispersion of particles within a solvent (usually a low-molar-mass liquid). Thermodynamics (Brownian motion and collisions) favours the clumping of small particles, and this can be increased by flow. However, particles over 1 pm tend to settle under gravity, unless stability measures have been considered (matching the density of the particle to that of the medium, increasing the Brownian/gravitational force ratio, electrostatic stabilization, steric stabilization). Other complications can occur in the dynamics of suspensions, such as particle migration across streamlines, particle inertial effects and wall slip (Larson, 1999). 

Interstellar gas and icy or refractory dust composed of silicates and carbonaceous material provide the raw material for the formation of stars and planets. More than 4 billion years ago, the gravitational collapse of an interstellar cloud led to the formation of a protosolar disk (the solar nebula) with a central condensation developing into our sun (42,43). Clumps of small particles in the solar nebula grew bigger, accreted more and more material, eventually forming planets or moons. 

A common simplifying assumption is that matter is distributed uniformly throughout the universe, subject to gravitational interaction. On this basis Newton could argue that in a universe of limited size all matter would eventually clump together in a central mass. Dynamic equilibrium, as observed, can only develop in an infinite universe. The resultant gravitational field should vanish everywhere, but local instabilities can give rise to the formation of stars and solar systems. The metric of such a system is clearly Euclidean. 

Jeans instability Instability in a cloud of gas in space due to fluctuations in the density of the gas, causing the matter in the cloud to clump together and lead to gravitational collapse. The conditions under which this occurs were worked out by Sir James Hopwood Jeans (1877-1946) in terms of Newtonian gravity. The analogous analysis of this problem using general relativity theory is the basis of the theory of structure formation. 

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