Planetary Sciences American and Soviet Research/Proceedings from the U.S.-U.S.S.R. Workshop on Planetary Sciences (1991) / Chapter Skim
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7. Formation of Planetesimals
7. Formation of Planetesimals
Pages 82-97
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From page 82... ...
Previous models of coagulation assumed that aggregates were compact bodies with uniform density, but it is likely that early stages of grain coagulation produced fractal aggregates having densities that decreased with increasing size. Fractal structure, even if present only at sub-millimeter size, greatly slows the rate of coagulation due to differential settling and delays the concentration of solid matter to the central plane.
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From page 83... ...
It is necessary to understand the aerodynamic processes that affected these small bodies in order to understand how planetesimals formed. The most common assumption is that planetesimals resulted from localized gravitational instabilities within a dust layer in the central plane of the nebular disL Such a layer is assumed to form by settling of grains through the quiescent gas due to the vertical component of solar gravity.
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From page 84... ...
It is plausible to assume that the temperature and density decrease with increasing heliocentric distance. Some accretion disk models of the nebula have ~ approximately constant, but equation (3)
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From page 85... ...
where m is the particle mass, V its velocity relative to the gas, and FD is the drag force. The functional form of ED depends on the Knudsen number (ratio of mean free path of gas molecules to particle radius)
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From page 86... ...
In addition to the problem of settling time scale, there is another argument for growth of particles by sticking. A very slight amount of turbulence in the gas would suffice to prevent gravitational instability.
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From page 87... ...
A particle would tend to settle toward the central plane until systematic settling velocity is of the same order as the turbulent velocity, Vie. From this condition, we can estimate the turbulent velocity that allows the dust layer to reach a particular density (Weidenschilling 1988)
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From page 88... ...
If the solids/gas ratio exceeds unity, and the particles are strongly coupled to the gas by drag forces, then the layer behaves as a unit, with gas and dust tending to move at the local Kepler velocity. There is then a velocity difference of magnitude /`V between the dust layer and the gas on either side.
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From page 89... ...
A typical result of those simulations shows particle growth dominated by differential settling. Because the growth rate increases with z, large particles form in the higher levels first, and "rain out" toward the central plane through the lower levels.
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From page 90... ...
For a fractal aggregate, te increases much more slowly with size. Meakin has developed computer modeling procedures to determine the mean projected area of an aggregate, as viewed from a randomly selected direction (Meakin and Donn 1988; Meakin, unpublished)
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From page 91... ...
We assume that in the free molecular regime, when aggregates are smaller than the mean free path of a gas molecule (> cm in typical nebular models) , te is proportional to the mass per unit projected area (m/A)
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From page 92... ...
D = 3 assumes coagulation produces a spherical body with the density of the separate components (liquid drop coalescence)
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From page 93... ...
COAGULATION AND SETTLING OF FRACTAL AGGREGATES We have modeled numerically the evolution of a population of particles in the solar nebula with fractal dimension of 2.11, using the response time of equation (18~. The modeling program is based on that of Weidenschilling (1980~.
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From page 94... ...
s or t0 4 for D = 3. Thus, particle sizes increase more rapidly for thermal coagulation of fractal aggregates, due to their larger collisional cross-sections.
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From page 95... ...
assumes that the mass available to the larger aggregate is in much smaller particles, so that the relative velocity is essentially equal to the larger body's settling rate. Thermal coagulation tends to deplete the smallest particles most rapidly, creating a narrowly peaked size distribution, and rendering differential settling ineffective.
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From page 96... ...
The time scale for settling to the central plane may have been one or two orders of magnitude greater than estimates which assumed compact particles. The inefficiency of settling by "raining out" suggest that a significant fraction of solids remained suspended in the form of small particles until the gas was dispersed; the solar nebula probably remained highly opaque.
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From page 97... ...
Span ScL 51:133. idenschUling, S.1.
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