Planetesimal Formation in the Protoplanetary Nebula

In this talk we will address two distinct phases of planetesimal formation, each of which is fundamentally dependent upon the coupled interactions of particles and turbulent nebula gas. It has been shown both numerically and experimentally that 3-D (three dimensional) turbulence concentrates aerodynamically size-selected particles by orders of magnitude. In a previous review chapter we illustrated the initial predictions of Turbulent Concentration (TC) as applied to the solar nebula. We predicted the particle size which will be most effectively concentrated by turbulence; it is the particle which has a gas drag stopping time equal to the overturn time of the smallest (Kolmogorov scale) eddy. The primary uncertainty is the level of nebula turbulence, or Reynolds number Re, which can be expressed in terms of the standard nebula eddy viscosity parameter alpha = Rev(sub m)/cH, where v(sub m) is molecular viscosity, c is sound speed, and H is vertical scale height. Several studies, and observed lifetimes of circumstellar disks, have suggested that the level of nebula turbulence can be described by alpha = 10(exp -2) - 10(exp -4). There is some recent concern about how energy is provided to maintain this turbulence, but the issue remains open. We adopt a canonical minimum mass nebula with a range of alpha is greater than 0. We originally showed that chondrule-sized particles are selected for concentration in the terrestrial planet region if alpha = 10(exp -3) - 10(exp -4). In addition, Paque and Cuzzi found that the size distribution of chondrules is an excellent match for theoretical predictions. One then asks by what concentration factor C these particles can be concentrated; our early numerical results indicated an increase of C with alpha, and were supported by simple scaling arguments, but the extrapolation range was quite large and the predictions (C is approximately equal to 10(exp 5) - 10(exp 6) not unlikely) uncertain. The work presented here, which makes use of our recent demonstration that the particle density field is a multifractal with flow-independent properties provides a far more secure ground for such predictions. We also indicate how fine-grained dust rims on chondrules might enter into constraining the situation. Once large particles (meter-size mass equivalent) reach the midplane, perhaps in the form of dense aggregates of the sort formed in 3D turbulence, they remain stable against gravitational instability but might grow rapidly by accretion of their drifting neighbors, depending on the level of global turbulence.