Quasi-Equilibrium Density Distributions of Small Dust Aggregations in the Solar Nebula

The rotational velocity of a fluid element around the midplane of the solar nebula increased as dust settled toward the midplane. The Kelvin and Helmholtz instability due to velocity difference of a dust-rich region and a dust-poor region should have occurred and the dust layer became turbulent when the Richardson number decreased below the critical value. Then, dust aggregations stirred up due to turbulent diffusion and were prevented to settle further. In this paper, the sizes of dust aggregations are assumed to be equal to or smaller than the typical radius of chondrules (~0.3 mm). In this case, even very weak turbulence stirs up dust aggregations. Therefore a dust density distribution is considered to be self regulated so that the Richardson number is nearly equal to the critical value. The quasi-equilibrium dust density distribution is derived analytically by assuming that the Richardson number is equal to the critical value. The derived dust density at the midplane is much smaller than the critical density of the gravitational stability, if the solar composition of dust to gas ratio is assumed. On the other hand, the dust aggregations concentrate around the midplane and the dust layer becomes gravitationally unstable, if more than 97% (at 1 AU from the Sun) of the gaseous components have been dissipated from the nebula, leaving dusty components. Two alternative scenarios of planetesimal formation are proposed: planetesimals were formed by (1) mutual sticking of dust aggregations by nongravitational forces or by (2) gravitational instabilities in the nebula where the dust to gas ratio is much larger than the ratio with solar elemental abundance. Case (2) might be realized due to dissipation of the nebular gas and/or addition of dust by the bipolar outflow. In case (1), chondrule sizes do not indicate the maximum size of dust aggregations in the solar nebula.