Grain growth in the turbulent accretion disk solar nebula

We have studied the coagulation of grains in the turbulent accretion disk solar nebula, considering turbulent diffusion, radial drift, and supply of interstellar grains by accreting interstellar cloud. The space-time dependent mass spectrum of grains and the Rosseland mean grain opacity have been calculated. Before the accretional effect becomes noticeable, the mass spectrum n( m) is well-described by n( m) ∝ m^-1.31 for large grains and n( m) ∝ m^-1.03 for small grains. The boundary is at the grains with the friction times comparable to the inner time scale of the turbulence. If the turbulence is fully developed, the growth time of grains is about 20 to 40 times shorter than that for the laminar nebula. In case of weak turbulence with velocity fluctuation of 0.03 × sound speed, the time scale is the same order as that in the laminar nebula. The accretion builds up the reservoir of interstellar grains, from which new generations of grains grow. Finally the spectrum reaches a steady state, crudely approximated by n( m) ∝ m^-2. The grain opacity keeps constant as long as the mean grain radius of the first generation is smaller than the wavelength of radiation. The rapid increase is found at the end of this Rayleigh limit stage, and subsequently the opacity decreases as nearly (time) ^-2 owing to the grain growth. But the opacity increases again when the grains of the second generation grow as large as the wavelength and approaches a steady value. From these results, we have tried to describe the evolution of the nebula and the formation of planetesimals.