The Brownian Motion of Dust Particles in the Solar Nebula: An Experimental Approach to the Problem of Pre-planetary Dust Aggregation

Abstract

Laboratory experiments were performed to study the Brownian motion of μm-sized dust grains and small aggregates under pre-planetary nebula conditions, i.e., in a thin gas atmosphere (Epstein drag regime), in the ballistic limit, and under microgravity conditions. The results of these experiments, i.e., the grain diffusivities, are in quantitative agreement with theoretical predictions for single spherical grains. Deviations from particle sphericity, i.e., in our case aggregates consisting of monodisperse spherical grains, cause only minor deviations between the Epstein drag formula for spheres and our experimental results for equal particle cross section. Thus, we find a quantitative agreement of our measurements with the Epstein relationD∝ 1/σabetween grain diffusivity and geometrical (aerodynamic) cross section.The results of our investigations can be used for the calculation of the gas–grain stopping time τf= ϵ (m/σa) (1/ρgvm) which, in turn, is an important grain characteristic for the calculation of pre-planetary dust aggregation. Here,mand σaare the mass and the aerodynamic, i.e., geometric cross section of the grain, ρgandvmare the mass density of the gas and the mean thermal velocity of the gas molecules, and ϵ is a proportionality factor which we determined to be ϵ = 0.68 ± 0.10. The gas–grain stopping time describes the strength of grain coupling to a given gas motion and its value determines relative velocties and, hence, collision frequencies between dust grains due to sedimentation, drag-induced orbital decay, and gas turbulence in the solar nebula.