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The streaming instability and Kelvin--Helmholtz instability are consideredthe two major sources causing clumping of dust particles and turbulence in thedust layer of a protoplanetary disk as long as we consider the dead zone wherethe magneto-rotational instability does not grow. Extensive numericalsimulations have been carried out in order to elucidate the condition for thedevelopment of particle clumping caused by the streaming instability. In thispaper, a set of two parameters suitable for classifying the numerical resultsis proposed. One is the Stokes number that has been employed in previous worksand the other is the dust particle column density that is nondimensionalizedusing the gas density in the midplane, Keplerian angular velocity, anddifference between the Keplerian and gaseous orbital velocities. The magnitudeof dust clumping is a measure of the behavior of the dust layer. Usingthree-dimensional numerical simulations of dust particles and gas based onAthena code v. 4.2, it is confirmed that the magnitude of dust clumping for twodisk models are similar if the corresponding sets of values of the twoparameters are identical to each other, even if the values of the metallicity(i.e., the ratio of the columns density of the dust particles to that of thegas) are different.

Two key parameters controlling particle clumping caused by streaming instability in the dead-zone dust layer of a protoplanetary disk