Clump formation due to the gravitational instability of a multiphase medium in a massive protoplanetary disc

Planetary systems form in gas-dust protoplanetary discs via the growth of solid bodies. In this paper, we show that the most intriguing stage of such growth --- namely, the transformation of 1-10 m boulders into kilometre-sized planetesimals --- can be explained by a mechanism of gravitational instability. The present work focused on the origin of self-gravitating clumps in which planetesimal formation could take place. Our computer simulations demonstrated that such clumps of gas and boulders formed due to the development of a two-phase instability. This instability revealed a so-called 'mutual influence effect' in the protoplanetary disc, where the dynamics of the system were determined by the collisionless collective motion of a low-mass subdisc composed of primary solids. We found that a 0.1 $c_s$ velocity dispersion in the boulder subdisc was sufficient to cause the formation of self-gravitating clumps of gas and boulders. In such regimes, the time needed for the formation of the collapsing objects was less than the boulders' dissipation time in the density waves of the medium.