turbulent viscosity when going from $256^3$ to $512^3$ (see [Sect. \[s:gas\]]{}). Therefore we had to use a stronger gravity in this paper, $\tilde{G}=0.5$ compared to $\tilde{G}=0.2$ in J07, to see bound particle clumps (planetesimals) forming. We discuss the implications of using a higher disc mass further in our conclusions.

In all simulations we divide the particle component into four size bins, with friction time $\varOmega\tau_{\rm f}=0.25,0.50,0.75,1.00$, respectively. The particles drift radially because of the headwind from the gas orbiting at velocity $u_y=-\Delta v$ relative to the Keplerian flow [@Weidenschilling1977a]. It is important to consider a distribution of particle sizes, since the dependence of the radial drift on the particle sizes can have a negative impact on the ability of the particle mid-plane layer to undergo gravitational collapse [@Weidenschilling1995].

The Minimum Mass Solar Nebula has column density $\varSigma_{\rm g}=1700(r/{\rm
AU})^{-1.5}\,{\rm g\,cm^{-2}} \approx150\,{\rm g\,cm^{-2}}$ at $r=5\,{\rm AU}$ [@Hayashi1981], and thus $\tilde{G}=0.042$ according to [Eq. (\[eq:Sigma\])]{}. Since we use $\sim$10 times higher value for $\tilde{G}$, the mean free path of gas molecules is only $\lambda$$\sim$$10\,{\rm cm}$. Therefore our choice of dimensionless friction times $\varOmega\tau_{\rm f}=0.25,0.50,0.75,1.00$ puts particles in the Stokes drag force regime [@Weidenschilling1977a]. Here the friction time is independent of gas density, 