A "no-drift" runaway pile-up of pebbles in protoplanetary disks II. Characteristics of the resulting planetesimal belt

Abstract: Forming planetesimals from pebbles is a major challenge in our current understanding of planet formation. In a protoplanetary disk, pebbles drift inward near the disk midplane via gas drag and they may enter a dead zone. In this context, we identified that the backreaction of the drag of pebbles onto the gas could lead to a runaway pile-up of pebbles, the so-called no-drift mechanism. We improve upon the previous study of the no-drift mechanism by investigating the nature and characteristics of the resultant planetesimal belt. We performed 1D diffusion-advection simulations of drifting pebbles in the outer region of a dead zone by including the backreaction to the radial drift of pebbles and including planetesimal formation via the streaming instability. We considered the parameters that regulate gas accretion and vertical stirring of pebbles in the disk midplane. In this study, the pebble-to-gas mass flux ($F_{\rm p/g}$) was fixed as a parameter. We find that planetesimals initially form within a narrow ring whose width expands as accumulating pebbles radially diffuse over time. The system finally reaches a steady-state where the width of the planetesimal belt no longer changes. A non-negligible total mass of planetesimals (more than one Earth mass) is formed for a disk having $F_{\rm p/g} \gtrsim 0.1$ for more than $\sim 10-100$ kyr with nominal parameters: a gas mass flux of $\gtrsim10^{-8} {\rm M}\oplus$/yr, $\tau{\rm s} \simeq 0.01-0.1$, $\alpha_{\rm mid} \lesssim 10^{-4}$, and $\alpha_{\rm acc} \simeq 10^{-3}-10^{-2}$ at $r \lesssim 10$ au, where $r$, $\tau_{\rm s}$, $\alpha_{\rm mid}$, and $\alpha_{\rm acc}$ are the heliocentric distance, the Stokes number, and the parameters in a dead zone controlling the efficiencies of vertical turbulent diffusion of pebbles (i.e., scale height of pebbles) and gas accretion of the $\alpha$-disk (i.e., gas surface density), respectively.