Planetesimal formation around the snow line: II. Dust or pebbles?

Context. Forming planetesimals is a major challenge in our current understanding of planet formation. Around the snow line, icy pebbles and silicate dust may locally pile up and form icy and rocky planetesimals via a streaming instability and/or gravitational instability. The scale heights of both pebbles and silicate dust released from sublimating pebbles are critical parameters that regulate the midplane concentrations of solids. Aims. Here, using a realistic description of the scale height of silicate dust and that of pebbles, we wish to understand disk conditions for which a local runaway pile-up of solids (silicate dust or icy pebbles) occurs inside or outside the snow line. Methods. We performed 1D diffusion-advection simulations that include the back-reaction (the inertia) to radial drift and diffusion of icy pebbles and silicate dust, ice sublimation, the release of silicate dust, and their recycling through the recondensation and sticking onto pebbles outside the snow line. We used a realistic description of the scale height of silicate dust obtained from a companion paper and that of pebbles including the effects of a Kelvin-Helmholtz instability. We study the dependence of solid pile-up on distinct effective viscous parameters for turbulent diffusions in the radial and vertical directions (αDr and αDz) and for the gas accretion to the star (αacc) as well as that on the pebble-to-gas mass flux (Fp/g). Results. Using both analytical and numerical approaches, we derive the sublimation width of drifting icy pebbles which is a critical parameter to characterize the pile-up of silicate dust and pebbles around the snow line. We identify a parameter space (in the Fp/g - αacc - αDz(= αDr) space) where pebbles no longer drift inward to reach the snow line due to the back-reaction that slows down the radial velocity of pebbles (we call this the "no-drift"region). We show that the pile-up of solids around the snow line occurs in a broader range of parameters for αacc = 10-3 than for αacc = 10-2. Above a critical Fp/g value, the runaway pile-up of silicate dust inside the snow line is favored for αDr∕ αacc ≪ 1, while that of pebbles outside the snow line is favored for αDr∕ αacc ~ 1. Our results imply that a distinct evolutionary path in the αacc - αDr - αDz - Fp/g space could produce a diversity of outcomes in terms of planetesimal formation around the snow line.