Monte Carlo Simulation of Dust Particles in a Protoplanetary Disk: Crystalline to Amorphous Silicate Ratio in Comets

Abstract

The observationally inferred crystalline abundance in silicates in comets, which should have been formed in the outer region of a protoplanetary disk, is relatively high (∼10%–60%), although crystalline silicates would be formed by the annealing of amorphous precursors in the inner disk region. In order to quantitatively address this puzzle, we performed a Monte Carlo simulation of the advection/diffusion of silicate particles in a turbulent disk in a setting based on the pebble accretion model: pebbles consisting of many small amorphous silicates embedded in an icy mantle are formed in the outer disk region, silicate particles are released at the snow line, crystalline silicate particles are produced at the annealing line, silicate particles diffuse beyond the snow line, and they eventually stick to drifting pebbles to return to the snow line. In the simple case without sticking and with steady pebble flux, we show through the simulations and analytical arguments that the crystalline components in silicate materials beyond the snow line are robustly and uniformly ≃5%. On the other hand, in a more realistic case with sticking and with a decaying pebble flux, the crystalline abundance increases to ∼20%–25%, depending on the ratio of the decay to diffusion timescales. This abundance is consistent with the observations. In this investigation, we assume a simple steady-accretion disk. The simulations coupled with the disk evolution are needed for a more detailed comparison with observed data.