  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
annealing of amorphous precursors in the disk inner region. In order to
quantitatively address this puzzle, we have performed Monte Carlo simulation of
advection/diffusion of silicate particles in a turbulent disk, in the setting
based on pebble accretion model: pebbles consisting of many small amorphous
silicates embedded in icy mantle are formed in the disk outer region, silicate
particles are released at the snow line, crystalline silicate particles are
produced at the annealing line, the silicate particles diffused beyond the snow
line, and they eventually stick to drifting pebbles to come back to the snow
line. In a simple case without the sticking and with a steady pebble flux, we
show through the simulations and analytical arguments that crystalline
components in silicate materials beyond the snow line is robustly and uniformly
~ 5%. On the other hand, in a more realistic case with the sticking and with a
decaying pebble flux, the crystalline abundance is raised up to ~ 20-25%,
depending on the ratio of decay and 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 is
needed for more detailed comparison with observed data.
