A protoplanetary disk is the place where the chemical diversity of dust, the original consitutients of planets, is formed through various chemical reactions. Because a variety of reactions occurs over a wide temperature range, the chemical diversity of dust results in the radial gradient of chemical properties. This study aims to predict “a reaction line” of a certain reaction in a protoplanetary disk.
We made 3D Monte Carlo simulations to evaluate the progress of fictitious irreversible reactions, of which progress is given by the Johnson-Mehl-Avrami equation, of dust moving diffusively and advectively in steady accretion disks with uniform viscous heating. We evaluated trajectories of 10,000 dust particles well coupled with disk gas with different sets of alpha viscosity (0.01 and 0.001) and mass accretion rates (1, 0.1, and 0.01 solar mass/Myr). The reaction parameters varied in the ranges of the Avrami index of 0.5?4.0, the logarithm of pre-exponential factor (1/sec) of 10?60, and the activation energy (kJ/mol) of 20?1000. The highest temperature that each particle experienced before the reaction proceeds up to a certain reaction degree (0.8, 0.9, or 0.99) was recorded.
Histograms of the highest temperature were fitted by the log-normal distribution. We define the mode temperature and the dispersion of the distribution as a reaction line temperature and its dispersion. We obtained semi-analytical formulas for the reaction line temperature and its dispersion by comparing between a reaction timescale and a local diffusive timescale of dust to explain the numerical results. The prediction formulas, given as a function of the reaction parameters and the disk parameters, reproduce the numerical simulations within 5.5% for the reaction line temperature and 24% for the dispersion in a wide temperature range. The obtained equations can be a powerful tool to discuss the progress of various reactions and their spatial distribution.