10:15 AM - 10:30 AM
[PCG20-06] Prediction Equation of Reaction Line: 3D Monte Carlo Simulation of Dust Particles
in a Protoplanetary Disk
Keywords:Protoplanetary disk, Protosolar disk, Reaction line, Dust, Chemical reaction
Solar-System celestial bodies formed through accumulation of dust in the Sun’s protoplanetary disk. Chemical reactions of dust in the dynamically evolving protoplanetary disk played an essential role in making chemically diverse bodies. Various reactions such as evaporation, condensation, solid-gas reaction, and crystallization occur in a wide range of temperature in different regions of the protoplanetary disk.
There have been several studies discussing chemical reactions of dust particles moving inward by accretion and randomly by diffusion (e.g., Ciesla & Sandford 2012; Okamoto & Ida 2022), but no systematic and comprehensive investigation has been made for various chemical reactions occurring at different temperatures in protoplanetary disks. In this study, we focus on developing a prediction equation of “reaction line temperatures” of various irreversible chemical reactions, considering dust particle movement in a steady accretion disk.
Three-dimensional Monte Carlo simulations (Ciesla 2010, 2011) were performed to evaluate trajectories of dust particles. The steady accretion disk model, heated by uniform viscous heating (α-viscosity model) is adopted. We assumed that the dust opacity is 2.5 cm2 g-1 and the central star has a solar mass Msun. We adopted α of 10-2 and 10-3 and the steady accretion rate Mflow of 10-6, 10-7 and 10-8 Msun yr-1. Ten thousand dust particles, of which movements were assumed to be well coupled with gas, were released at the H2O snowline in the disk midplane for each parameter set. The calculations continued for 106 years at the maximum.
The progress of fictitious irreversible reactions expressed by the Johnson-Mehl-Avrami (JMA) equation were examined. The degree of reaction, X, is set to be zero at the release from the snowline. For each timestep of the Monte Carlo simulation, the increment δX calculated by the differentiated JMA equation with local T at the instantaneous position of the particle is added to X. In order to simulate various chemical reactions, the activation energy of the fictitious reactions ranged from 20 to 1000 kJ/mol, the logarithm of pre-exponential factors (s-1) from 10 to 60, and the Avrami index from 0.5 to 4 to simulate reactions occurring at ~200–1500 K. The simulations showed that the highest temperature (Tmax,Xrec) that each particle experiences before the degree of reaction (X) exceeds a certain level Xrec (0.8, 0.9 and 0.99) form a distribution that can be fitted with the log-normal distribution. Different reactions show different Tmax,Xrec distributions, suggesting that the distribution shows a specific temperature range, where a reaction effectively proceeds. All histograms of Tmax,Xrec were fitted by the log-normal distributions, and the representative parameters, the mode temperature (Tline) and its dispersion (σline), were obtained. The Tline and σline for various reactions vary depending on reaction parameters and disk parameters, and are used as the reaction line temperature and its dispersion.
We found that the reaction line temperature and its dispersion, obtained in the simulation, can be semi-theoretically explained comparing a reaction timescale with a local diffusive transport timescale of dust particles because the reaction of a dust particle proceeds effectively while the dust particle stays in the region. We obtained prediction equations of Tline and σline of various reactions as a function of reaction parameters and disk parameters (viscosity and mass accretion rate). The predicted equations well explain Tline and σline in the numerical simulations in a wide range of reaction temperatures within 5.5% and 24 %, respectively.
The prediction equations of “reaction lines” developed in this study can be a powerful tool to discuss the chemical evolution of the early Solar System caused various reactions at different locations of the disk.
There have been several studies discussing chemical reactions of dust particles moving inward by accretion and randomly by diffusion (e.g., Ciesla & Sandford 2012; Okamoto & Ida 2022), but no systematic and comprehensive investigation has been made for various chemical reactions occurring at different temperatures in protoplanetary disks. In this study, we focus on developing a prediction equation of “reaction line temperatures” of various irreversible chemical reactions, considering dust particle movement in a steady accretion disk.
Three-dimensional Monte Carlo simulations (Ciesla 2010, 2011) were performed to evaluate trajectories of dust particles. The steady accretion disk model, heated by uniform viscous heating (α-viscosity model) is adopted. We assumed that the dust opacity is 2.5 cm2 g-1 and the central star has a solar mass Msun. We adopted α of 10-2 and 10-3 and the steady accretion rate Mflow of 10-6, 10-7 and 10-8 Msun yr-1. Ten thousand dust particles, of which movements were assumed to be well coupled with gas, were released at the H2O snowline in the disk midplane for each parameter set. The calculations continued for 106 years at the maximum.
The progress of fictitious irreversible reactions expressed by the Johnson-Mehl-Avrami (JMA) equation were examined. The degree of reaction, X, is set to be zero at the release from the snowline. For each timestep of the Monte Carlo simulation, the increment δX calculated by the differentiated JMA equation with local T at the instantaneous position of the particle is added to X. In order to simulate various chemical reactions, the activation energy of the fictitious reactions ranged from 20 to 1000 kJ/mol, the logarithm of pre-exponential factors (s-1) from 10 to 60, and the Avrami index from 0.5 to 4 to simulate reactions occurring at ~200–1500 K. The simulations showed that the highest temperature (Tmax,Xrec) that each particle experiences before the degree of reaction (X) exceeds a certain level Xrec (0.8, 0.9 and 0.99) form a distribution that can be fitted with the log-normal distribution. Different reactions show different Tmax,Xrec distributions, suggesting that the distribution shows a specific temperature range, where a reaction effectively proceeds. All histograms of Tmax,Xrec were fitted by the log-normal distributions, and the representative parameters, the mode temperature (Tline) and its dispersion (σline), were obtained. The Tline and σline for various reactions vary depending on reaction parameters and disk parameters, and are used as the reaction line temperature and its dispersion.
We found that the reaction line temperature and its dispersion, obtained in the simulation, can be semi-theoretically explained comparing a reaction timescale with a local diffusive transport timescale of dust particles because the reaction of a dust particle proceeds effectively while the dust particle stays in the region. We obtained prediction equations of Tline and σline of various reactions as a function of reaction parameters and disk parameters (viscosity and mass accretion rate). The predicted equations well explain Tline and σline in the numerical simulations in a wide range of reaction temperatures within 5.5% and 24 %, respectively.
The prediction equations of “reaction lines” developed in this study can be a powerful tool to discuss the chemical evolution of the early Solar System caused various reactions at different locations of the disk.