1. A Gas Grain Model of ISM Cores with Moment Equations to Treat Surface Chemistry Yezhe Pei & Eric Herbst The Ohio State University June 25 th, 2010 65 th International Symposium on Molecular Spectroscopy, Columbus OH

2. Chemistry in Interstellar Cloud Cores A Gas Grain Model with Moment Equations – P. 2 65 th International Symposium on Molecular Spectroscopy, Columbus OH Introduction chemistry of Interstellar Medium (ISM) in gas phase and on grain surfaces; importance of surface chemistry modeling method - deterministic: rate equations - stochastic: Monte Carlo, master equations, etc RY Tauri

3. Chemistry in Interstellar Cloud Cores A Gas Grain Model with Moment Equations – P. 2 65 th International Symposium on Molecular Spectroscopy, Columbus OH Introduction chemistry of Interstellar Medium (ISM) in gas phase and on grain surfaces; importance of surface chemistry modeling method - deterministic: rate equations over-estimate surface production - stochastic: Monte Carlo, master equations, etc RY Tauri

4. Chemistry in Interstellar Cloud Cores A Gas Grain Model with Moment Equations – P. 2 65 th International Symposium on Molecular Spectroscopy, Columbus OH Introduction chemistry of Interstellar Medium (ISM) in gas phase and on grain surfaces; importance of surface chemistry modeling method - deterministic: rate equations over-estimate surface production - stochastic: Monte Carlo, master equations, etc un-manageable for large network RY Tauri

5. Chemistry in Interstellar Cloud Cores A Gas Grain Model with Moment Equations – P. 2 65 th International Symposium on Molecular Spectroscopy, Columbus OH Introduction chemistry of Interstellar Medium (ISM) in gas phase and on grain surfaces; importance of surface chemistry modeling method - deterministic: rate equations over-estimate surface production - stochastic: Monte Carlo, master equations, etc un-manageable for large network - Moment Equations method developed by Biham et al RY Tauri

6. Moment Equations for Surface Network (1) A Gas Grain Model with Moment Equations – P. 3 65 th International Symposium on Molecular Spectroscopy, Columbus OH Take H+H  H2 as an example: -- P(N): probability of N atoms on a grain -- F: flux --W: desorption rate -- A: diffusion rate F A W

7. Moment Equations for Surface Network (2) A Gas Grain Model with Moment Equations – P. 4 65 th International Symposium on Molecular Spectroscopy, Columbus OH Use the identity and cut-off conditions to reduce the 3 rd and higher orders

8. Moment Equations for Surface Network (3) A Gas Grain Model with Moment Equations – P. 5 65 th International Symposium on Molecular Spectroscopy, Columbus OH Reference: Barzel, B., & Biham, O., J. Chem. Phys., 127,144703 (2007)‏

9. Dilemma of Moment Equations Method A Gas Grain Model with Moment Equations – P. 6 65 th International Symposium on Molecular Spectroscopy, Columbus OH Dilemma of moment equations method works well for small system, e.g., H₂O and CH₃OH producing network For large Standard Gas-Grain Network (655 species and ~7000 reactions), use moment equations for surface chemistry, rate equations for gas phase chemistry, and couple them Hybrid Method of Moment Equations and Rate Equations for surface reactions (we switch to use rate equations when a species abundance goes more than 1-per-grain)

10. Dilemma of Moment Equations Method A Gas Grain Model with Moment Equations – P. 7 65 th International Symposium on Molecular Spectroscopy, Columbus OH Dilemma of moment equations method works well for small system, e.g., H₂O and CH₃OH producing network For large Standard Gas-Grain Network (655 species and ~7000 reactions), use moment equations for surface chemistry, rate equations for gas phase chemistry, and couple them negative abundances! Hybrid Method of Moment Equations and Rate Equations for surface reactions (we switch to use rate equations when a species abundance goes more than 1-per-grain)

11. Dilemma of Moment Equations Method A Gas Grain Model with Moment Equations – P. 7 65 th International Symposium on Molecular Spectroscopy, Columbus OH Dilemma of moment equations method works well for small system, e.g., H₂O and CH₃OH producing network For large Standard Gas-Grain Network (655 species and ~7000 reactions), use moment equations for surface chemistry, rate equations for gas phase chemistry, and couple them negative abundances! Hybrid Method of Moment Equations and Rate Equations for surface reactions (we switch to use rate equations when a species abundance goes more than 1-per-grain) integrator freezes

12. Dilemma of Moment Equations Method A Gas Grain Model with Moment Equations – P. 7 65 th International Symposium on Molecular Spectroscopy, Columbus OH Dilemma of moment equations method works well for small system, e.g., H₂O and CH₃OH producing network For large Standard Gas-Grain Network (655 species and ~7000 reactions), use moment equations for surface chemistry, rate equations for gas phase chemistry, and couple them negative abundances! Hybrid Method of Moment Equations and Rate Equations for surface reactions (we switch to use rate equations when a species abundance goes more than 1-per-grain) integrator freezes Hybrid Method works for middle-sized system

13. My Gas Grain model consists of large gas phase network: 458 species, > 5000 reactions middle-sized surface network: 21 species 18 reactions H O C N CH CH₂ CH₃ CH₄ NH NH₂ NH₃ H₂ H₂0 O₂ OH CO CO₂ HCO H₂CO H₃CO CH₃OH Middle-Size Gas-Grain Model (1) A Gas Grain Model with Moment Equations – P. 8 65 th International Symposium on Molecular Spectroscopy, Columbus OH Surface Network

14. A Gas Grain Model with Moment Equations – P. 9 65 th International Symposium on Molecular Spectroscopy, Columbus OH Two phases couple via desorption and accretion Rate Equations for gas phase chemistry Hybrid Method for grain surface chemistry: use moment equations when the abundance is smaller than 1-per-grain; otherwise rate equations. Middle-Size Gas-Grain Model (2)

15. A Gas grain Model with Moment Equations – P. 10 65 th International Symposium on Molecular Spectroscopy, Columbus OH Result (1) Grain Radius=0.1 μm T=10KT=15KT=20K

16. A Gas grain Model with Moment Equations – P. 11 65 th International Symposium on Molecular Spectroscopy, Columbus OH Result (2) Grain Radius=0.01 μm Discrepancies appear at higher T and smaller grain sizes where stochastic effect becomes noticeable T=15K T=20K

17. Conclusions and Future Work A Gas Grain Model with Moment Equations – P. 12 65 th International Symposium on Molecular Spectroscopy, Columbus OH Conclusions: hybrid of moment equations and rate equations works for middle-sized surface network For low temperatures and large grain sizes, this method agrees well with pure rate equations Next Step: compare the results of this method with those of other stochastic methods like Monte Carlo, also with results of modified-rate equations

18. Acknowledgements A Gas Grain Model with Moment Equations – P. 13 65 th International Symposium on Molecular Spectroscopy, Columbus OH Dr. Ofer Biham Dr. Rob Garrod Our group members: George Hassel, Paul Rimmer, Nanase Harada Thank you all!