Transcript pei_moment_talk.ppt

65th International Symposium on Molecular Spectroscopy, Columbus OH
A Gas Grain Model of ISM Cores
with Moment Equations to Treat
Surface Chemistry
Yezhe Pei & Eric Herbst
The Ohio State University
June 25th, 2010
Chemistry in Interstellar Cloud Cores
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
65th International Symposium on Molecular Spectroscopy, Columbus OH
A Gas Grain Model with Moment Equations – P. 2
Chemistry in Interstellar Cloud Cores
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
65th International Symposium on Molecular Spectroscopy, Columbus OH
A Gas Grain Model with Moment Equations – P. 2
Chemistry in Interstellar Cloud Cores
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
65th International Symposium on Molecular Spectroscopy, Columbus OH
A Gas Grain Model with Moment Equations – P. 2
Chemistry in Interstellar Cloud Cores
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
65th International Symposium on Molecular Spectroscopy, Columbus OH
RY Tauri
A Gas Grain Model with Moment Equations – P. 2
Moment Equations for Surface Network (1)
Take H+HH2 as an example:
-- P(N): probability of N atoms on a grain
-- F: flux
--W: desorption rate
-- A: diffusion rate
P (N)  F[P(N 1)  P(N)] W[(N  1)P(N 1)  NP(N)]
 A[(N  2)(N  1)P(N 2)  N(N  1)P(N)]
W
F
A
65th International Symposium on Molecular Spectroscopy, Columbus OH
A Gas Grain Model with Moment Equations – P. 3
Moment Equations for Surface Network (2)
Use the identity
d Nk
dt

Nm a x
 N P (N)
k
N 0
and cut-off conditions to reduce the 3rd and higher orders
dN
d N2
dt
 F  W N  2A( N2  N )
dt
 F  (2F  W  4A) N  (2W  4A) N2
65th International Symposium on Molecular Spectroscopy, Columbus OH
A Gas Grain Model with Moment Equations – P. 4
Moment Equations for Surface Network (3)
Reference:
Barzel, B., & Biham, O.,
J. Chem. Phys., 127,144703 (2007)
65th International Symposium on Molecular Spectroscopy, Columbus OH
A Gas Grain Model with Moment Equations – P. 5
Dilemma of Moment Equations Method
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)
65th International Symposium on Molecular Spectroscopy, Columbus OH
A Gas Grain Model with Moment Equations – P. 6
Dilemma of Moment Equations Method
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)
65th International Symposium on Molecular Spectroscopy, Columbus OH
A Gas Grain Model with Moment Equations – P. 7
Dilemma of Moment Equations Method
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
65th International Symposium on Molecular Spectroscopy, Columbus OH
A Gas Grain Model with Moment Equations – P. 7
Dilemma of Moment Equations Method
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
65th International Symposium on Molecular Spectroscopy, Columbus OH
A Gas Grain Model with Moment Equations – P. 7
Middle-Size Gas-Grain Model (1)
Surface Network
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
H  H  H2
H  O  OH
H  OH  H2 O
H  CO  HCO
H  HCO  H2 CO
H  H2 CO  CH2 OH
H  CH2 OH  CH3 OH
H  C  CH
H  CH  CH2
H  CH2  CH3
H  CH3  CH4
H  N  NH
H  NH  NH2
H  NH2  NH3
O  O  O2
O  CO  CO2
O  HCO  CO2  H
H2  OH  H2 O  H
65th International Symposium on Molecular Spectroscopy, Columbus OH
A Gas Grain Model with Moment Equations – P. 8
Middle-Size Gas-Grain Model (2)
• 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.
65th International Symposium on Molecular Spectroscopy, Columbus OH
A Gas Grain Model with Moment Equations – P. 9
Result (1) Grain Radius=0.1 μm
T=10K
T=15K
65th International Symposium on Molecular Spectroscopy, Columbus OH
T=20K
A Gas grain Model with Moment Equations – P. 10
Result (2) Grain Radius=0.01 μm
T=15K
T=20K
Discrepancies
appear at
higher T
and smaller
grain sizes
where
stochastic
effect
becomes
noticeable
65th International Symposium on Molecular Spectroscopy, Columbus OH
A Gas grain Model with Moment Equations – P. 11
Conclusions and Future Work
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
65th International Symposium on Molecular Spectroscopy, Columbus OH
A Gas Grain Model with Moment Equations – P. 12
Acknowledgements
• Dr. Ofer Biham
• Dr. Rob Garrod
• Our group members: George Hassel, Paul Rimmer, Nanase Harada
• Thank you all!
65th International Symposium on Molecular Spectroscopy, Columbus OH
A Gas Grain Model with Moment Equations – P. 13