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Chemistry Databases and Reaction Networks for Stellar
Atmospheres
Inga Kamp & Sven Wedemeyer-BöhmInga Kamp & Sven Wedemeyer-Böhm
• CO in the Sun as a motivation• Chemical networks: various approaches & solvers• Implementation in CO5BOLD• Rate quality and completeness of the network• Prospects for larger networks and different species
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Collaborators:Sven Wedemeyer-Böhm (KIS, Freiburg)Bernd Freytag (Los Alamos)Matthias Steffen (AIP, Potsdam)Jo Bruls (KIS, Freiburg)Oskar Steiner (KIS, Freiburg)Werner Schaffenberger (Graz)
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CO observations in the SunCO observations in the Sun
CO (v = 1) fundamental and (v =2) first overtone bands suggest that the temperature decreases monotonically outwards - no temperature minimum
Solution: inhomogeneous atmosphere with coexisting hot and cool areas
Cool areas maybe caused by a runaway process: CO formation and subsequent enhanced CO cooling lead to a “cooling catastrophe”
[Ayres & Testerman 1981]
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Chemical NetworksChemical Networks
Three different approaches:
Instantaneous Chemical Equilibrium (ICE)
Chemical Equilibrium (CE)
Time dependent chemistry with advection (TD)
The chemistry depends on local quantities such as T, n andthe solution is calculated for t=∞ (stationary solution)
The chemistry depends on local quantities such as T, n andthe solution is advanced over t of the hydro timestep
The chemistry depends on local quantities such as T, n; the solution of the previous timestep is advected according to the hydrodynamical flow before the chemistry solution is advanced over t of the hydro timestep
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Two methods:
Equilibrium Constants
Rate Coefficients
€
P(i) = Pi + Pi+ + Pi− + wki
k
∑ Pk
P(i) = Pi + K i+
Pi
Pe−
+ K i−PiPe− + wki
k
∑Pi
wki
Pjwk
j
...Plwk
l
K(T)pk
Pij =Pi
w i
Pjw j
K p (T)
fictious partial pressurefor each atom(!)
€
n(i) = k jki
jk
∑ n jnk − ni kijk
jk
∑ n j particle densityfor each species(!)
and
€
Pi = nikTpre-tabulatedequilibriumconstants
parametrizedrate coefficients
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Three solvers:
Dvode
Newton-Raphson
Neural Networks
Initial value ODE solver for stiff systems with adjustable stepsize h
Iterative solution of a non-linear system of equations
Approximation of a set of non-linear continous functions with Nh neurons
€
N(T,n(H),n(e),m) = v jj
Nh∑ σ w jTT + w j
H n(H) + w jen(e) + u j[ ]
€
˙ y = f (t,y) ∩ y(t0) = y0
y n +1 = a0y n + a1yn−1 + a2y n−2 + a3y n−3 + a4 y n−4 + hb−1 f (t n +1,y n +1)
5th order BDF (Gear)
€
Fi(x1, x2,...,xn ) = 0
F(x + δx) = F(x) + J ⋅δx + O(δx 2)⇒ J ⋅δx = −F
xnew = xold + δx
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Three solvers:
Dvode
Newton-Raphson
Neural Networks
Initial value ODE solver for stiff systems with adjustable stepsize h
Iterative solution of a non-linear system of equations
€
˙ y = f (t,y) ∩ y(t0) = y0
y n +1 = a0y n + a1yn−1 + a2y n−2 + a3y n−3 + a4 y n−4 + hb−1 f (t n +1,y n +1)
5th order BDF (Gear)
€
Fi(x1, x2,...,xn ) = 0
F(x + δx) = F(x) + J ⋅δx + O(δx 2)⇒ J ⋅δx = −F
xnew = xold + δx
T
n(H)
n(e-)
Pi fictious
partial pressure
[Asensio Ramos & Socas-Navarro 2005]
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[Wedemeyer-Böhm, Kamp, Freytag, Bruls 2004]
The COThe CO55BOLD Chemical BOLD Chemical NetworkNetwork
Operator splitting:
1) Continuity equation (advection) 2) Rate equation (chemistry)
Chemistry is the limiting factor in computing time --> networks have to besmall to be feasible
COCO
chemistry advection chemistryadvection
tn-1 tn tn tn+1 tn+1
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[Wedemeyer-Böhm, Kamp, Freytag, Bruls 2004]
8 species: H, C, O, MH2, CO, CH, OH
27 reaction rates
Neutral-neutral reactions: Rij = A (T/300)B exp(-C/T) ninj
Three-body reactions: Rij = A (T/300)B ninjn(M)
The COThe CO55BOLD Chemical BOLD Chemical NetworkNetwork
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The COThe CO55BOLD Chemical BOLD Chemical NetworkNetwork
[Wedemeyer-Böhm, Kamp, Freytag, Bruls 2004]
8 species: H, C, O, MH2, CO, CH, OH
27 reaction rates
Neutral-neutral reactions: Rij = A (T/300)B exp(-C/T) ninj
Three-body reactions: Rij = A (T/300)B ninjn(M)
M
M
M
M
M
M
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C + OH branching ratiosO + CH Rij(300K) = 2.25 10-11
CO + H Rij(300K) = 1.81 10-11
CO + H C + O + H
5000 K range
Souces for reaction rates:critical evaluation of theliterature
UMIST (Le Teuff et al. 2000)Konnov’s combustion database(Konnov 2000)Baulch et al. (1972, 1976)Westley (1980)Ayres & Rabin (1996)
The COThe CO55BOLD Chemical BOLD Chemical NetworkNetwork
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5000 K range
combustion data
Ayres & Rabinderived rate fromdetailed balancebetween H+COand C+OH (5000K)
UMIST is based onWestley (1980),but differs by afactor 5!
We use originalrate by Westley(1980)
The COThe CO55BOLD Chemical BOLD Chemical NetworkNetwork
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The COThe CO55BOLD Chemical BOLD Chemical NetworkNetwork
Parameter study for extended network:
H, C, O, M, H2, CO, CH, OH and 27 reaction rates
vs.
H, C, O, M, H2, CO, CH, OH, N, NH, N2, NO, CN and 58 reaction rates
result after ∆t = 0.1 s
Difference of CO number density in the (T,n) parameter range of the solar atmosphere
[Asensio Ramos et al. 2003]
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The COThe CO55BOLD Chemical BOLD Chemical NetworkNetwork
Average CO number density over height:
At heights above ~600 km, CE and ICE are no longer good approximations for the chemistry; TD becomes important
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The COThe CO55BOLD Chemical BOLD Chemical NetworkNetwork
TD/UICE
TD/CE
CE/UICE
no difference
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OutlookOutlook
• Add more species, OH and CH might be interesting for the Sun--> networks have to be tested and have to stay small.
• Use a solver that allows better optimization --> Heidelberg group (DAESOL, Bauer et al. 1997)
• More laboratory measurements!!!! Many rates are still guesses or vast extrapolation.
• Get better reaction rate databases (UMIST mostly for interstellar and circumstellar physics, Konnov’s database not well documented and maintanance unclear, database of equilibrium constants not publicly available).
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Thank you!