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
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)
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]
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
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
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
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]
[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
[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
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
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
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
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]
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
The COThe CO55BOLD Chemical BOLD Chemical NetworkNetwork
TD/UICE
TD/CE
CE/UICE
no difference
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).
Thank you!
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