Chemistry Databases and Reaction Networks for Stellar Atmospheres

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


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)




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)


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)



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]


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


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!

Chemistry Databases and Reaction Networks for Stellar Atmospheres

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