OUTLINE OF A GAS-GRAIN CHEMICAL CODE. Dima Semenov MPIA Heidelberg

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1 OUTLINE OF A GAS-GRAIN CHEMICAL CODE Dima Semenov MPIA Heidelberg

2 MOTTO OF ASTROCHEMISTRY CODE DEVELOPMENT We had 5 ODE solvers, 9 Jacobi matrix inversion routines, several approaches to calculate reaction rates, a sensitivity analysis code half-full of bugs, and a whole galaxy of chemical ratefiles, photodissociation cross sections, desorption energies, reaction barriers, etc Also, a bunch of Monte Carlo, master equation, modified rate equation, and moments equation methods. Not that we needed all that for development of a gasgrain astrochemistry code, but once you get locked into a serious code development, the tendency is to push it as far as you can

3 OUTLINE Chemical kinetics Gas-phase processes Surface processes ALCHEMIC code Uncertainties Missing information

4 NEED OF ASTROCHEMICAL MODELING Vast variety of physically distinct environments Different evolutionary timescales Molecular emission lines are proxies to study physics Credit: Bill Saxton, NRAO/AUI/NSF Physics Chemistry Radiative Transfer

5 PHYSICAL CONDITIONS IN VARIOUS ASTROPHYSICAL OBJECTS Interstellar medium: Tkin~ K, n ~ cm -3 PDRs & protoplanetary disks: Tkin~ K, n ~ cm -3 Circumstellar shells: Tkin ~300 3,000 K, n<10 14 cm -3 Earth atmosphere at sea level: Tkin~300 K, n~ cm -3 Very different intensities of UV, X-rays, and cosmic rays radiation field

6 WHAT WE NEED TO DESCRIBE CHEMISTRY Gas-phase processes: rate coefficients, barriers, branching ratios, temperature-dependence, Gas-grain interactions: grain properties, sticking probabilities, desorption efficiencies, Surface processes: mobilities of adsorbed species, high-energy processing of ices, diffusion between monolayers,

7 CHEMICAL KINETICS: FIRST ORDER Rate of formation and destruction proportional to the concentration of one reactant Example: photodissociation of AB: AB + hν A + B Loss of AB per unit volume per second is: dn(ab)/dt = -kn(ab) cm -3 s -1, where k is photodissociation rate in s -1 Name Representation Example Rate Ionization A + hν C + hν ~10 Dissociation AB + hν A + B CO + hν C + O ~10 Desorption A(g) A (hν or T) H2 ~0-10

8 CHEMICAL KINETICS: SECOND ORDER Rate of formation and loss proportional to the concentration of two reactants A + B C + D k ~ <σv> cm 3 s -1 Loss of A and B per unit volume per second is: dn(a)/dt = -kn(a)n(b), where n(x) is volume number density of molecule X Formation of C and D per unit volume per second is: dn(c)/dt = +kn(a)n(b) cm 3 s -1

9 CHEMICAL KINETICS: SECOND ORDER Radiative association Name Representation Example Rate A + B AB + ν C + ~10 Ion-molecule A + CO + H ~10 Neutral-neutral A + B C + D O + CH ~10 Charge transfer A + C + ~10 Radiative recombination Dissociative recombination A + Mg ~10 AB HCO ~10 Accretion A + g A(g) H2 Surface reaction A(g) + B(g) AB(g) H(g) + H (g) Arrhenius rate: Here, α is rate coefficient (cm 3 s -1 ), β is temperature-dependence, and γ is barrier (K)

10 ASTROCHEMICAL REACTION DATABASES Mainly gas-phase processes Most recent models contain ~5000 gas-phase reactions between ~450 (up to 13 atoms): UMIST: Ohio State Univ.: Kinetic Database for Astrochemistry: models High-T reactions, fractionation, etc.

11 A MAJOR DIFFICULTY: GAS-GRAIN INTERACTIONS AND SURFACE PROCESSES

12 ACCRETION Accretion rate: Arrival timescale for CO at 10 K is : ~ 3 days for density of 10 4 cm -3 and 1000 A grains

13 TWO TYPES OF BINDING SITES CHEMISORPTION WELL H PHYSISORPTION WELL H Weak electrostatic (van der Waals) binding, energy ~ mev " Binding energies ~ chemical bond energies: ~ ev

14 DESORPTION ( Thermal evaporation rate: k des (T d ) = ν(i)exp E ) des T d Here, ν is characteristic vibration frequency (~10 12 s -1 ) and Edes is desorption energy (K) CRP-induced thermal evaporation rate: k crd = fk des (70 K), Here, f is a ratio of grain cooling timescale to the heating timescale (depends on grain properties!) Photoevaporation rate: k Y δ 2 I UV Here, Y is UV yield of ~ 0.1%, δ is a surface site radius, I UV is UV intensity

15 SURFACE PROCESSES Accretion to a surface site Hopping/tunneling to a neighboring site If it finds a reactant, then reaction may occur Excess of energy is (partly?) absorbed by dust lattice

16 SURFACE TIMESCALES Freeze-out time: [V(πr 2 n d )] -1 ~ 10 9 /n(cm -3 ) years Thermal hopping time: ν 0-1 exp(e b /kt) Tunneling time: ν 0-1 exp[(4πa/h)(2me b ) 1/2 ] Thermal desorption time: ν 0-1 exp(e D /kt) Usually, E b ~ x E D, so hopping time < desorption time " For H at 10K: E D = 300K, tunneling time ~ s, hopping time ~ s Tunneling > hopping only for lightest species (H, D, HD, H 2 ) For O: E D ~ 800 K, hopping time ~ s For S: E D ~ 1100 K, hopping time ~ 250 s

17 COMPUTATIONAL CHEMISTRY Physical conditions, diffusion coefficient & flow data Initial abundances of species A chemical network log(abundance) CO A numerical solver log(time) Benchmarking

18 ASTROCHEMICAL CODES ALCHEMIC (MPIA Heidelberg): gas-grain NAHOON (Bordeaux Obs.): gas-grain, uncertainties MONACO (MPE Garching): gas-grain, Monte Carlo stochastic chemistry ASTROCHEM (Grenoble): gas-grain OSU codes (now at Univ. of Virginia): gas-grain, warm-up Y. Aikawa s code Many codes for photon-dominated chemistry (CLOUDY, Meudon, UCL_CHEM, Leiden, etc., see Roellig et al. 2007)

19 ALCHEMIC (SEMENOV ++ 10) OSU.2007/KIDA with recent updates to the rates Deuterium network with high-t chemistry (Albertsson et al. 2013) Ortho/para states of H 2, H + + 2, H 3 (Albertsson et al. 2014a) Single-sized silicate grains (~1000 A, dust/gas mass ratio is 1%) UV, X-rays, cosmic rays (new photorates from van Dishoeck et al. 2006) Photodissociation of surface species Reactive desorption (Garrod & Herbst 2006), 1 5% Only Langmuir-Hinshelwood mechanism, rate equations approach 15 elements, ~1260 species and reactions

20 ALCHEMIC (SEMENOV ++ 10) Automatically generated ODE Stiff ODE solver DVODE (ODEPACK on Netlib) Sparse, automatically generated Jacobi matrix MA48 Harwell library to solve sparse systems of algebraic equations Multi-CPU parallelization Laminar/1D-/2D-turbulent mixing Typical performance for a TMC1-like 0D model (single grid cell): ~ 1 10 s of CPU time

21 656 species ALCHEMIC INPUT 7907 reactions

22 ALCHEMIC OUTPUT Input data Time-dependent absolute concentrations Rates Human-/machinereadable format

23 ASTROCHEMISTRY MODELS ARE UNCERTAIN Wakelam et al. >2005, Vasyunin et al. >2004, Tacquet et al. 2012,... Modeled gas-phase abundances are uncertain by factors of 2 10 Analysis was done only for gas-phase reactions!

24 VARIOUS APPROACHES TO DESCRIBE SURFACE CHEMISTRY Standard chemical kinetics (rate equations approach) A part of a large gas-grain ODE system " Rate equations depend on an average abundance that can drop below 1 on a grain => unphysical! Makes ODE system more stiff => slows down codes by ~ x10

25 VARIOUS APPROACHES TO DESCRIBE SURFACE CHEMISTRY Accretion-limited approach (modified rate equations) Standard surface rate is accretion limited to allow 2 reactants to be on the grain " Is not an exact method, has its own limitations Slows down the code further Caselli et al. 1998, Garrod et al. 2009,...

26 VARIOUS APPROACHES TO DESCRIBE SURFACE CHEMISTRY Master equation (probability) approach: describe the chemical state of the system in terms of propensity functions Monte-Carlo method to calculate probabilities to arrival of individual particles at surface and their surface recombinations Accurate by design! Very slow for realistic large gas-grain systems Tielens & Hagen (1982), Stancheva et al. (>2002), Vasyunin et al. >(2008), Chang & Herbst (2014)

27 GAS-GRAIN MODELS SEEM FEASIBLE Agundez & Wakelam (2013) About 70 80% agreement for 50 observed species in TMC1

28 PROBLEMS Many rate coefficients are not experimental and/or have large uncertainties Chemisorption vs. physisorption Desorption/binding energies on/to various surfaces Properties of surface: roughness, sites of various energies, Reactive desorption, UV yields, CRP desorption for bigger/smaller grains What happens in the bulk ice? Diffusion between ice monolayers? In situ recombination of freshly created radicals? How surface rate uncertainties affects modeling results?

29 CONCLUSIONS Errors using inadequate data are much less than those using no data at all. " Charles Babbage ( )