1. Astrochemistry Les Houches Lectures September 2005 Lecture 2 T J Millar School of Physics and Astronomy University of Manchester PO Box88, Manchester M60 1QD

2. Grain Surface Time-scales Collision time: t c = [v H (πr 2 n d )] -1 ~ 10 9 /n(cm -3 ) years Thermal hopping time:t h = ν 0 -1 exp(E b /kT) Tunnelling time:t t = v 0 -1 exp[(4πa/h)(2mE b ) 1/2 ] Thermal desorption time: t ev = ν 0 -1 exp(E D /kT) Here E b ~ 0.3E D, so hopping time < desorption time For H at 10K, E D = 300K, t t ~ 2 10 -11, t h ~ 7 10 -9 s Tunnelling time < hopping time only for lightest species (H, D) For O, E D ~ 800K, t h ~ 0.025 s. For S, E D ~ 1100K, t h ~ 250 s, t t ~ 2 weeks Heavy atoms are immobile compared to H atoms

3. Formation of H 2 Gas phase association of H atoms far too slow, k ~ 10 -30 cm 3 s -1 Gas and dust well-mixed In low-density gas, H atoms chemisorb and fill all binding sites (10 6 ) per grain Subsequently, H atoms physisorb Surface mobility of these H atoms is large, even at 10 K. H atoms scans surface until it finds another atom with which it combines to form H 2

4. Formation of Molecular Hydrogen Gas-Phase formation: H + H → H 2 + hνvery slow, insignificant in ISM Grain surface formation: Langmuir-Hinshelwood (surface diffusion) Eley-Rideal (direct hit)

5. Grain Surface Chemistry Zero-order approximation: Since H atoms are much more mobile than heavy atoms, hydrogenation dominates if n(H) > Σ n(X), X = O, C, N Zero-order prediction: Ices should be dominated by the hydrogenation of the most abundant species which can accrete from the gas-phase Accretion time-scale: t ac (X) = (S X v X σn d ) -1, where S X is the sticking coefficient ~ 1 at 10K t ac (yrs) ~ 10 9 /n(cm -3 ) ~ 10 4 – 10 5 yrs in a dark cloud

6. Interstellar Ices Mostly water ice Substantial components: - CO, CO 2, CH 3 OH Minor components: - HCOOH, CH 4, H 2 CO Ices are layered - CO in polar and non-polar ices Sensitive to f > 10 -6 Solid H 2 O, CO ~ gaseous H 2 O, CO

7. Results from a pseudo-time dependent model with T=10K, n(H 2 )=10 6 cm -3 Fractional abundances varying over time

8. Models - History 1950-1972 – Grain surface chemistry – H 2, CH, CH + 1973-1990 – Ion-neutral chemistry – HD, DCO + 1990-2000 – Neutral-neutral chemistry – HC 3 N 2000-date – Gas/Grain interaction – D 2 CO, ND 3 10,000 reactions, 500 species

9. Dense Clouds H 2 forms on dust grains Ion-neutral chemistry important Time-scales for reaction for molecular ion M + –10 9 /n(H 2 )for fast reaction with H 2 –10 6 /n(e)for fast dissociative recombination with electrons –10 9 /n(X)for fast reaction with X Since n(e) ~ 10 -8 n, dissociative recombination is unimportant for ions which react with H 2 with k > 10 -13 cm 3 s -1 ; Reactions with X are only important if the ion does not react, or reacts very slowly, with H 2.

10. Oxygen Chemistry H 3 + + O  OH + + H 2 M OH + + H 2  H 2 O + + HM H 2 O + + H 2  H 3 O + + HM H 3 O + + e  O, OH, H 2 OM Destruction of H 2 O: He +, C +, H 3 +, HCO +,.. (M) Destruction of OH: He +, C +, H 3 +, HCO +,..,

11. Oxygen Chemistry O + OH  H + O 2 M for T > 160K, fast C + OH  H + CO N + OH  H + NOM for T > 100K, fast S + OH  H + SOM at T = 300K, fast Si + OH  H + SiO C + O 2  CO + OM for T > 15K, fast

12. Oxygen Chemistry Conclude: We should be able to explain the abundances of H 2 O (all reactions measured) - of OH (no i-n reactions measured, important n-n reactions measured) - of O 2 (all reactions measured) But we cannot !!!

13. Kinetic Calculation hmain.f hodes.f inputhouches.f dvode1.f subs.f h.rates h.specs hdata.out Initialises GEAR GEAR codes File of ODEs Rate file Species file Pseudo-time-dependent calculation – physical parameters remain fixed with time

14. hmain.f FRAC(I) – initial abundances for e,H2,He,O,C,N,Mg Rate file – I, R1, R2, P1, P2, P3, P4, α, β, γ k(I) = α(T/300) β exp(-γ/T) cm 3 s -1 k(I) = αexp(-γA V ) if R2 = PHOTON, A V in mags k(I) = αγ/(1-ω) if R2 = CRPHOT, ω = albedo (= 0.5) k(I) = α if R2 = CRP Several k(I) have unphysical values at 10K (negative γ), these are reset in hmain.f Initial abundances of all species are set in hmain.f

15. hodes.f (Algebraic) conservations are used to determine the abundances of e-, H2, and He Grain surface rate for H2 formation set in hodes.f and included as a loss term in the ODE for H atoms Term for accretion can be included in hodes.f YDOT(I) = -S X v X σn d n(I) = -S X An(I)/m 1/2 (I) where S X = 0 for H, H 2, He and their ions, = 1 otherwise Some collisions may not lead to sticking, eg X + with a negatively charged grain, but to new gas-phase products Grain surface chemistry and physics can lead to additional ODEs

16. Modelling task Download gzipped tarfile: http://jupiter.phy.umist.ac.uk/~tjm/tjm.html Unzip (gunzip) and extract (tar –xvf example.tar): Run makefile: make Run job: houches Tasks: Can you make O2 and H2O agree with observational abundances (upper limits) in dark clouds (TMC-1, L134N)? Can you make NO agree with its abundance in TMC-1? Web sites: www.rate99.co.uk and www.astrochemistry.net

17. Modelling task Elemental abundance variations Vary rate coefficients of key reactions Include accretion on to dust grains Vary density, temperature, visual magnitude, cosmic ray ionisation rate Consider abundances at early-time (10 5 yrs) and steady state (if the latter exists)