Astrochemistry Les Houches Lectures September 2005 Lecture 2

1. AstrochemistryLes Houches LecturesSeptember 2005Lecture 2 T J Millar School of Physics and Astronomy University of Manchester PO Box88, Manchester M60 1QD

2. Grain Surface Time-scales Collision time: tc = [vH(πr2nd)]-1 ~ 109/n(cm-3) years Thermal hopping time: th = ν0-1exp(Eb/kT) Tunnelling time: tt = v0-1exp[(4πa/h)(2mEb)1/2] Thermal desorption time: tev = ν0-1exp(ED/kT) Here Eb ~ 0.3ED, so hopping time < desorption time For H at 10K, ED = 300K, tt ~ 2 10-11, th ~ 7 10-9 s Tunnelling time < hopping time only for lightest species (H, D) For O, ED ~ 800K, th ~ 0.025 s. For S, ED ~ 1100K, th ~ 250 s, tt ~ 2 weeks Heavy atoms are immobile compared to H atoms

3. Formation of H2 Gas phase association of H atoms far too slow, k ~ 10-30 cm3 s-1 Gas and dust well-mixed In low-density gas, H atoms chemisorb and fill all binding sites (106) 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 H2

4. Formation of Molecular Hydrogen Gas-Phase formation: H + H → H2 + hν very 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) > Σn(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: tac(X) = (SXvXσnd)-1, where SX is the sticking coefficient ~ 1 at 10K tac (yrs) ~ 109/n(cm-3) ~ 104 – 105 yrs in a dark cloud

6. Interstellar Ices Mostly water ice Substantial components: - CO, CO2, CH3OH Minor components: - HCOOH, CH4, H2CO Ices are layered - CO in polar and non-polar ices Sensitive to f > 10-6 Solid H2O, CO ~ gaseous H2O, CO

7. Results from a pseudo-time dependent model with T=10K, n(H2)=106 cm-3 Fractional abundances varying over time

8. Models - History 1950-1972 – Grain surface chemistry – H2, CH, CH+ 1973-1990 – Ion-neutral chemistry – HD, DCO+ 1990-2000 – Neutral-neutral chemistry – HC3N 2000-date – Gas/Grain interaction – D2CO, ND3 10,000 reactions, 500 species

9. Dense Clouds • H2 forms on dust grains • Ion-neutral chemistry important • Time-scales for reaction for molecular ion M+ • 109/n(H2) for fast reaction with H2 • 106/n(e) for fast dissociative recombination with electrons • 109/n(X) for fast reaction with X Since n(e) ~ 10-8n, dissociative recombination is unimportant for ions which react with H2 with k > 10-13 cm3 s-1; Reactions with X are only important if the ion does not react, or reacts very slowly, with H2.

10. Oxygen Chemistry H3+ + O  OH+ + H2 M OH+ + H2  H2O+ + H M H2O+ + H2  H3O+ + H M H3O+ + e  O, OH, H2O M Destruction of H2O: He+, C+, H3+, HCO+, .. (M) Destruction of OH: He+, C+, H3+, HCO+, .. ,

11. Oxygen Chemistry O + OH  H + O2 M for T > 160K, fast C + OH  H + CO N + OH  H + NO M for T > 100K, fast S + OH  H + SO M at T = 300K, fast Si + OH  H + SiO C + O2  CO + O M for T > 15K, fast

12. Oxygen Chemistry Conclude: We should be able to explain the abundances of H2O (all reactions measured) - of OH (no i-n reactions measured, important n-n reactions measured) - of O2 (all reactions measured) But we cannot !!!

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

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)βexp(-γ/T) cm3 s-1 k(I) = αexp(-γAV) if R2 = PHOTON, AV 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) = -SXvXσndn(I) = -SXAn(I)/m1/2(I) where SX = 0 for H, H2, 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 (105 yrs) and steady state (if the latter exists)