ISM & Astrochemistry Lecture 2

1. ISM & AstrochemistryLecture 2

2. Protoplanetary Nebula The evolutionary stage between evolved stars and planetary nebula CRL 618 – many organic molecules Including the only extra-solar system detection of benzene, C6H6 Time scale of chemistry and evolution of this object is 600-1000 years

3. Molecule formation in shocks Supersonic shock waves: Sound speed ~ 1 km s-1 Shocks compress and heat the gas Hydrodynamic (J-type) shocks: immediately post-shock, density jumps by 4-6, gas temperature ~ 3000(VS/10 km s-1)2 Gas cools quickly (~ few tens, hundred years) and increases its density further as it cools – path lengths are small. MHD (C-type) shocks: shock front is preceded by a magnetic precursor, gas density and temperature change continuously, ions and neutrals move at different velocities – path lengths are large Importance for chemistry: Endothermic neutral-neutral reactions can occur.

4. Interstellar and Circumstellar Molecules

5. One-body reactions Photodissociation/photoionisation: Unshielded photorates in ISM:β0 = 10-10 s-1 Within interstellar clouds, characterise extinction of UV photons by the visual extinction, AV, measured in magnitudes, so that: β = β0exp(-bAV) where b is a constant (~ 1- 3) and differs for different molecules

6. Cosmic Ray Ionisation H3+: P.A.(H2) very low Proton transfer reactions very efficient Key to synthesising molecules He+: I.P.(He) very large Breaks bonds in reaction Key to destruction of molecules IS Chemistry efficient because He+ does not react with H2 H2 + crp → H2+ + e- H2+ + H2 → H3+ + H He + crp → He+ + e- He+ + H2 → products exothermic but unreactive

7. Two-body reactions Ion-neutral reactions: Neutral-neutral reactions: Ion-electron dissociative recombination (molecular ions) Ion-electron radiative recombination (atomic ions) Radiative association Three-body reactions (only if density is very large, 1013 cm-3)

8. Formation of Molecules Ion-neutral reactions: Activation energy barriers rare if exothermic Temperature independent (or inversely dependent on T) Neutral-neutral reactions: Often have activation energy barriers Often rate coefficient is proportional to temperature

9. Formation of Molecules Ion-electron dissociative recombination reactions: Fast, multiple products, inverse T dependence Atomic ion-electron radiative recombination recombination: Neutral complex stabilises by emission of a photon, about 1000 times slower than DR rate coefficients Radiative association: A+ + B → AB+ + hν Photon emission more efficient as size of complex grows, therefore can be important in synthesising large molecular ions CH3+ + H2 → CH5+ + h ν k(T) = 1.3 10-13(T/300)-1 cm3 s-1 CH3+ + HCN → CH3CNH+ + h ν k(T) = 9.0 10-9(T/300)-0.5 cm3 s-1

10. Chemical Kinetics A + B → C + D k = <σv> cm3 s-1 Loss of A (and B) per unit volume per second is: dn(A)/dt = - kn(A)n(B) cm-3 s-1 where n(A) = no. of molecules of A per unit volume Formation of C (and D) per unit volume per second is: dn(C)/dt = + kn(A)n(B) cm-3 s-1 - Second-order kinetics – rate of formation and loss proportional to the concentration of two reactants

11. First-order kinetics A + hν→ C + D β (units s-1) Loss of A (and B) per unit volume per second is: dn(A)/dt = - βn(A) cm-3 s-1 where β= photodissociation rate of A (s-1) Aside: The number, more accurately, flux of UV photons or cosmic-ray particles, is contained within βor ς - First-order kinetics – rate of formation and loss proportional to the concentration of one reactant

12. General case • dn(Xj)/dt = Σklm[Xl][Xm] + Σ βn[Xn] • - [Xj]{Σkjl[Xl] + Σ βj} m-3 s-1 • or d[X]/dt = FX – LX[X] • Need to solve a system of first-order, non-linear ODEs • - solve using GEAR techniques • Steady-state approximation – rate of formation = rate of loss • FX = LX[X]ssso that [X]ss = FX/LX • Need to solve a system of non-linear algebraic equations • - solve using Newton-Raphson methods

13. Time scales d[X]/dt = FX – LX[X] For simplicity, assume FXand LXare constants and[X] = 0 att =0(initial condition) Solution is: [X,t] = (FX/LX){1 – e-Lxt} [X,t] = [X]ss{1 – e-t/tc} where tc = 1/LX Note: Ast → ∞, [X] → [X]ss Whent = tc, [X,tc] = 0.63[X]ss, so most molecular evolution occurs within a few timestc

14. 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 s, 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

15. 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

16. 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)

17. 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

18. 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