ISM & AstrochemistryLecture 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

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.

Interstellar and Circumstellar MoleculesH2 H3+ CH3 CH4 CH3OH CH3NH2 HCOOCH3 (CH3)2O (CH3)2CO

CO CH2 NH3 CH2NH CH3SH CH3CCH CH3C3N C2H5OH CH3C5N

CS NH2 H3O+ H2CCC C2H4 CH3CHO HC6H C2H5CN CH3CH2CHO

CN H2O H2CO c-C3H2 CH3CN c-CH2OCH2 C7H CH3C4H (CH2OH)2

C2 H2S H2CS CH2CN CH3NC CH2CHCN HOCH2CHO C8H HCOOC2H5

CH CCH c-C3H NH2CN CH2CHO HC5N CH3COOH HC7N HC9N

CH+ HCN l-C3H CH2CO NH2CHO C6H H2CCCHCN CH3CONH2 CH3C6H

HF HNC C2H2 HCOOH HC3NH+ CH2CHOH H2C6 CH3CHCH2 C6H6

CF+ HCO HCNH+ C4H H2CCCC C6H- CH2CHCHO C8H- C3H7CN

SiO HCO+ H2CN HC3N C5H NH2CH2CN HC11N

SiS HOC+ HCCN HCCNC HC4H C2H5OCH3

SiC N2H+ HNCO HNCCC HC4N

SiN HNO HOCN H2COH+ c-C3H2O

NH HCS+ HCNO C4H- CH2CNH

NO C3 HNCS SiH4 C5N-

SO C2O HSCN C5 C5N

SO+ C2S C3N SiC4

CP SO2 C3O CNCHO

PO N2O C3S

PN CO2 C3N-

HCl H2O+ HCO2+

KCl H2Cl+ CNCHO

AlCl OCS C-SiC2

OH MgNC AlF AlNC AlOH NaCl

OH+ MgCN SiNC CCP HCP FeO

SH NaCN CO+ O2 N2

CN- SiCN

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

Cosmic Ray Ionisation

H2 + crp → H2+ + e-

H2+ + H2 → H3

+ + H

He + crp → He+ + e-

He+ + H2 → products

exothermic but unreactive

H3+: P.A.(H2) very lowProton transfer reactions

very efficientKey to synthesising molecules

He+: I.P.(He) very largeBreaks bonds in reaction

Key to destruction of molecules

IS Chemistry efficient because He+ does not react with H2

Two-body reactionsIon-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)

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

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

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

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 β or ς

- First-order kinetics – rate of formation and loss proportional to the concentration of one reactant

General case

dn(Xj)/dt = Σ klm[Xl][Xm] + Σ βn[Xn]

- [Xj]{Σ kjl[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]ss so that [X]ss = FX/LX

Need to solve a system of non-linear algebraic equations

- solve using Newton-Raphson methods

Time scales d[X]/dt = FX – LX[X]

For simplicity, assume FX and LX are constants and [X] = 0 at t =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: As t → ∞, [X] → [X]ss

When t = tc, [X,tc] = 0.63[X]ss, so most molecular evolution occurs within a few times tc

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

Formation of H2

Gas phase association of H atoms far too slow, k ~ 10-30 cm3 s-1

Gas and dust well-mixedIn low-density gas, H atomschemisorb and fill all bindingsites (106) per grain

Subsequently, H atoms physisorbSurface mobility of these H atoms is large, even at 10 K.H atoms scans surface untilit finds another atom with which it combines to form H2

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)

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

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