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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