AstrochemistryLes Houches Lectures

September 2005Lecture 2

T J MillarSchool of Physics and Astronomy

University of ManchesterPO Box88, Manchester M60 1QD

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

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

Results from a pseudo-time dependent model with T=10K, n(H2)=106 cm-3

Fractional abundances varying over time

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

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.

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+, .. ,

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

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 !!!

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

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 magsk(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

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

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

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)