Astrochemistry University of Helsinki, December 2006 Lecture 3

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AstrochemistryUniversity of Helsinki, December
2006Lecture 3

• T J Millar, School of Mathematics and Physics
• Queens University Belfast,Belfast BT7 1NN,
  Northern Ireland

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Grain Surface Time-scales
Collision time tc vH(pr2nd)-1
109/n(cm-3) years Thermal hopping time th
?0-1exp(Eb/kT) Tunnelling time tt
v0-1exp(4pa/h)(2mEb)1/2 Thermal desorption
time tev ?0-1exp(ED/kT) Here Eb 0.3ED, so
hopping time lt desorption time For H at 10K, ED
300K, tt 2 10-11, th 7 10-9 s Tunnelling
time lt 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
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Grain Surface Chemistry
Zero-order approximation Since H atoms are much
more mobile than heavy atoms, hydrogenation
dominates if n(H) gt Sn(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) (SXvXsnd)-1, where SX is
the sticking coefficient 1 at 10K tac
(yrs) 109/n(cm-3) 104 105 yrs in a dark
cloud
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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 gt 10-6 Solid
H2O, CO gaseous H2O, CO
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Grain Surface Chemistry

• Deterministic (Rate Coefficient) Approach

Basics Define an effective rate coefficient
based on mobility (velocity) and mean free path
before interaction (cross-section). Let ns(j) be
surface abundance (per unit volume) of species i
which has a gas phase abundance n(i). Then we can
write the usual differential terms for formation
and loss of grain species allowing for surface
reaction, accretion from the gas phased and
desorption from the grain. Technique Solve the
set of coupled ODEs which describe grain surface
and gas phase abundances (approximately doubles
the no. of ODEs) Problem Rate equations depend
on an average being a physically meaningful
quantity ok for gas but not for grains 4
grains 2 H atoms average 0.5 H atoms per
grain BUT reaction cannot occur unless both H
atoms are actually on the same grain
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Grain Surface Chemistry

• Stochastic (Accretion Limit) Approach

Basics Reaction on the surface can only occur if
a particle arrives while one is already on the
surface the rate of accretion limits
chemistry Technique Monte-Carlo method attach
probabilities to arrival of individual particles
and fire randomly at surface according to these
probabilities Caselli et al. 1998, ApJ, 495, 309
Agreement between rate and MC poor for low values
of n(H) as expected
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Grain Surface Chemistry

• Stochastic (Accretion Limit) Approach

Solution? Improve method of calculating surface
rate coefficients Problem Modifications cannot
be a priori you need a MC calculation and
these are impossible for large numbers of
species Caselli et al. 1998, ApJ, 495, 309
Fully modified rate approach
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Grain Surface Chemistry

• Stochastic (Accretion Limit) Approach

Solution? Master Equation Reaction depends on
the probabilities of a particular number of
species being on the grains e.g. PH(0), PH(1),
PH(2), PH(N), PO(0), PO(1), Biham et al.
2001, ApJ, 553, 595 Green et al. 2001, AA, 375,
1111 Technique Integrate the rates of change of
probabilities, eg dPH(i)/dt Problem Formally,
one has to integrate an infinite number of
equations
For a system of H only dP(i)/dt kfrP(i-1) -
P(i) kev(i1)P(i1) iP(i) 0.5kHH(i2)(i
1)P(i2) i(i-1)P(i) for all I 0 to
infinity For larger systems, eg O, OH, H2O, H,
H2, the ODEs get very complex even the steady
state solution is difficult to solve
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Protoplanetary Disks
Thin accretion disks from which protostar
forms Inflow from large radii (100 AU) onto
central protostar Temperature of outer disk is
cold (10 K) n(H2) 1016 1021 m-3 Molecular gas
is frozen on to dust grains in outer
disk Temperature of inner disk is 100 K at 10
AU, 1000 K at 1 AU Ices evaporate in inner disk
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Density and temperature profiles
Hotter surface layer Thicker disk
Some processes deuterium fractionation,
freeze-out, thermal desorption very sensitive
to low T regime Some processes H2 reactions
very sensitive to high T regime
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Disk ionization degree at 1 Myr
Surface (UV, X-rays)
Intermediate (X-rays)
Midplane (CR, RN)
Semenov, Wiebe, Henning
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Chemical differentiation in z-direction

• Surface layer (hot)
• PDR-like chemistry (X-rays and UV),
• H, He, C, CN, C2H
• Intermediate layer (warm)
• Rich molecular chemistry (X-rays), surface
  reactions, desorption,
• CS, CO, NH3, H2CO, HCO, HCNH, NH4, H3CO, S,
  He
• Midplane (cold)
• Dark chemistry (CR and RN), total freeze out,
• Metal ions, H3, HCO, N2H , H2D, D2H, D3

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Molecular Ice Distributions
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Molecular Distributions
Markwick, Ilgner, Millar, Henning, Astron.
Astrophys., 385, 632 (2002)
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Vertical Diffusion
Radial accretion No vertical mixing
Radial accretion Vertical diffusion
Ilgner, Henning, Markwick, Millar, Astron.
Astrophys., 415, 613 (2004)
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Modelling scheme
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Star-Forming Hot Cores
Density 106 - 108 cm-3 Temperature 100-300
K Very small UV field Small saturated molecules
NH3, H2O, H2S, CH4 Large saturated molecules
CH3OH, C2H5OH, CH3OCH3 Large deuterium
fractionation Few molecular ions - low ionisation
? f(CH3OH) 10-6
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Modelling G34.30.15
Use 2-D continuum radiative transfer code to fit
dust spectrum gives Td(r) and n(r) Use these to
calculate Tgas(r) Adopt initial molecular ice
abundances (inner core) and elemental abundances
(outer envelope) Follow chemistry at several
depth points as mantles evaporate due to
(time-dependent) heating by central source.
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Parents and Daughters(Chemical Clocks)
Evaporated mantle molecules (parents) are
protonated and become reactive Form more complex
species (daughters) on time-scale of 103-104 yr
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Surface Trapping
Detailed spatial (and temporal) distributions
depend on details of surface binding energies,
the detailed process by which species evaporate,
and the grain temperature Can induce lots of
small scale structure amenable to interferometers
(particularly ALMA).