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The abundances of gaseous H2O
and O2 in dense cloud cores
Eric Herbst & Helen Roberts
The Ohio State University
CURRENT GAS-PHASE MODEL NETWORKS
4,000 reactions; 10-20% "studied";
400 species through 13 atoms in size
elements: H, He, N, O, C, S, Si, Fe, Na, Mg, P, Cl
elemental abundances: “low metal”
photodestruction: external, internal (via cosmic rays)
Successes for quiescent cores:
(1)Reproduces 80% of abundances
including ions, radicals, isomers
(2)Predicts strong deuterium fractionation
106 sites
TYPES OF SURFACE REACTIONS
REACTANTS: MAINLY MOBILE
ATOMS AND RADICALS
A +
H +
B 
H  H2
AB
association
X  XH (X = O, C, N, CO,
etc.)
WHICH CONVERTS
H +
O  OH  H2O
C  CH  CH2  CH3  CH4
N  NH  NH2  NH3
CO  HCO  H2CO  H3CO  CH3OH
X + Y  XY
??????????
MODELLING DIFFUSIVE
SURFACE CHEMISTRY
Rate Equations
dNH/dt = kaccnH - kevapNH - KH-HNHNH
Advantages gas-phase and grain
chemistry are coupled in
time-dependent
calculations
Problems averages obtained only
Accurate if large numbers
of reactive species on
grains; reality is that
small numbers may exist
especially for H
Rates of Diffusion
• Standard astrochemical (e.g. Hasegawa et al.
1991) for silicates
• Versions for amorphous carbon and for water ice
• Slow H (P1): H slowed down to olivine (carbon)
value of Pirronello et al. (1997)
• Slow (P2): all other species slowed proportionally
• All networks contain evaporation and cosmic-ray
desorption; some contain photo processes
MORE ACCURATE METHODS
FOR SURFACE RATES
• Modified rate approach – available but
semi-empirical; used here and by a few
other groups.
• Stochastic methods – soon to be available
STOCHASTIC METHODS
Based on solution of master equation,
which is a kinetic-type equation in
which one calculates not
concentrations but probabilities that
certain numbers of species are
present. Can solve directly (Hartquist,
Biham) or via Monte Carlo realization
(Charnley). Current status: not yet
programmed for large models
Some predicted gas-phase
abundances (10 K; 104 cm-3)
P2 Energies
Some predicted surface
abundances (10 K; 104 cm-3)
TMC-1
SWAS UPPER LIMITS WRT H2
• H2O
• O2
• 7.0(-08)
• 3.2(-06) (Odin claims
7.7(-08) towards
ammonia)
Overall and particular agreement:
pure gas-phase (low metals)
Same but with C/O = 1
Percentage agreement for gasgrain models
2nd peak despite depletion
Agreement for specific species
Is late-time CO depletion serious???
L134N
SWAS UPPER LIMITS WRT H2
• H2O
• O2
• 3.0(-07)
• 3.4(-06) (Odin claims
1.7(-07) towards
ammonia)
Percentage agreement for gas-grain
models
Ageement for specific species
Source: r Oph
SWAS VALUES WRT H2
• H2O
• O2
• 3.0(-09)
• <3(-07) (Odin claims
<9.3(-08) towards a)
Gas-phase abundances for P2, 20
K, 105 cm-3
P1 similar at 15 K
Specific agreement
Same with amorphous carbon
grains
CONCLUSIONS
• Current generation of our gas-grain models
gives best agreement for water and oxygen
at long times for 10 K sources
• Chemistry and physics of desorption critical
and poorly known
• Depletion at long times from gas in
agreement with results on pre-stellar cores
including deuterium fractionation